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1. 69 5 10 Example 15 Masonry model with hardening and softening LAW z22 70 5 11 Example 16 Masonry model with hardening and softening LAW z22 71 5 12 Example 17 Masonry model with hardening and softening LAW z22 72 5 13 Example 18 Masonry model LAW 20 shear test 1 7 5 14 Example 19 Masonry model LAW 20 Shear test 2 74 5 15 Example 20 Wood model LAW 33 uniaxial compressive 75 5 16 Example 21 Wood model LAW 33 uniaxial tensile 77 5 17 Example 22 Single Joint Shear Test LAW 1 10 79 5 18 Example 23 Single Joint Tensile Test LAW 1 101 80 multiPlas USER S MANUAL January 2013 6 REFERENCES 81 7 APENDIX USER INFERFACE USERMPLS 83 7 1 1 LAW 99 404 0 0 83 7 1 2 Requirements of ANSYS Release 139 83 7 1 3 User materials mmultblas 60 mene nn nnn nn nn ann tre nennen nen 84 mul
2. 0 9 quarzh Zuschl ge 0 8 E kalksteinh Zuschl ge 0 0 6 0 5 0 4 0 3 compression strength 0 2 0 1 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 temperature C Fig 3 14 Temperature dependency of concrete pressure resistance from 6 11 0 05 0 045 0 04 0 035 0 03 0 025 0 02 0 015 em f cr compression strain 0 01 0 005 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 temperature C Fig 3 15 Temperature dependency of concrete compression strain from 6 11 multiPlas USER S MANUAL January 2013 21 Beton Zuschl ge kalksteinh Zuschl ge LL IMEEM E 241 0005 02 1 0005 002 i a 002 200 300 400 50086 0015 _ 00325 04 0015 0055 soo oss 005 005 06 0025 0035 700 800 900 1000 250044 0505 0045 06 005 0 045 1100 J O Jj Tab 3 1 Temperature dependency of concrete material values from 6 11 In multiPlas up to 11 temperatures pressure points and respective strains em can be predefined The associated limit strains are assumed according to Tab 3 1 Interim values are linearly interpolated The temperature dependency of the concrete tensile strength is implemented in multiPlas using the Data from 6 11 s Fig 3 16 1 2 0 8
3. Fig 3 18 models of the stress strain relation in case of pressure load above LAW 20 below LAW 22 multiPlas USER S MANUAL January 2013 24 3 3 7 2 Nonlinear stress strain relation under tensile load perpendicular to the bed joints For the behaviour under tensile stress perpendicular to the bed joints a stress strain relation with exponential softening is available The stress strain relation is shown in Fig 3 19 The conclusions that are done in 3 3 6 2 are valid here as well OZug f Zug Fig 3 19 stress strain relation under tensile load perpendicular to the bed joints 3 3 7 3 Nonlinear stress strain relation in case of shear load of bed joint The shear failure of the bed joints which could be observed in the test case can be described by an exponential degradation of the cohesion C and linear reduction of the friction angle 0 to residual friction angle pr The corresponding assumed stress strain line is shown in Fig 3 20 The softening model for the cohesion C was chosen analogical to the approach described in chapter 3 3 6 2 Hereby it is assumed that for completely diminishing of the cohesion a fracture energy Gj mode adhesion shear strength has to be dissipated This has been experimentally established by van der Pluijm 6 27 The tension and shear softening are synchronized T Oy tanpo 5 Fig 3 20 Nonlinear stress strain relation in case of shear of bed join
4. Ed A Jl NND Fa NA F F TAH e L A E F s A A Tzx parameter fmz strength tensile strength ffaktor friction angle unit length unit heigth lap length Fig 3 17 Ganz material model for masonry 6 17 multiPlas USER S MANUAL January 2013 F8 F16 9 F17 F10 F18 23 Tension failure brick Compressive failure masonry Shear failure masonry brick failure Tension failure parallel to bed joint brick failure Shear failure masonry Shear failure bed joint Tension failure bed joint Tension failure bed joint under high horizontal pressure Staircase shaped shear failure Tension failure of masonry parallel to bed joints joint failure Tab 3 2 Material model for masonry meaning of the flow criteria The orthotropic nonlinear stress strain behaviour of masonry is described using the corresponding softening and hardening models 6 17 3 3 7 1 Nonlinear stress strain relation under pressure load For simulation of a nonlinear stress strain relation under pressure load two models are available s Fig 3 18 The stress strain relation complies with the DIN 1045 1 Law 22 model for concrete shown in chapter 3 3 6 1 which also applies for vertical pressure load The model Law 20 within Fig 3 18 is often sufficiently accurate for practical applications ja Im zl Lo Em gt Eml Cu
5. 0 6 0 4 rel tensile strength 0 2 0 100 200 300 400 500 600 700 800 temperature C Fig 3 16 Temperature dependency of the tensile strength of concrete from 6 11 For the temperature dependency of steel reinforcement we refer to 6 11 It can be taken into account by the standard parameters of ANSYS tb bkin oder tb mkin multiPlas USER S MANUAL January 2013 22 3 3 7 Simulation of regular masonry using the Ganz yield condition For describing the orthotropic strength of a regular masonry an extended spatial masonry model was implemented which uses the Ganz yield criterion 6 23 6 17 It is the foundation of the Swiss masonry norm SIA 177 2 and complies with the fracturing model of Mann contained in DIN 1053 6 24 as well as with the natural stone masonry model suggested by Berndt 6 25 In the Ganz masonry model an additionally interaction with a horizontal load parallel to the longitudinal joint is considered The necessary material parameters of this model are compression and tensile strength of the masonry the friction angle and the cohesion between brick and joint as well as the brick dimensions The multisurface yield condition Fig 3 17 represents the different failure mechanisms of regular masonry formation The meaning of the yield criteria are given in Tab 3 2 an F4o F r u A i 2 10 18 E et Fi Fy an Oz E pem Fs Fis FMF yy
6. em mm wm em wm Eu 4 2 Input parameter compression stress domain multiPlas USER S MANUAL January 2013 35 4 2 5 LAW 9 Concrete Kmi an Elem geps maxit cutmax dtmin Elnt ktuser 11 Base material parameter for reference temperatur e g room temperatur Km5 Km Kmo Km10 Km11 uz maw Tg Be wr 777 LAW Km Ky D Elem Rd uniaxial compression strength Rz uniaxial tensile strength recommendation Rz 0 1 Rd for normal concrete Ru biaxial compression strength recommendation Ru 1 2 Rd for normal concrete Our dilatancy factor tensile stress domain 0 lt 6 2 1 Ou 0 25 dilatancy factor in compression stress domain 0 lt 6 2 1 recommendation 6 1 00 Hardening softening function mlaw switch for softening function 0 linear softening up to a predefined limit strain after DIN EN 1992 1 2 1 exponential softening with fracture energy 2 like 0 but with mixed softening model hydrostatic and deviatoric part Hardening and softening function stress strain function in compression stress domain Ka plastic strain at compression strength Rd Em Rd E Qi start of nonlinear hardening recommendation Q 0 33 Q residual stress plateau recommendation Q 0 2 mlaw 1
7. 50 of tensile strength of units nue y 0 9 geometrical parameter for as y distance of the head joints mean value al distance of the bed joints mean value lap length phi friction angle bed joints C cohesion bed joints phir residual friction angle bed joints psi dilatancy angle usually 20 ka plastic strain hence softening begins eta r ratio of residual compressive strength initial compressive strength fracture energy MODE tensile failure normal to bed joint s fracture energy MODE tensile failure stones horizontal Gr fracture energy MODE II shear failure of bed joint s Gin strain energy compressive failure direc orientation of the joints in relation to the element coordinate system 0 x normal to bed joint normal to head joint 2 normal to longitudinal joint 1 2 normal to bed joint y normal to head joint x normal to longitudinal joint 2 y normal to bed joint x normal to head joint z normal to longitudinal joint dreid switch for the three dimensional strength monitoring 0 for 2D F1 to F10 1 for 2 5D F1 to F10 F6 with Tau res 2 for 3D F1to F18 if dreid 2 fmz compressive strength of the masonry normal to longitudinal joint ftz tensile strength normal to longitudinal joint stone tensile strength ftzz geometric parameter of e g 22 10 nue z value of decrease of the uniaxial horizontal MW com
8. RSYS 0 PowerGraphics EFACET 1 AVRES Mat DMX 70 369 SMX 70 369 0 7 819 15 638 23 456 dus i 39 094 46 913 5421232 62 551 70 369 Lastschritt 4 Auflast Total deformation usum mm ANSYS 10 0 JAN 24 2006 E EK al NODAL SOLUTION STEP 4 SUB 10 TIME 4 EPPLEOV AVG PowerGraphics EFACET 1 AVRES Mat DMX 70 369 SMX 221006 0 100 10 500 04 LOOE 03 100 02 a OL Lastschritt 4 Auflast Equivalent plastic strain multiPlas USER S MANUAL January 2013 5 4 Example 9 MOHR COULOMB anisotropic bsp9 dat 1850 kN m test Mohr Coulomb anisotrop 2 LAW 10 FE model test Mohr Coulomb anisotrop 2 LAW 10 Total deformation usum m max usum 0 019961 m multiPlas 3000 kN m ANSYS 10 0 JAN 25 2006 08 09 55 NODAL SOLUTION STEP 1 SUB TIME USUM AVG RSYS 0 gt PowerGraphics EFACET 1 AVRES Mat DMX 019961 SMX 019961 0 002218 004436 006654 008871 011089 013307 015525 017743 019961 AN Rock with 2 joint blades 1st joint amp 85 B 0 2nd joint a 5 90 Elements SOLID 45 test Mohr Coulomb anisotrop 2 LAW 10 Equivalent plastic strain EPPL EQV max eppl 0 281 E 03 62 ANSYS 10 0 JAN 25 2006 08 10 32 NODAL SOLUTION STEP 1 313E 04 625E 04 938E 04 125 03 156 03 188 03 219 03 250E 03 281E 03 USER S MANUAL January 2013 63 5 5 Examp
