ME EN 7960 Special topics: COMPUTATIONAL CONSTITUTIVE
Contents
1. This document contains the syllabus and other first day information for ME EN 7960 Special topics COMPUTATIONAL CONSTITUTIVE MODELING Expected to be of interest to students in Bioengineering Physics Geophysics Materials Science and Metallurgy This front page is an informal description of the course serving as a teaser to help students decide if this class is of interest The official syllabus draft begins on page 2 Constitutive modeling refers to the development of equations describing the way that materials respond to various stimuli In classical deformable body mechanics a simple constitutive model might predict the stress required to induce a given strain the canonical example is Hooke s law of isotropic linear elasticity More broadly a constitutive model predicts increments in some macroscale state variables of interest such as stress entropy polarization etc that arise from changes in other macroscale state variables strain temperature electric field etc Constitutive equations are ultimately implemented into a finite element code to close the set of equations required to solve problems of practical interest This course describes a few common constitutive equations explaining what features you would see in experimental data or structural behavior that would prompt you to select one constitutive model over another how to use them in a code how to test your understanding of the model how to check if t2. and the final result should be boxed Discussion How might the result be used Is the answer reasonable Discussion includes sanity checks that note features such as the magnitude and sign are reasonable the solution reduces as expected in a special case all steps in the derivation obey indicial notation rules the same solution is obtained in two very different ways e g by hand and by using math software the physical units are correct etc You can even say that your answer agrees with a similar problem found online URL must be given or your solution agrees with an independent analysis performed using alternative software such as an FEM code The use of symbolic software Matlab Mathematica Maple etc as well as collaboration on concepts and procedures is expected encouraged and occasionally even required Collaboration does not sanction copying You are allowed to submit only work that you have completed individually Submitting any work that is not the result of your own effort and or not written in your own words is considered cheating by both you and the student who allowed the work to be copied Academic misconduct may result in a failing grade dismissal from the program or the University revocation of the student s degree or certificate or other sanctions See the Student Handbook for further details Late homework policy subject to change based on discussion with students during first week of class Unless otherwise
3. announced homework is due one week after it is assigned Late homework is not accepted To make up for this tough stance the following strange formula will be used homework grade on scale from 0 to 100 50 14 Exp a J gt H H h where h is your total amassed homework points and H is the total number of available homework points Suppose for example that you earn 74 of the available homework points h 0 74H Rather than getting a C by a conventional grading scale the above formula would improve your homework grade to a B The bonus and resubmittal policies below further compensate for the no late homework policy Bonus policy Can you boost your grade by doing extra work Yes but not at the end of the semester as a last minute attempt to fix a low grade Bonus points will be awarded for extra work if it is 1 clearly beyond the scope of the assignment 2 relevant to the assignment and 3 handed in with the assignment Resubmittal policy Students may not resubmit homework to recover points lost in the first submittal except when the instructor extends an invitation to the entire class to do so Tentative agenda likely to change based on student interests and abilities Week 1 Aug 23 amp 25 Review of continuum kinematics with algorithms such as a demonstration that iterative polar decomposition is more accurate than the exact solution which is prone to round off error Homework write the begin
4. e a satisfactory grade the second time may not be able to graduate Fall Semester 2011 Withdrawal Procedures See the Class Schedule or web for more details Please note the difference between the terms drop and withdraw Drop implies that the student will not be held financially responsible and a W will not be listed on the transcript Withdraw means that a W will appear on the student s transcript and tuition will be charged Drop Period No