9. N R4 3 ni ace s Eu Er e Fig 3 12 stress strain relation in multiPlas mlaw 0 2 mlaw 1 3 3 6 2 Nonlinear deformation behaviour during tensile load Concrete tends to soften relatively brittle with local appearances of cracks For including this into the context of a continuum model a homogenized crack and softening model is needed The crack itself does not appear in the topology description of the structure but is described by its impact on stress and deformation state 6 16 6 21 The softening process is formulated respectively to the energy dissipation caused by the occurance of cracks For the complete cracking the fracture energy concerning the crack surface has to be G dissipated The used model has its origin within the crack band theory of Bazant Oh 6 6 It states that cracks develop within a local process zone Its width crack band width is a material specific constant To avoid a mesh dependency of the softening and to assess the fracture energy correctly a modification of the work equation is necessary For a given width of the crack band and a given fracture energy the volume fracture energy can be computed via G 9 T 3 22 PR where Qr volume fracture energy Gr fracture energy hpr crack band width For meshing of the structure with elements which are larger than the expected width of the crack band the stress strain relationship has to be modified in such a wa
10. UY AVG RSYS 0 PowerGraphics EFACET 1 AVRES Mat DMX 26 317 SMN 26 317 SMX 3 389 25 317 2 3 016 19 715 16 415 13 114 Lastschritt 2 Vertical displacement uy mm of the steel tube arc ANSYS 11 0SP1 FEB 12 2008 11737199 NODAL SOLUTION STEP 2 SUB 64 TIME 2 USUM AVG RSYS 0 PowerGraphics EFACET 1 Lastschritt Total displacement usum mm multiPlas USER S MANUAL January 2013 Lastschritt 2 Equivalent plastic strain multiPlas 59 ANSYS 11 0SP1 FEB 12 2008 12 02 07 NODAL SOLUTION STEP 2 SUB 64 TIME 2 EPPLEQV AVG PowerGraphics EFACET 1 AVRES Mat DMX 66 78 SMX 207498 0 100 10 500 04 100 03 207498 USER S MANUAL January 2013 60 Reference solution Example 8 Calculation with LAW 40 DRUCKER PRAGER bsp8 dat Beispiel 8 FE Model Load history Load step 1 Self weight Installation layer MAT1 steel tube arc stiffened Load step 2 Self weight Installation layer MAT3 steel tube arc stiffened Load step 3 Self weight Installation layer MAT4 steel tube arc stiffened Load step 4 Load ANSYS 10 0 JAN 24 2006 230109131 NODAL SOLUTION STEP 4 EFACET 1 LA D e Lastschritt 4 Auflast Vertical displacement uy mm of the steel tube arc multiPlas USER S MANUAL January 2013 61 ANSYS 10 0 JAN 24 2006 23409158 NODAL SOLUTION STEP 4 SUB 10 TIME 4 USUM AVG
11. multi Plas USER S MANUAL January 2013 ec nfail nfail l dF dS assoziiert cc DF 1 1 1 0d0 cc DF 2 1 0 0d0 ec DF 3 1 0 0d0 DF 4 1 20 0d0 cc DF 5 1 0 0d0 cc DF 6 1 0 0d0 dFl dKappal cc 1 ftx 2 h o0ftx G 1 dkappal dLambda cc DK 1 1 21 0d0 cc ENDIF C Abfrage Kriterium Fn TAF cc IF Fn ge eps THEN C Versagen Kriterium Fn cc F n Fn cc nfail nfail l JF ds Ec DFil n cc DF 2 n cc DF 3 n z ee DF 4 n cc DF 5 n z ac DF 6 n c z B nicht assoziierte Fliessregel C do dS GE DF 1 20 ce DF 2 20 cc DF 3 20 cc DF 4 20 cc DF 5 20 ec 6 20 dFn dKappa cc dkappa dLambda cc DE aaa a ENDIF RETURN END multiPlas 86 USER S MANUAL January 2013 Contact amp Distributors Germany amp worldwide Dynardo GmbH Steubenstra e 25 99423 Weimar Tel 49 0 3643 900 830 Fax 49 0 3643 900 839 www dynardo de contact dynardo de Dynardo Austria GmbH Office Vienna Wagenseilgasse 14 1120 Vienna Austria www dynardo at contact dynardo at Germany CADFEM GmbH Marktplatz 2 85567 Grafing b Munchen Germany www cadfem de science computing ag Hagellocher Weg 73 72070 T bingen Germany WWwW science computing de Austria CADFEM Austria GmbH Wagenseilgasse 14 1120 Wien Austria www cadfem at Switzerland CADFEM Su
12. 2 6 LAW 11 Fixed Crack Model ___ 2 4 5 6 09 10 040 mm li 17111142 4150 j KK Ausg 81 70 Hem sp mn CIL Material parameter Ss ftx tensile strength in x direction fracture energy Mode 1 tensile failure fir residual tensile strength for numerical stabilization Notes fixed and smeared crack model in x direction with exponential softening used equivalent length for volume elements 3 for shell plane elements h N iNT N iNT with number of integration points Vg element volume Ag element area multiPlas USER S MANUAL January 2013 38 4 2 7 LAW 20 Masonry Linear Softening 112 hB 4 5 6 8 09 10 11 20 jay psi DO 17 Be Tza D bte 51 60 GE FJ G FB G FJ ftr Le Ausg 81 70 Hem jeps igeps madti jamin me Dn os mo p Material parameter fmx uniaxial compression strength of masonry normal to the bed joints fmy uniaxial compression strength of masonry normal to the head joints fmy x fmx ftx tensile strength normal to the bed joints C tan phi ftxx ftxx 10 ftx geometrical parameter for Fg fty tensile strength normal to the head joints
13. 600 400 200 Longitudinal einaxial Zug Radial einaxial Zug multiPlas OZ x10 2 OA x10 5 3 8 USER S MANUAL January 2013 16 4 10 3 8 Tangential einaxial Zug multiPlas USER S MANUAL January 2013 79 5 17 Example 22 Single Joint Shear Test LAW 1 10 bsp22 dat MAT1 multiPlas material LAW1 elastic material eqv plastic strains shear stress vs total shear strain 7 Initial cohesion C 1000 5 Residual cohesion 0 multiPlas USER S MANUAL January 2013 80 5 18 23 Single Joint Tensile Test LAW 1 10 elz dat MAT1 multiPlas material LAW1 single element under uniaxial tension load tensile stress vs total tensile strain Initial strength 1000 Residual Tension 1000 DEER 200 100 er 4 1 2 1 1 8 Dernong AM Initial strength Tension 1000 Residual Tension 0 Spannung y multiPlas USER S MANUAL January 2013 81 6 REFERENCES 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 multiPlas ANSYS Users Manual for ANSYS Rev 11 0 Analysis Guides ANSYS Inc Houston Can onsburg ANSYS Users Manual for ANSYS Rev 11 0 Commands ANSYS Inc Houston
14. MOHR COULOMB and the DRUCKER PRAGER yield criterion differ in the elastic stress domain The difference of the surrounded area in the deviator cut plane is 15 at the maximum For some problem formulations it can be necessary to limit the elastic stress domain to the area given by the MOHR COLOUMB yield criterion In cases if MOHR COULOMB or TRESCA alone lead to poor con vergence or even divergence it can be reasonable to use a combination of the yield criteria to stabilize the numerical computation It has to be kept in mind that this combination is reasonable only for numerical stabilization It leads inevi tably to differences in the results contratry to the sole usage of the yield criterion by MOHR COULOMB The return mapping of the stress is not commutaded exactly for both criteria MOHR COULOMB and DRUCKER PRAGER Therefore the permissibility of these result has to be checked individually multiPlas USER S MANUAL January 2013 16 3 3 6 Concrete modelling using modified DRUCKER PRAGER model The yield condition consists of two yield criteria equations 3 19 3 20 whereby the concrete strength can be described closed to the reality as well in the compressive as in the tensile domain ef Q 3 19 V3 2RR p 7n BR R R 3 R F 0 0 9 3 20 B R R 8 ___ _ 2R R R where Om hydrostatic stress lo second invariant of the de
15. as a path plot along the border x 0 U sum 0 046891 m EPPL EQV 0 003238 multiPlas USER S MANUAL January 2013 55 Reference solution Example 4 Calculation with LAW 41 MOHR COULOMB DRUCKER PRAGER bsp4 dat Number of substeps iterations 4 9 cpu time 4 M CPU 1 70 GHz 14 41 sec 762 26 454 52 143 11 832 103 521 129 21 154 899 180 588 206 277 231 966 31 655 0 aktiver Erddruck Stresses in load step 2 as path plots along the boundary x 0 aktiver Erddruck Coefficient of earth pressure sx sy in load step 2 as a path plot along the border x 0 maximale Gesamtverschiebung U sum 0 047003 m maximale plastische Vergleichsdehnung EPPL EQV 0 003361 multiPlas USER S MANUAL January 2013 56 5 3 Examples 5 to 8 Kienberger Experiment G6 6 13 LU 4m lm Figure 6 Geometry of laboratory testing Table 4 Soil characteristics Density sat fas ER Table 5 Steel m characteristics ER De me Les a an Calculation material and geometric nonlinear Convergence bound at 1 to 2 of the L2 norm of the residual forces In ANSYS the convergence criterion is defined as default value of 0 1 of the L2 norm of the residual forces That means that all residual forces have to be transferred to the load vector ex cept 0 1 of the Root Mean Square In the following calculations a convergence criterion
16. be tween 1 and 2 has been used According to experience convergence criteria between 1 and 2 are precisely enough to verify equilibrium conditions Cohesion 0 means no tensile resp compressive strength of the material Hence result con vergence problems so that the convergence bound has to be increased compared with the de fault value to achieve a solution Element types Solid45 und Shell63 Load history Load step 1 self weight Sand Load step 2 load multiPlas USER S MANUAL January 2013 57 Reference solution Example 5 Calculation with LAW 1 MOHR COULOMB bsp5 dat 2 ANSYS 10 0 12 2006 12 00 10 NODAL SOLUTION STEP 2 SUB 11 TIME 2 UY RSYS 0 PowerGraphics 1 AVRES Mat DMX 22 792 SMN 22 792 SMX 2 875 192 19 94 17 088 Qo Cn Lu Vertical displacement uy mm of the steel tube arc Reference solution Example 6 Calculation with LAW 40 DRUCKER PRAGER bsp6 dat 1 ANSYS 10 0 12 2006 11 19 22 NODAL SOLUTION STEP 2 SUB 12 TIME 2 UY AVG RSYS 0 PowerGraphics EFACET 1 LA D LA LA Vertical displacement mm of the steel tube arc multiPlas USER S MANUAL January 2013 58 Reference solution Example 7 Calculation with LAW 41 MOHR COULOMB DRUCKER PRAGER bsp7 dat ANSYS 11 0SP1 FEB 12 2008 1202727 NODAL SOLUTION STEP 2 SUB 64 TIME 2
17. bed joint joint failure multiPlas USER S MANUAL January 2013 Output for LAW 33 scale 1 10 100 1000 10 000 100 000 1 000 000 10 000 000 100 000 000 Output for LAW 40 scale 4 10 Output for LAW 41 scale 4 10 100 1000 10 000 100 000 49 active yield criterion F1 tensile failure longitudinal F2 compressive failure longitudinal F3 shear failure parallel to the LT plane F4 tensile shear failure parallel to the LT plane F5 compressive failure radial F6 tensile shear fail parallel to the LR plane F7 compressive failure tangential shear failure separation plane tensile failure separation plane active yield criterion DRUCKER PRAGER active yield criterion tensile failure MOHR COULOMB isotropic DRUCKER PRAGER tensile failure isotropic If several flow conditions are active at once then the activity pointer are added up For example SRAT 101 for LAW 1 with separation planes stands for shear failure MOHR COULOMB isotropic and shear failure on the second separation plane The scaling settings for the output are done using the cval command in ANSYS eg CVAL all 0 5 1 10 100000 ples nl srat for LAW 41 multiPlas USER S MANUAL January 2013 50 5 VERIFICATION EXAMPLES 5 1 Example 1 Earth pressure at rest Se im 10m Beispiel 1 FE model Material assumptions material 1 to 3 sand Angle of inner friction Cohesion Constrained modulus Coeffici
18. deviator cut plane is 15 at its maximum In the standard literature of soil mechanics the general usage of Mohr Coulomb material models is sug gested Yield graphs according to Drucker and Prager do in fact generally overestimate the bearing strength For brittle materials concrete rock composite flow conditions on the basis of Mohr Coulomb as well as composite flow conditions on the basis of Drucker Prager are used in the standard literature multiPlas USER S MANUAL January 2013 10 3 3 2 MOHR COULOMB isotropic yield criterion These yield criteria depend only on the two material parameters cohesion c and inner friction angle T compressive meridian 30 tensile meridian 9 30 Om Fig 3 3 MOHR COULOMB isotropic yield criterion The yield criterion is sing o cos SNG cose 3 11 5 where 0 0 3 12 3 Berl 3 13 33 36 gz 3 14 2 Om hydrostatic stress P second invariant of the deviatoric main stresses third invariant of the deviatoric main stresses Lode angle multiPlas USER S MANUAL January 2013 11 Necessary material parameters the ANSYS material model MOHR COULONB isotropic inner friction angle phi cohesion f tensile strength in case of tension cut off y dilatancy angle psi The residual strength can be defined The residual strength is initiated after the yield strength has be
19. dilatancy factor 0 can be calculated via the ratio of the beta values from Fig 3 8 with the help of the friction angle and the dilatancy angle w From equation 4 1 this could calculated by pang Dan plo Blo 3 8 sing Aw siny Bly A Please note that a non associated flow rule however lead to asymmetric deformation matrices and may result in pure convergence behaviour multiPlas USER S MANUAL January 2013 29 4 COMMANDS 4 1 Material Models Mohr Coulomb Tresca isotropic tension cut off isotropic Mohr Coulomb anisotropic tension cut off anisotropic for up to 4 joint sets 8 Cement modified Drucker Prager stress dependent nonlinear hardening softening 9 Concrete nonlinear hardening softening Temperature Dependency 1 199 oS O The material library multiPlas was implemented within the ANSYS user interface userpl The activation is realized by using the tb commands Mohr Coulomb anisotropic tension cut off anisotropic for up to 4 joints tb user mat 80 material number toda 1 LAW allocation of the data field with the selected material model LAW and the material parameters see the following sections 4 2 multiPlas USER S MANUAL January 2013 30 4 2 TBDATA Declaration 4 2 1 LAW 1 10 Mohr Coulomb 0 10 LAW phig Cg psig phig Cg Tension Tension number of EX be Se ea Dem
20. 0 0 000 0 000 0 000 0 000 1090 nfail 2 wr 22 output of the local iteration sequence with trialstresses violated yield criterias plastic multiplicators plastic and elastic increments of strain Means for LAW 1 2 10 F1 shear failure MOHR COULONMB isotropic F2 shear failure 1 joint F3 shear failure 2 joint F4 shear failure 3 joint Fb shear failure 4 joint F6 tensile failure isotropic F7 tensile failure 1 joint F8 tensile failure 2 joint F9 tensile failure 3 joint F10 tensile failure 4 joint multiPlas USER S MANUAL January 2013 46 for LAW 9 F1 DRUCKER PRAGER F1 tensile domain tensile compressive domain F2 DRUCKER PRAGER F2 compressive tensile domain compressive domain for LAW 20 22 F1 F11 stone tensile failure F2 F12 compression failure of the masonry F3 F13 shear failure of the masonry stone failure F4 F14 tensile failure of the masonry parallel to bed joint stone failure F5 F15 transition section between F1 F3 F4 resp F11 F13 F14 F6 shear failure of bed joints F7 tensile failure of bed joints F8 F16 tensile failure of bed joints on horizontal compressive stress F9 F17 staircase shaped shear failure of bed and head joints F10 F18 tensile failure of the masonry parallel to the bed joint joint failure for LAW 40 F2 DRUCKER PRAGER for LAW 41 F1 shear failure MOHR COULOMB isotropic F2 DRUCKER PRAGER F6 tensile failure isotropic 4 3 2 Remarks for choo
21. 2 el weee 1 joint 21 30 psi phi Tension alpha beta Tension 2 joint AN mem e ri 4 joint a op ase Base material parameter Isotropic Mohr Coulomb phig friction angle Cg cohesion psig dilatancy angle phig residual friction angle Lo residual cohesion Tension tensile strength Tension cut off lt Cg tan phig Tension residual tensile strength 2Cg tan phig Temperature dependency rsp moisture dependency The temperature dependent strength is realised over the temperature dependence of the cohesion tempd switch for temperature dependency 0 no temperature dependency 1 temperature dependence of the cohesion 1 reference temperature with 100 strength see field 3 T2 5 temperatures at C in ascending order relative cohesion Cg Ti Cg Anisotropic Mohr Coulomb up to 4 joint sets phi joint friction angle joint cohesion psi joint dilatancy angle phi joint residual friction angle joint residual cohesion Tension joint tensile strength Tension cut off lt Cg tan phi Tension joint residual tensile strength 2Cg tan phi direction of anisotropic joint system The transformation into the element coordinate system is defined by two angles alpha beta see Fig 3 4 and Fig 3 6 alpha negative rotation about Z axis beta positive rotation about Y axis Volume referred moisture as temperature equivalent interpreted multiPlas US
22. 22 Masonry Nonlinear Hardening Softening 40 4 2 9 LAW 33 Orthotropic Boxed Value Model 42 4 2 10 LAW 40 Geological 43 4 2 11 LAW 41 Combination Mohr Coulomb Drucker Prager resp TRESCA vs MISES 44 4 3 Numerical control variables 45 4 3 1 Choice of the numerical control 45 4 3 2 Remarks for choosing the material parameters 46 4 3 3 Remarks and tips for using multiPlas in nonlinear structural analysis 46 4 4 Remarks for 0 48 5 VERIFICATION EXAMPLES nn energie 50 5 1 Example 1 Earth pressure at rest 50 5 2 Examples 2 to 4 Earth pressure at rest and active earth 52 5 3 Examples 5 to 8 Kienberger Experiment G6 6 181 56 5 4 Example 9 MOHR COULONB anisotropic 62 5 5 Example 10 Concrete model DRUCKER PRAGER singular LAW 9 63 5 6 Example 11 Concrete model DRUCKER PRAGER singular LAW 9 65 9 7 Example 12 Masonry model with softening 20 67 5 8 Example 13 Masonry model with softening _ 20 68 5 9 Example 14 Masonry model with hardening and softening _ 22
23. 3 6 5 7 Example 12 Masonry model with softening LAW 20 eld dat Uniaxial compressive test vertical 1 0 or G d OQ u 10 2 8 ei SE Dehnung multiPlas USER S MANUAL January 2013 68 5 8 Example 13 Masonry model with softening LAW 20 eld dat Uniaxial compressive test horizontal or G d OQ u 10 2 2 4 1 6 Dehnung multiPlas USER S MANUAL January 2013 69 5 9 Example 14 Masonry model with hardening softening LAW 22 eld dat Uniaxial compressive test vertical 10 1 0 02 10 2 ef multiPlas USER S MANUAL January 2013 70 5 10Example 15 Masonry model with hardening softening LAW 22 eld dat Uniaxial compressive test horizontal 02 10 2 multiPlas USER S MANUAL January 2013 71 5 11Example 16 Masonry model with hardening softening LAW 22 elz dat Uniaxial tensile test vertical Spannung SX 10 3 Dehnung multiPlas USER S MANUAL January 2013 72 5 12Example 17 Masonry model with hardening softening LAW 22 elz dat Uniaxial tensile test horizontal or a d en u St Dane sh Dehnung multiPlas USER S MANUAL January 2013 13 5 13 Example 18 Masonry model LAW 20 shear test 1 Benchmar
24. 3T plastic strain at softening up to Qu Ku Eu Qu Rd E Qu stress level see Fig 4 3 Softening function stress strain function in tensile stress domain mlaw 0 bzw 2 Qir residual plateau Kir plastic limit strain mlaw 1 Gi fracture energy Mode 1 tensile failure Temperature dependency Temperature dependency is available for mlaw 0 2 utz switch for temperature dependency of tensile strength 0 off 1 Tis temperature at which a linear temperature dependent reduction of the tensile strength begins see Fig 3 16 Tie temperature up to which the linear temperature dependent reduction of the tensile strength takes place see Fig 3 16 Bie residual plateau for tensile strength Rz T Rz T2 11 temperatures please enter in ascending order Bei temperature dependent normalized compressive strength Rd Ti Rd Kmi plastic strain with reaching the compressive strength for Ti multiPlas USER S MANUAL January 2013 36 Q C mlaw 0 2 1 Oi Qr Kmi nach Tab 3 4 1 mlaw 1 Qu Foo Qi Qu Kmi Q Ker Ke Fig 4 3 Input parameter in compression stress domain Overview input parameter of softening function in tensile stress domain Input parameter for mlaw 0 2 Kir Input parameter for mlaw 1 N Gi Ktr K Fig 4 4 Input parameter in tensile stress domain multiPlas USER S MANUAL January 2013 3 4
25. 6670 kN m Elements Solid45 Load history 1st Load step Earth pressure in a result of the gravity Boundary conditions lower boundary y 0 UX Uy UZ 0 side boundary x 0 bzw 10 ux 0 side boundary z 0 bzw 1 uz 0 2nd load step Activation of the active earth pressure by rotation of the side boundary x 0 about the base point horizontal top point displacement multiPlas USER S MANUAL January 2013 53 Reference solution Example 2 Calculation with LAW 1 MOHR COULOMB bsp2 dat Number of substeps iterations 4 18 cpu time 4 M CPU 1 70 GHz 21 9 sec 544 25 657 50 774 19 891 101 008 126 125 151 242 2176 395 201 476 226 593 ln aktiver Erddruck Stresses in load step 2 as path plots along the boundary x 0 aktiver Erddruck Coefficient of earth pressure sx sy in load step 2 as a path plot along the border x 0 U sum 0 047487 m EPPL EQV 0 003927 multiPlas USER S MANUAL January 2013 54 Reference solution Example 3 Calculation with LAW 40 DRUCKER PRAGER bsp3 dat Number of substeps iterations 4 8 cpu time 1x 4 M CPU 1 70 GHz 13 4 sec 113 26 632 52 549 18 466 104 383 130 3 156 217 182 134 208 051 233 968 259 885 0 aktiver Erddruck Stresses in load step 2 as path plots along the boundary x 0 aktiver Erddruck Coefficient of earth pressure sx sy in load step 2
26. Canonsburg ANSYS Users Manual for ANSYS Rev 11 0 Elements ANSYS Inc Houston Canonsburg ANSYS Users Manual for ANSYS Rev 11 0 Theory ANSYS Inc Houston Canonsburg ANSYS Users Manual for ANSYS Rev 11 0 Verification ANSYS Inc Houston Canonsburg Bazant Z P Oh B H Crack band theory for fracture of concrete Materials and Struc tures RILEM 93 16 S 155 177 Chen W F Constitutive Equations for Engineering Materials Vol 2 Plasticity and Model ing Elsevier Amsderdam London New York Tokyo 1994 Deutscher Ausschuss f r Stahlbeton Heft 525 zu DIN 1045 1 Ausgabe 2003 Beut Verlag DIN 1045 1 Tragwerke aus Beton Stahlbeton und Spannbeton Teill Bemessung und Konstuktion Beuth Verlag Ausgabe Juli 2001 DIN EN 1992 1 1 Eurocode 2 Bemessung und Konstruktion von Stahlbeton und Spannbetontragwerken Teil 1 1 Allgemeine Bemessungsregeln und Regeln f r den Hochbau Ausgabe Oktober 2006 DIN EN 1992 1 2 Eurocode 2 Bemessung und Konstruktion von Stahlbeton und Spannbetontragwerken Teil 1 2 Allgemeine Regeln Tragwerksbemessung f r den Brandfall Ausgabe Nov 2005 Hintze D Zur Beschreibung des physikalisch nichtlinearen Betonverhaltens bei mehr achsigem Spannungszustand mit Hilfe differentieller Stoffgesetze unter Anwendung der Methode der finiten Elemente Hochschule f r Architektur und Bauwesen Weimar Disser tation 1986 Kienberger H ber das Verformungsverhalten v
27. ER S MANUAL January 2013 31 4 2 2 LAW 2 Modified Drucker Prager Emp e joint m TR 1 d 21 30 psi C Tension alpha beta Tension 2 joint Gel mem mme 3 joint el Ir FFF rf et 4 joint M 29 qme eme men ume dmn made emo Base material parameter Hd uniaxial compression strength Rz uniaxial tensile strength Ru biaxial compression strength Remark ideal elastic plastic behaviour with associated flow rule Combination with joints anisotropic Mohr Coulomb up to 4 joint sets phi joint friction angle joint cohesion psi joint dilatancy angle phi joint residual friction angle joint residual cohesion Tension joint tensile strength Tension cut off 2Cg tan phi Tension joint residual tensile strength lt Cg tan phi direction of anisotropic joint system The transformation into the element coordinate system is defined by two angles alpha beta see Fig 3 4 and Fig 3 6 alpha negative rotation about Z axis beta positive rotation about Y axis multiPlas USER S MANUAL January 2013 32 4 2 3 LAW 5 Modified Drucker Prager temperature dependent Geen UT EL I UM LI LL mm e e akad emm ae mm kel a Base material parameter for reference temperatur e g room temperatur Rd uniaxial compression strength Rz uniaxi
28. HEORY OF THE MULTIPLAS MATERIAL MODELS IN ANSYS 3 1 Basics of elasto plasticity in multiPlas The material models in multiPlas uses a rate independent plasticity The material models are character ized by the irreversible strain that occurs once yield criteria are violated It is assumed that the total strain vector can be divided into a elastic and a plastic component 4 e 3 1 where elastic strain vector EPEL plastic strain vector EPPL The plastic strains are assumed to develop instantaneously that is independent of time The yield criterion lt 0 3 2 where o stress vector hardening parameter limit the stress domain If the computed stress using the elastic deformation matrix exceeds the yield criteria F gt 0 then plastic strain occurs Plastic strains will computed by flow rule de 490 3 3 00 where A plastic multiplier which determines the amount of plastic straining Q plastic potential which determines the direction of plastic straining The plastic strains reduce the stress state so that it satisfies the yield criterion F 0 By using associated flow rules the plastic potential is equal the yield criterion and the vector of plastic strains is arranged per pendicularly to the yield surface 3 4 using non associated flow rules QzF 3 5 effects that are known from experiments like dilatancy can be controlled more realistic
29. HR COULOMB anisotropic yield criterion 12 3 3 4 Yield criterion according to DRUCKER PRAGER 14 3 3 5 Combination of flow condition according to MOHR COULOMB and DRUCKER PRAGER or FRESCA and WON MIS ee BEDAN NGE SENENG 15 3 3 6 Concrete modelling using modified DRUCKER PRAGER 16 3 3 Simulation of regular masonry using the Ganz yield condition 22 3 3 8 Wood modelling using boxed value model 25 3 4 Blue 28 A OOMMAND ee ee aaa ee 29 4 1 Maternal EE 29 4 2 RSR RE B e cusiM 30 4 2 1 LAW 1 10 Mohr 30 4 2 2 LAW 2 Modified nnns 31 4 2 3 LAW 5 Modified Drucker Prager temperature dependent 32 4 2 4 LAW 8 Modified Drucker Prager calibrated stress dependent nonlinear hardening Mortar MOSER EE 33 4 2 5 LAW 9 enee a aaa nee 35 4 2 6 LAW 11 Fixed Crack Model J s cicciccccciccccncassecenenattsiienecatsdewanetetoasieesunesstedenscntsdewssatedecseedadentceties 37 4 2 7 LAW 20 Masonry Linear Softening 38 4 2 8 LAW
30. In general the uniaxial stress strain relationship of concrete is characterized by three domains linear elastic domain which generally reaches up to about a third of the compressive strength This is followed by increasingly bent run until the compressive strength is reached The nonlinear relation between stress and strain is caused by an initially small number of micro cracks which merge with higher stress levels The achievement of the compressive strength is associated with the forming of fracture surfaces and cracks which are aligned parallel to the largest main stress The softening area is characterized by a decreasing strength Finally it leads to a low residual Strain level The slope of the decreasing branch is a measure for the brittleness of the material Fig 3 11 shows the typical nonlinear stress strain relation of normal concrete in uniaxial compressive tests 6 9 0 7 lt 0 Fig 3 11 Nonlinear stress strain relation uniaxial compression test of normal concrete used in codes DIN 1045 1 6 9 and EC2 6 10 In Fig 3 12 the stress strain relation which is available in multiPlas is shown Thereby linear softening mlaw 0 2 or parabolic exponential softening mlaw 1 be chosen Up to reaching the strain e the parabola equation as seen in Fig 3 11 is used multiPlas USER S MANUAL January 2013 18 Od Msn Ga pn NS VN N N KH hs
31. R hats 2 2 2 F 59 es 4 709 4 0 p ers Iais Radial Compression of fiber compression failure radial F 1 0 Crack parallel to LR Plane 2 2 2 e o 2 4 4 4 0 5 I0 f Qn frn Qn Tangential Compression of fiber F 2 Qn 0 3 3 8 1 Nonlinear deformation behaviour fic EI TE Ile i EL c1 Etc2 Fig 3 23 Stress strain relation compression in fiber direction longitudinal multiPlas 26 3 25 3 26 3 27 3 28 3 29 3 30 3 31 USER S MANUAL January 2013 27 fre Index R radial Index T tangential _ ERce m Ree LLL _ Ke eg l ERCA CRc2 ERC Fig 3 24 Stress strain relation compression perpendicular to fiber direction radial or tangential fam fami Index d direction L longitudinal radial T tangential Index m mode t tension s shear E bzw Gg fame 3 Fig 3 25 Stress strain relation for shear and tension multiPlas USER S MANUAL January 2013 28 3 4 Dilatancy The strict adherence of the stability postulations of Drucker usually requires an associated yield constitu tive law e g dilatancy angle friction angle But in reality for some materials the calculated volume strains are significantly larger than those determined by experiments In
32. al tensile strength Ru biaxial compression strength Remark ideal elastic plastic behaviour with associated flow rule Temperature dependency utz switch for temperature dependency of tensile strength 0 off 1 Tis temperature at which a linear temperature dependent reduction of the tensile strength begins see Fig 3 16 temperature up to which the linear temperature dependent reduction of the tensile strength takes place see Fig 3 16 Bre residual plateau for tensile strength Rz Tig Rz T2 11 temperatures in C please enter in ascending order Bei temperature dependent normalized compressive strength Rd Ti Rd multiPlas USER S MANUAL January 2013 33 4 2 4 LAW 8 Modified Drucker Prager calibrated stress dependent nonlinear hardening Mortar Cement Base material parameter Rd uniaxial compression strength Rz uniaxial tensile strength Ru biaxial compression strength Out dilatancy factor in tensile stress domain 0 lt dy 2 1 dilatancy factor compression stress domain 0 lt gt 1 recommendation 1 00 elastic modulus Gr fracture energy Mode 1 tensile failure Nonlinear deformation behaviour under multiaxial compression om 0 Stress domain 2 Stress domain 1 Stress domain 4 lt M Stress domain 3 p EEN T ot 0 005 4015 020 Ry E Om Fig 4 1 Compression stress domains Parameter for stress strain relat
33. ally The hardening softening function Q x describes the expansion and the reduction of the initial yield sur face dependant on the load path as well as the translation of the yield criterion in the stress domain For the strain driven hardening softening equations in multiPlas the scalar value serves as a weighting fac tor for plastic strain dk del 3 6 The introduction of a separate softening function for each strength parameter made it possible to formu late an orthotropic softening model that is dependent from the failure mode Existing relations for exam ple shear tension interaction mixed mode were recognised multiPlas USER S MANUAL January 2013 8 The numerical implementation of the plasticity models is carried out using the return mapping method 6 17 6 18 6 22 The return mapping procedure is used at the integration point for the local iterative stress relaxation It consists of two steps 1 elastic predictor step tr al tot ou 0 D de 3 7 2 plastic corrector step local iterative procedure dA 00 3 8 do __ 2 3 2 Multisurface plasticity The consideration of different failure modes rsp failure mechanisms of a material is possible by a yield surface built up from several yield criteria In the stress domain then a non smooth multisurface yield cri terion figure develops The elastic plastic algorithm has to deal with singularities at intersections from different yie
34. bal local dtmin minimum time increment of the ANSYS command deltim dtmin ktuser 1 given setting to build the elasto plastic tangent matrix at the local plane of the integration point 1 Elnt switch for Element Integration 0 full integration 1 reduced integration activation of the output control debug resp control modus for developers or users when necessary wr output key Elem element number Intp number of the integration point 4 3 1 Choice of the numerical control variables eps 10 shall not be chosen to small 10 at and maxit 10 local iteration steps shall be enough at least as many as active yield surfaces but not to be chosen too small geps 10 for double precision maxinc must be larger than global and local load increments separately and also than the product e g at dtmin 0 05 maxinc gt 1 0 05 gt 20 cutmax 5 maxinc gt 2 gt 32 maxinc gt 20 32 gt 640 cutmax 4 output control wr 1 output of the violated yield criterias ck A A Ax A A Xx START mpls5 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkxk Elem 436 intpt 1 KTFORM 0 5000 KFSTEQ 0 KFIRST 0 LAW 1 kkkkkkkkkkxk START LOCAL STRAIN INCREMENT kkkkkkkkkkkkkkkkk START LOCAL ITERATION kkkkkkkkkkkkkkkkkkkkkkkxk kkk Kontrollausgabe Fliesskriterien 1060 F value 1 6 70 165 0 000 0 000 0 000 0 000 96 647 1070 F value 7 12 0 000 0 000 0 000 0 000 0 000 0 000 1080 F value 13 18 0 000 0 00
35. dynamic software amp engineering License agreement Copyright of this product and its attachments by DYNARDO GmbH All unauthorized copying multiplica tion and reengineering of this product and its documentation is strictly prohibited Guarantee reference dynardo GmbH takes greatest care in developing software and tests all products thoroughly Despite the user is fully responsible for the application of this software and is obliged to check correctness of the re sults obtained dynardo GmbH takes no liability for any damage caused by the use of this software by incorrectness of results or by misinterpretation Registered trademark All trademarks and product name specified in this documentation are registered trademarks of dynardo GmbH 1 Int FO DUNST ON NAN 5 2 INSTALLATION INSTRUCTIONS Dessen een 6 2 1 How to start ANSYS Mechanical APDL with multiPlas 6 2 2 How to use ANSYS Workbench with 6 3 THEORY OF THE MULTIPLAS MATERIAL MODELS IN 7 3 1 Basics of elasto plasticity in multblas 7 3 2 Multisurface plasticity E 8 3 3 Computed yield eurtaces 9 3 3 1 Introduction yield surfaces of basic material models 9 3 3 2 MOHR COULOMB isotropic yield criterion 10 3 9 3 MO
36. e plastic activity is path depended A plastic activity can be activated and deactivated more than once during a load case The plastic activity is identified by a characteristic nl srat Output for LAW 1 10 scale active yield criterion 1 shear failure MOHR COULONB isotropic 10 shear failure 1 separation plane 100 shear failure 2 separation plane 1000 shear failure 3 separation plane 10 000 shear failure 4 separation plane 100 000 tensile failure isotropic 1 000 000 tensile failure 1 separation plane 10 000 000 tensile failure 2 separation plane 100 000 000 tensile failure 3 separation plane 1 000 000 000 tensile failure 4 separation plane Output for LAW 2 9 scale active yield criterion 1 DRUCKER PRAGER joint 1 tensile space tensile compressive space 10 DRUCKER PRAGER joint 2 compressive tensile space compressive space Output for LAW 20 22 scale active yield criterion 1 stone tensile failure 10 compressive failure of the masonry 100 shear failure of the masonry stone failure 1000 tensile failure of the masonry parallel to bed joint stone failure 10 000 transition section between F1 F3 F4 resp F11 F13 F14 100 000 shear failure of bed joints 1 000 000 tensile failure of bed joints 10 000 000 tensile failure of bed joints on horizontal horizontal compressive stress 100 000 000 staircase shaped shear failure of bed and head joints 1 000 000 000 tensile failure of the masonry parallel to the
37. en exceeded The uniaxial compressive strength corresponds with the friction angle and cohesion as shown below 620 GE d 3 15 sinQ 2 multiPlas USER S MANUAL January 2013 12 3 3 3 MOHR COULOMB anisotropic yield criterion For the definition of joints separation planes or strength anisotropies the position of the yield surface depends on the position of the two joint angles The two angles First Angle and Second Angle B describe the position of the joint separation plane rotation against positive rotational direction about the z axis D rotation in positive rotational direction about the y axis Fig 3 4 Angle definition of the joint The yield criterion is o tang C 0 3 16 Tres Fig 3 5 MOHR COULOMB anisotropic yield criterion where Tres shear stress the joint normal stress perpendicular to the joint Necessary material parameters the ANSYS material model MOHR COULOMB anisotropic position angle of the family or separation planes friction angle C cohesion f tensile strength in case of tension cut off y dilatancy angle multiPlas USER S MANUAL January 2013 13 Residual strength can be defined The residual strength is initiated after the yield strength has been ex ceeded XJ y 90 B 90 X 2 Element coord
38. ent of earth pressure at rest Density Therefore Poisson s ratio Shear modulus Young s modulus Boundary conditions lower boundary y 0 side boundary x 0 bzw 10 side boundary z 0 bzw 1 multiPlas 30 c 0 Es 40000 kN m 0 5 1 8 t m lik 0 333 i 2V Es 10000 kN m theory see 6 19 E 2 1 v G 26670 kN m USER S MANUAL January 2013 51 Elements Solid45 Load history 1st Load step installation 1st layer material 1 2nd Load step installation 2nd layer material 2 3rd Load step installation 3rd layer material 3 Reference solution bsp1 dat path plots along the boundary at x 0 109 18 155 39 5 bs D45 70 49 87 935 105 38 122 825 140 27 157 715 175 16 0 1 3 5 DIST Einbau 3 Stresses in load step 3 4 3 7 9 DIST Coefficient of earth pressure sx sy in load step 3 Einbau 3 Lage multiPlas USER S MANUAL January 2013 52 5 2 Examples 2 to 4 Earth pressure at rest and active earth pressure M Beispiel 2 bis 4 FE model Material assumption material 1 Angle of inner friction 30 residual strength or 30 Angle of dilatancy y 30 Cohesion c 0 Elastic modulus Es 40000 kN m Coefficient of earth pressure at rest 0 5 Density 1 8 Therefore Poisson s ration 0 333 Shear modulus G 10000 kN m Young s modulus E 2
39. iate Research Teaching Advanced and Teaching Mechanical versions products For detailed information see the Guide to ANSYS User Programmable Features a 7 1 3 User materials in multiPlas The user interface usermpls is in the actual version multiPlas Release 2 0 a non sufficient tested Feature This interface offers the user a personal enhancement of the material library multiPlas in ANSYS The results of own implementations are in the responsibility of the user multiPlas USER S MANUAL January 2013 85 SUBROUTINE usermpls LAW up F DF ka eppli FK DK nfail eps ncomp sigtr sigm sigdev inv2 inv3 sigs ta0 iott wr o0 User definierte mehrflaechige Fliessbedingung in multiplas c mehrflaechige Fliessbedingung mit max 18 Flieskriterien Basis userpl input arguments variable type sze intent description LAW int sc in Materialmodell Nr hier 99 up dp ar 58 in tbdata Input Werte eppli dp ar 18 6 in Vektor plastischer Dehnungskomponenten d einz Fliesskriterien eps dp sc in Abbruch Toleranz f F gt 0 sigtr dp ar ncomp Trial Spannungsvektor sigm dp sc in Hydrostat Spannung sigdev dp ar 6 in Deviatorspannung inv2 dp sc in J2 zweite Deviatorinvariante inv3 dp sc in J3 dritte Deviatorinvariante tad sc in ta0 sqrt 2 0d0 3 0d0 inv2 iott int SC n Ausgabesteuerung wr int sc in Schalter fuer Ausgabeumfang output arguments va
40. ilibrium Therefore a global incrementing is im portant in the case of softening The value dtmin in the tb data fiel has to be identical to the value of dtmin that is used by ANSYS the solution phase deltim dtanfang dtmin dtmax If no convergent solution could be found decrease incrementation dtmin increase the global convergence criteria cnvtol f Newton Raphson full usage of consistent elasto plastic tangent or Newton Raphson init starting stiff ness is supported For the practical problems Newton Raphson init is recommended Especially when considering geometric nonlinearities or when working with EKILL EALIVE the full Newton Raphson method is necessary multiPlas USER S MANUAL January 2013 48 4 4 Remarks for Postprocessing Plastic effective strain EPPLEQV The plastic effective strain shows the quantitative activity and is used for pointing out the areas in which local load shifting or material failure crack forming take place 2 1 2 2 2 Bx TEL 8 2 2 E 2 pl xy pl yz pl y _ 2 pleqv Plastic activity activity NSLRAT The plastic activity shows which qualitative plastic activities are taking place in the current equilibrium state They are used for illustration which of the flow criteria is active that means not satisfied within the respective are of the structure This enables deducting the type and cause of the load shifting The pointer of th
41. inate system XJ Yj 2 joint coordinate system 90 B 0 Fig 3 6 Examples for the angle definition of joints multiPlas USER S MANUAL January 2013 14 3 3 4 Yield criterion according to DRUCKER PRAGER Wi 3 O5 al Fig 3 7 Flow conditions according to DRUCKER PRAGER The Drucker Prager yield criterion is og tpo 9 3 17 The plasticity potential is 9o 3 18 where Om hydrostatic stress s 3 12 lo second invariant of the deviatoric main stresses s 3 13 0 dilatancy factor The Drucker Prager yield criterion can approximate the Mohr Coulomb failure condition as circumlocutory cone or as inserted to a cone see Fig 3 8 Using the material liprary multiPlas calculation of arbitrary multiPlas USER S MANUAL January 2013 15 interim values blending with Mohr Coulomb failure conditions are possible as well Necessary material parameters in the ANSYS multiPlas material model DRUCKER PRAGER are Band Both parameters are connected to cohesion and angle of friction by the following formula 6 8 6 sing 43 3 sing 43 3 _ 6 05 _ 6 5 3 3 sing 3 3 sino Fig 3 8 Drucker Prager yield criterion as circumlocutory cone left or inserted to a cone right 3 3 5 Combination of flow condition according to MOHR COULOMB and DRUCKER PRAGER or TRESCA and von MISES As shown in Fig 3 8 the
42. ions Stress domain 1 or ov lt 0 05 uniaxial compression test Emit strain at compression strength Rd Qi start of nonlinear hardening Qui compression stress level see Fig 4 2 Eu strain at softening up to Qu residual stress plateau see Fig 4 2 multiPlas USER S MANUAL January 2013 34 Stress domain 2 0 05 2 or ov lt 0 15 Qi start of nonlinear hardening strain at compression strength Que compression stress level see Fig 4 2 Eyo strain at softening to Us residual stress plateau see Fig 4 2 fst2 factor increase in compressive strength Stress domain 3 0 15 2 or ov lt 0 30 start nonlinear hardening compression stress level see Fig 4 2 Eis strain at stress level strain at compression strength Qs compression stress level see Fig 4 2 strain at stress level Qus residual stress plateau see Fig 4 2 fst3 factor increase in compressive strength at Stress domain 4 0 30 2 or ov start nonlinear hardening compression stress level see Fig 4 2 i4 strain at stress level Qi Emi4 strain at compression strength Qua compression stress level see Fig 4 2 u4 strain at stress level Qua residual stress plateau see Fig 4 2 fst4 factor increase in compressive strength at ema NI I I I I I I L I I I I I man am wn wn
43. isse Wittenwilerstrasse 25 8355 Aadorf www cadfem ch Czech Republic Slovakia Hungary SVS FEM s r o Skrochova 3886 42 615 00 Brno Zidenice Czech Republic www svsfem cz Russia CADFEM CIS Suzdalskaya Str 46 203 111672 Moscow www cadfem cis ru India CADFEM Engineering Services India 6 3 887 MCP Arcade 4th Floor Raj Bhavan Road Somajiguda Hyderabad 500 082 www cadfem in USA CADFEM US Inc 3 Research Drive Greenville SC 29607 www cadfem us com Japan TECOSIM Japan Limited Mimura K2 Bldg 401 1 10 17 Kami kizaki Urawa ku Saitama shi Saitama 330 0071 Japan www tecosim co jp Technology Inc A 208 Seoul Hightech Venture Genter 29 Gonghang daero 61 gil Gangseo gu Seoul 157 030 Korea www caetech co kr TaeSung S amp E Inc Kolon Digital Tower 2 10F Seongsu dong 2 ga Seongdong gu Seoul 333 140 Korea www tsne co kr China PERA GLOBAL Holdings Inc Standard Chartered Tower 201 Century Avenue Suite 7 B C Shanghai 200120 www peraglobal com
44. ive ideal elastic plastic modified stone Cement bilinear 00402 Drucker Prager Concrete associative ideal elastic plastic yes Concrete Cement nonlinear hardening Concrete Stone Brick non associative and softening Tension cut off rotated cracking residual strength anisotropic Material Models es yes Joints jointed Rock Cohesive bilinear Mohr Coulomb Zones non associative residual strength nonlinear hardening mE Masonry Ganz Masonry non associative softening bilinear Tsai Wu Wood associative ideal elastic plastic multilinear hardening boxed value Wood associative and softening fixed cracking residual strength Tension cut off Cohesive Zones associative exponential softening Additionally all Mohr Coulomb Models are coupled with a tension cut off yield surface In simulations of joint materials e g jointed rock it is possible to arrange the joint sets arbitrarily Isotropic and anisotropic Mohr Coulomb yield surfaces can be combined in manifold ways Up to 4 joint sets can be associated with an isotropic strength definition MultiPlas has been successfully applied in nonlinear simulations of and concrete as well as in stability analysis of soil or jointed rock multiPlas USER S MANUAL January 2013 2 INSTALLATION INSTRUCTIONS multiPlas provides a customized executable ANSYS EXE for ANSYS The multiPlas package is deliv ered as a single zip file e g mu
45. k test according to 6 17 S 140f Loading plate 18cm Masonry wall 2 x 2 m Fundamentplatte d 18 cm BR Stone format 40x20 ANSYS 11 0OSP1l MAY 19 2008 16 40 16 NODAL SOLUTION STEP 2 SUB 144 TIME 1200 EPPLEQV AVG PowerGraphics EFACET 1 AVRES Mat DMX 03 SMX 039359 003 006 Foundation plate 18 Versuch Zwl Lastschritt Horizontallast multiPlas USER S MANUAL January 2013 5 14 19 Masonry model LAW 20 Shear test 2 Benchmark test according to 6 17 S 140f Ppa A A A AAA A A 444 lI um la la eh d zt Er Stone format 20x20 Versuch ZW1 Lastschritt Horizontallast multiPlas m EHE e En eme IT v oM S A H 4 ANSYS 11 0SP1 NODAL SOLUTION STEP 2 SUB 134 TIME 1200 EPPLEOV AVG PowerGraphics EFACET 1 USER S MANUAL January 2013 75 5 15 20 Wood model LAW 33 uniaxial compressive tests el test holz33 dat x10 1 0 Longitudinal einaxial Druck 10 1 125 0 Radial einaxial Druck multiPlas USER S MANUAL January 2013 76 Tangential einaxial Druck multiPlas USER S MANUAL January 2013 77 5 16 21 Wood model LAW 33 uniaxial tensile tests el test holz33 dat x10 1 2000 1800 1600 1400 1200 Spannung 1000 800
46. k und Dynamik der Luft und Raumfahrtkonstruktionen Universit t Stuttgart Dissertation 1995 USER S MANUAL January 2013 6 22 6 23 6 24 6 25 6 26 6 27 82 Will J Beitrag zur Standsicherheitsberechnung im gekl fteten Fels in der Kontinuums und Diskontinuumsmechanik unter Verwendung impliziter und expliziter Berech nungsstrategien Bauhaus Universit t Weimar Dissertation 1999 Berichte Institut f r Strukturmechanik 2 99 Ganz H R Mauerwerkscheiben unter Normalkraft und Schub ETH Z rich Institut f r Baustatik und Konstruktion Dissertation Birkh user Verlag Basel 1985 Mann W M ller H Schubtragf higkeit von gemauerten W nden und Voraussetzungen f r das Entfallen des Windnachweises Berlin Ernst u Sohn In Mauerwerk Kalender 1985 Berndt E Zur Druck und Schubfestigkeit von Mauerwerk experimentell nachgewiesen an Strukturen aus Elbsandstein Bautechnik 73 S 222 234 Ernst amp Sohn Berlin 1996 Grosse M Zur numerischen Simulation des physikalisch nichtlinearen Kurzzeit tragverhaltens von Nadelholz am Example von Holz Beton Verbundkonstruktionen Disser tation Bauhaus Universit t Weimar 2005 Pluijm R van der Shear behaviour of bed joints Proc 6th Noth American Masonry Con ference S 125 136 1993 multiPlas USER S MANUAL January 2013 83 7 APENDIX USER INFERFACE USERMPLS 7 1 1 LAW 99 User Material ml rr romp Biel isot
47. ld criteria e g F1 to F2 as represented in Fig 3 1 3 1 Intersection between the two flow 1 and 2 50 40 SCH 20 10 The consistent numerical treatment of the resulting multi surface plasticity must deal with the possibility that many yield criteria are active simultaneously This leads to a system of n j equations T Set of active d Em jc dA 4 j The solution of this system of equations generates the stress return to flow criteria or within the intersection of flow criterias Contrary to single surface plasticity exceeding the flow criterion is no longer a sufficient criterion for activity of the plastic multiplier for each active yield criterion An activity criterion needs to be checked dA gt 0 3 10 This secures that the stress return within the intersection is reasonable from a physical point of view multiPlas USER S MANUAL January 2013 3 3 Computed yield surfaces 3 3 1 Introduction yield surfaces of basic material models MOHR COULOMB Sonderfall TRESCA lt ARGYRIS DRUCKER PRAGER Sonderfall MISES Fig 3 2 Cut in the deviator plane of different flow figures Miscellaneous yield criteriona of soil or rock mechanics generally describe flow figures which lie in be tween the flow figure of Mohr Coulomb and of Drucker Prager The difference in the area surrounded by the yield surface elastic stress domain in the
48. le 10 Concrete model DRUCKER PRAGER singular LAW 9 eld dat Uniaxial compressive tests 0 SY 400 800 1200 1600 2000 Spannung 2400 2800 3200 3600 4000 x10 2 4 3 2 1 0 Dehnung Stress strain diagram 20 C mlaw 0 1 AN x10 1 0 400 800 1200 1600 2000 Spannung 2400 2800 3200 3600 10 2 4 5 Se 2 9 sch See D 5 4 3 1 0 Dehnung Stress strain diagram 20 C mlaw 1 multiPlas USER S MANUAL January 2013 64 a D 42 x10 2 2 Dehnung Stress strain diagram 800 C mlaw 0 multiPlas USER S MANUAL January 2013 65 5 6 Example 11 Concrete model DRUCKER PRAGER singular LAW 9 elz dat Uniaxial tensile tests 4000 3600 3200 2800 2400 2000 Spannung 1600 1200 800 400 SY x10 3 0 2 4 8 1 sd 43 5 7 9 Dehnung Stress strain diagram 20 C mlaw 0 1 AN 4000 3600 3200 2800 2400 2000 Spannung 1600 1200 400 SY x10 3 0 4 8 1 2 1 6 2 2 6 1 1 4 1 8 Dehnung Stress strain diagram 20 C mlaw 1 multiPlas USER S MANUAL January 2013 66 Spannung ST 10 3 4 1 5 Dehnung Stress strain diagram 400 C mlaw 0 T er 02 4 5 Dehnung Stress strain diagram 800 C mlaw 0 multiPlas USER S MANUAL January 201
49. ltiPlas 418 ansys145 64bit zip Please extract this file into an arbitrary directory e g C Program Files ANSYS Inc 145 A new sub directory multiPlas 4 1 8 is created Please notice the full path to your multiPlas installation There is no further installation required for multiPlas In addition the multiPlas license file e g dynardo client lic must be copied into one of the following direc tories the application installation directory the Program Files Dynardo Common files directory Unix config Dynardo Common the users home directory Unix HOME Windows HOMEPATH the current working directory For any further questions of licensing please contact your system administrator or write an E mail to support dynardo de 2 1 How to start ANSYS Mechanical APDL with multiPlas The ANSYS Mechanical APDL Product Launcher can be used to start ANSYS Mechanical APDL with multiPlas After starting the launcher choose the Customization Preferences tab In the field Custom ANSYS executable browse to the ANSYS EXE in your multiPlas installation directory This procedure is summarized in Fig 2 1 ramm nn A iid kr Verte Leg NISI Bun 1 a select tab customization preferences browse to file ANSYS EXE in multiPlas installation directory start ANSYS Beaded mm Fig 2 1 start multiPlas in ANSYS Mechanical APDL via launcher Another p
50. ly the case for primary stress conditions can be done Do never chose dilatancy or friction angle as 0 0 because this can lead to unbalanced forces which can not be relocated A cohesion c 0 e g sand implies that the material does not have any uniaxial compressive or tensile strength First the material therefore has to be iterated into a stable position This leads very often to convergence difficulties so it is advised to use an adequately small value instead of zero for the cohesion while using the MOHR COULOMB LAW 1 yield conditions The automatic time stepping is called directly from the routine it can be switched on via autots on multiPlas USER S MANUAL January 2013 47 The global load step bisection can be disabled by choosing large value for cutmax In the case of a local bisection no hints are written out Be careful not to use too large values for maxinc and simultaneous suppression of the global bisection This may lead to a large computational effort Newton Raphson Equilibrium iteration In this case request the cause by use the global bisection Multi surface plasticity fundamentally is a physical path dependent phenomenon Therefore a global in crementation in order to represent the relocation of force correctly is of utmost importance In the multi surface routines softening residual strength is only introduced in at the equilibrium states so only after reaching the global Newton Raphson equ
51. nal pressure domain starting point of the parabolic hardening longitudinal stress ratio to fLc plastic strain at reaching fLc level softening due to generation knik bands KI plastic strain at reaching gt KI plastic strain at reaching the hardening due to compaction e Youngs modulus in the hardening area due to compaction E relation of stress and strain radial tangential pressure domain Starting point of the parabolic hardening longitudinal stress ratio to fLc 1 plastic strain at reaching fLc Qree softening due to generation of knik bands KRc2 plastic strain at reaching c Erce Youngs modulus in the hardening area due to compaction Werte f r tangentiale Richtung Index R T relation of stress and strain tensile area and shear domain Qumr ratio residual strength initial strength plastic strain at reaching the residual strength For both dimensions applies Index direction L longitudinal radial T tangential Index m mode t tension s shear For graphical explanation of the material values see Fig 3 23 Fig 3 24 and Fig 3 25 multiPlas USER S MANUAL January 2013 43 4 2 10 LAW 40 Geological Drucker Prager m 3111 a EE rer I I 61 77 nm geps maxit cutmax maxinc Iktuser DRUCKER PRAGER beta material pa
52. on biegeweichen im Boden eingebette ten Wellrohren mit geringer Ubersch ttung Rep Osterreich Bundesministerium f Bauten Technik Stra enforschung Heft 45 1975 Kr tzig W Mancevski D Polling R Modellierungsprinzipien von Beton In Baustatik Baupraxis 7 Hrsg Meskouris Konstantin RWTH Aachen Balkema Verlag Rotterdam 1999 S 295 304 Ottosen N S A Failure Criterion for Concrete Journal of the Eng Mech Div ASCE 103 S 527 535 1977 Polling R Eine praxisnahe sch digungsorientierte Materialbeschreibung von Stahlbeton f r Strukturanalysen Ruhr Universit t Bochum Dissertation 2000 Schlegel R Numerische Berechnung von Mauerwerkstrukturen in homogenen und dis kreten Modellierungsstrategien Dissertation Bauhaus Universit t Weimar Universi tatsverlag 2004 ISBN 3 86068 243 1 Simo J C Kennedy J G Govindjee S Non smooth multisurface plasticity and visco plasticity Loading unloading conditions and numerical algorithms Int Journal for nu merical methods in engineering Vol 26 2161 2185 1988 Vermeer P A Materialmodelle in der Geotechnik und ihre Anwendung Proceedings Finite Elemente in der Baupraxis 1995 Vonk R A Softening of concrete loaded in compression Dissertation Delft University of Technology 1992 Weihe S Modelle der fiktiven Rissbildung zur Berechnung der Initiierung und Ausbrei tung von Rissen Ein Ansatz zur Klassifizierung Institut f r Stati
53. ossibility is to start ANSYS Mechanical APDL from command line using the option custom lt multiPlasDir gt ANSYS EXE where lt multiPlasDir gt must be replaced by the full absolute path to your multiPlas installation The following command line starts ANSYS Mechanical APDL with multiPlas in graphical mode C Programme ANSYS Inc v145 ansys bin winx64 ansys exe g custom lt multiPlasDir gt ANSYS EXE The corresponding command line for batch mode is C Programme ANSYS Inc v145 ansys bin winx64 ansys exe b lt InputFile gt o lt OutputFile gt custom lt multiPlasDir gt ANSYS EXE An example of the windows batch script is included in the shipment Note The path to the customized multiPlas executable must be enclosed in quotation marks For any further command line options please take a look at the ANSYS operations guide Operations Guide chapter 3 Running the ANSYS Program 3 1 Starting an ANSYS Session from the Command Level 2 2 How to use ANSYS Workbench with multiPlas In order to enable multiPlas in ANSYS Workbench the solver settings in Mechanical must be customized In ANSYS Mechanical e Select Solve Process Settings from menu Tools e Choose the solver settings to be modified and select Advanced e Add the following option to the field Additional Command Line Arguments custom lt multi PlasDir gt ANSYS EXE multiPlas USER S MANUAL January 2013 3 T
54. pressive strength fmz s F46 as 7 distance of the longitudinal joints stone breadth 7 amount of offset between longitudinal joints cr residual cohesion for numerical stabilization ftr residual tensile strength for numerical stabilization psir residual dilatancy for numerical stabilization multiPlas USER S MANUAL January 2013 39 tempd switch for temperature dependency 0 or no entry no temperature dependency E temperature dependency for compression and tension Overview of input parameters of the softening function for the compressive space Bee 11 stress strain relation softening function multiPlas USER S MANUAL January 2013 40 4 2 8 LAW 22 Masonry Nonlinear Hardening Softening Hye 3 5 16 _ sas la o dec Is Eo jais ajaa ur E ee ei 31 40 ladi a RR che paman PS NANA NANA NAN NANA NANA Ausg Material parameter fmx fmy ftx ftxx fty nue_y as y al dreid if dreid 2 fmz ftz ftzz nue z as Z 27 cr ftr psir multiPlas compressive strength of the masonry normal to the bed joint compressive strength of the masonry normal to the head joint fmy lt fmx tensile strength normal to the bed joint limit to C tan phi geometric parameter for e g 10 tensile strength normal to the head joint stone tensile s
55. rameter that determines the ascent of the Drucker Prager cone Sig_ yt strength value analogue cohesion delt dilatancy factor note ideal elasto plastic material model with associated or non associated flow rule multiPlas USER S MANUAL January 2013 44 4 2 11 LAW 41 Combination Mohr Coulomb Drucker Prager resp TRESCA vs MISES Lo e D _ GR add nd E a i wells e GE 60 _yt did alah E It LL Ll Lo Lol Isotropic MOHR COULOMB DRUCKER PRAGER phig frictional angle Cg cohesion psig dilatancy angle phig residual strength frictional angle Cg residual strength cohesion Tension tension cut off lt Cg tan phig Tension residual strength lt Cg tan phig beta material parameter that determines the ascent of the Drucker Prager cone Sig_ yt strength value analog cohesion delt dilatancy factor Remark Mohr Coulomb Tresca if friction angle 0 Drucker Prager v Mises if beta 0 multiPlas USER S MANUAL January 2013 45 4 3 Numerical control variables eps local convergence criteria Return Mapping geps criteria for singular systems of equations for multi area activity maxit Maximum amount of local iterations of the return mapping process cutmax amount of local bisections prior the activation of a global bisection maxinc maximum incrementation of a load step glo
56. riable type sze intent description F dp ar 18 out Fliesskriterien dp ar 6 25 out Partielle Ableitungen d Fliesskriterien u plast Potentiale ka dp ar 5 inout History Variablen kappa plast Dehnungsanteile Ver Entfest FK dp ar 18 out Partielle Ableitungen dF dkappa DK dp ar 5 18 out Partielle Ableitungen dkappa dLambda nfail int sc inout Zaehler verletzter Fliesskriterien 000000000000000000000000000000n INTEGER LAW nfail wr iott DOUBLE PRECISION up 58 F 18 DF 6 25 ka 5 eppli 18 6 a FK 18 DK 5 18 eps sigtr 6 sigm sigdev inv2 inv3 sigs ta0 hyd Funktionen von ANSYS 5 ANSYS UPF Programmers Manual cc EXTERNAL VZERO c weitere erf interne Variablen DOUBLE PRECISION Fl ftx c Bsp fuer Kontrollausgabe Entwickler Mode if wr ge 1 then write iott cc x ttrattat START usermpls aaa a cc endif update strain Softening parameter kappa cc 1 1 1 1 1 Oftx dexp h ftx G 1 ka 1 c Bsp fuer Kontrollausgabe Entwickler Mode cc if wr ge 4 then cc write iott Kontrollausgabe Softeningfkt in jexp write iott 2000 Oftx cc write iott 2010 1 cc endif cc2000 format 2000 1 1x F14 7 cc2010 format 2010 kappa l 1 1 1 14 7 C Abfrage Kriterium Fl cc ftx up 1 Fl sigtr 1 ftx Oftx ce IF Fl ge eps THEN C Zugversagen Kriterium Fl cc F 1 F1
57. rop 8 mm 1 User Parameter up1 up58 m per perpe pe per pne Ter a 58 free definable material parameters 7 1 2 Requirements of ANSYS Release 13 Installation Guides ANSYS Inc Windows Installation Guide Tahle 2 1 Operating System Requirements Platform OS ANSTYSWorkhench Compilers Intel EMBAT Windows Intel Fortran 10 1 54 Edition Yersion 2003 Microsof visual Studia 2005 Intel EMBAT AMDBANYindows Vista Professional Edition xh4 Intel ARs DI Windows XP Build Intel Fortran 10 1 2600 Yersion 5 1 Microsoft Visual Studia 2006 Intel 14 32 hit windows vista Professional Edition Compilers are required only if you will be using User Programmable Features or other customization options multiPlas USER S MANUAL January 2013 84 Advanced Guide Chapter 14 User Programmable Features and Nonstandard Uses 14 1 User Programmable Features UPFs User programmable features UPFs are ANSYS capabilities for which you can write your own FORTRAN routines UPFs allow you to customize the ANSYS program to your needs which may be a user defined material behavior option element failure criterion for composites and so on You can even write your own design optimization algorithm that calls the entire ANSYS program as a subroutine UPFs are available in the ANSYS Multiphysics ANSYS Mechanical ANSYS Structural ANSYS PrepPost and ANSYS Academic Assoc
58. sing the material parameters No material parameter should be ever set to 0 0 Even for residual strengths values above eps 100 should be chosen Dilatancy angles close to zero imply ideally smooth friction surfaces in a physical sense and can lead to extreme convergence difficulties This results from tension component which can not be removed in case of shear failure The dilatancy angle therefore should always be set at least to 17 The tension strength is limited to the intersection point of the Mohr Coulomb line plane and the normal friction axis C tan phi 4 3 3 Remarks and tips for using multiPlas in nonlinear structural analysis If an oscillation can be seen for a certain imbalance value the convergence for the load step can be achieved by increasing the convergence criteria in ANSYS slightly above the oscillation value In the fol lowing load case the convergence criteria can be set to the smaller value again In case of frequent error messages local return mapping failed the local number of iterations should be increased and the yield areas should be checked This output only occurs if wr 2 1 In case where problems occur from processing the polyhedral yield figure in case of unfortunate physi cally problematic choice of parameters the calculations sould be performed by using isotropic yield crite ria with the whole load at first Then a following calculation with activation of anisotropic yield criteria this is especial
59. t multiPlas USER S MANUAL January 2013 25 3 3 8 Wood modelling using boxed value model The multi surface material model for wood is based on a boxed value model from Grosse 6 26 The orthotropic material model is implemented in multiPlas via LAW 33 It considers the interactions between the longitudinal radial and tangential material behaviour of wood The yield conditions are shown in Fig 3 21 and Fig 3 22 The stress and strain functions implemented for describing the nonlinear deformation behaviour are shown in chapter 3 3 8 1 F gt Stimfl che fre fri LT Gleitfl che Fig 3 21 yield condition Interaction longitudinal vs radial Stimflache gt R ckseite _ Ir fr LR Gletfliche Fig 3 22 yield condition Interaction longitudinal vs tangential In multiPlas the following conventions for the direction of wood fibre have been made Radial K Axis of element coordinate systems Tangential Y Axis of element coordinate systems Longitudinal Z Axis of element coordinate systems This conventions hold for Cartesian and Cylindrical coordinate systems multiPlas USER S MANUAL January 2013 Following yield conditions are used Fiber rupture tensile failure longitudinal F o 3 f 0 Fiber compressions compression failure longitudinal F 0 3 f Qu z0 Crack parallel to LT Plane 69 Y o 4 2 4 1 0 J
60. that cases a deformation behav iour closer to reality can be described by using non associated flow rules The dilatancy angle describes the ratio of normal and shear translation in the Mohr Coulomb shear criterion It has two limits Dilatancy angle friction angle gt maximum plastic normal strain at shear strain associated plasticity Dilatancy angle 0 0 gt no plastic normal strain at shear not recommended limit case because of result ing numerical problems By replacing the friction angle by the dilatancy angle w within the yield condition rsp plastic potential function a non associated flow rule is obtained In addition to that it has to be considered that the dila tancy angle is only physically reasonable for dilatancy angle v lt friction angle 9 A dilatancy angle larger than the friction angle leads to generation of energy within the system For the Drucker Prager yield condition the plastic deformation behaviour can be controlled via a non associated flow rule by manipulating the dilatancy factor 6 Then the plastic potential is modified ing to the equations Q 0s B96 3 18 and 3 21 Thereby dilatancy factor 6 1 gt associated plasticity dilatancy factor 6 lt 1 gt non associated plasticity For the compressive domain 0 lt lt 1 is true In the tensile domain of the Drucker Prager a yield condi tion of 6 0 1 0 25 is recommended In case of prevalent shear strain the
61. tiPlas USER S MANUAL January 2013 1 INTRODUCTION This manual describes the use Dynardo s software product multiPlas for ANSYS multiPlas is a library of elasto plastic material models for ANSYS The elasto plastic material models in multiPlas enable the user to simulate elasto plastic effects of artifi cial materials e g steel or concrete and natural born materials e g soil or rock in geotechnics civil engineering as well as mechanical engineering In the context of finite element calculations with ANSYS multiPlas provides an efficient and robust algo rithm for the handling of single and multi surface plasticity The material models are based on elasto plastic flow functions with associated and non associated flow rules One special feature of the multiPlas material models is the combination of isotropic and anisotropic yield conditions The multiPlas material models are available for structural volume elements e g SOLID 45 SOLID 95 for structural shell elements e g SHELL 43 SHELL 93 and structural plane elements e g PLANE 42 PLANE 82 The following material models and features are provided Stress Strain Temperature Application Response Dependency isotropic Material Models Tresca Steel associative ideal elastic plastic Soil Rock Stone bilinear Mohr Coulomb Masonry non associative residual strength von Mises Steel associative ideal elastic plastic Drucker Prager Soil Stone associat
62. trength value of decrease of the uniaxial horizontal MW tensile strength fmy s Fa distance of head joints stone length distance of bed joints stone height amount of offset between head joints friction angle at the bed joint cohesion at the bed joint residual strength friction angle at the bed joint initial angle of dilatancy usually friction angle strain at reaching the uniaxial compressive strength of the masonry fmx ration residual compressive strength initial compressive strength strain at softening in the pressure range at 0 85 fmx Youngs modulus normal to the bed joint fracture energy MODE tensile failure normal to the bed joint s fracture energy MODE tensile failure of the stones horizontal fracture energy MODE II shear failure of the bed joint s orientation of the joints in relation to the element coordinate system 0 x normal to bed joint normal to head joint 2 normal to longitudinal joint 1 2 normal to bed joint y normal to head joint x normal to longitudinal joint 2 y normal to bed joint x normal to head joint 2 normal to longitudinal joint switch for the three dimensional strength monitoring 0 for 2D F1 to F10 1 for 2 50 F1 to F10 F6 with Tau res 2 for 3D F1 to F18 compressive strength of the masonry normal to longitudinal joint tensile strength normal to longitudinal joint stone tensile strength geometric parameter of e g f
63. tzz 10 ftx value of decrease of the uniaxial horizontal MW compressive strength fmz s distance of the longitudinal joints stone breadth amount of offset between longitudinal joints residual cohesion for numerical stabilization residual tensile strength for numerical stabilization residual dilatancy for numerical stabilization USER S MANUAL January 2013 41 Overview input parameter of the relation stress strain in the compressive space En u ee ha ee Y fmu 0 85 fm mr fm Ls 3 Lor KT ee EE een Eml E Eml Eu multiPlas USER S MANUAL January 2013 42 4 2 9 LAW 33 Orthotropic Boxed Value Model RB 9 1 ra Phi C ps ph G Tension laa CPP 0140 em jme Aw mes idm Yt Re 41 50 Ku Qar Kw Om Omas _ STEE e eps MM qp Material parameter fLt uniaxial tensile strength longitudinal resp parallel to the fiber direction uniaxial compressive strength longitudinal resp parallel to the fiber direction fRt uniaxial tensile strength radial uniaxial compressive strength radial uniaxial tensile strength tangential fTc uniaxial compressive strength tangential fRLs shear strength radial longitudinal fRTs shear strength radial tangential fILs shear strength tangential longitudinal fIRs shear strength tangential radial relation of stress and strain longitudi
64. viatoric main stresses uniaxial tensile strength uniaxial compression strength Ry biaxial compression strength 0 hardening and softening function in the pressure domain the tensile domain The plasticity potentials are Os where t c are dilatancy factors 3 21 Q T 6 The yield condition is shown in Fig 3 9 and Fig 3 10 in different coordinate systems The comparison with the concrete model made by Ottosen 6 15 is shown in Fig 3 9 and illustrates the advantages of the Drucker Prager model consisting of two yield criteria While there is a very good correspondence in the compressive domain the chosen Drucker Prager model can be well adjusted to realistic tensile strength In opposite to that the Ottosen model overestimates these areas significantly A further advantage lies within the description of the yield condition using the three easily estimable and generally known parameters R Rg and Ru Toct t c tt gt Drucker Prager like model Xj u Fig 3 9 Singular Drucker Prager flow conditions Illustrated in the octaeder system multiPlas USER S MANUAL January 2013 47 AN E d mo t a b Fig 3 10 Singular Drucker Prager flow condition a yield surface the main stress domain b Illustration the o o t y space 3 3 6 1 Nonlinear deformation behaviour in case of pressure load
65. y that the volume fracture energy reaches the following value Mpa Dr Or int h g h 3 23 where gnr volume fracture energy at the integration point h equivalent length multiPlas USER S MANUAL January 2013 19 This model guaranties consistent dissipation fracture energy during the softening process for different sizes of elements The stress strain lines available in multiPlas are shown in Fig 3 13 Thereby a linear elastic behaviour is assumed until the tensile strength is reached After that one of the following is assumed as consequence of tensile fracturing linear softening until the strain limit is reached mlaw 0 2 exponential softening mlaw 1 A hpr d snap Back Err Fig 3 13 Stress strain relation in multiPlas mlaw 0 2 mlaw 1 For the exponential softening model mlaw 1 one should assume G E f t h lt 3 24 for the length h in order to avoid the numerically unstable snap back phenomena This is preferably achieved by choosing a proper mesh size In multiPlas the equivalent length will calculated automatically multiPlas USER S MANUAL January 2013 20 3 3 6 3 Temperature dependency Information on the temperature dependencies of the material behaviour are included in DIN EN 1992 1 2 6 11 AS an example the temperature dependencies from pressure level are shown in Fig 3 14 Fig 3 15 and Tab 3 1

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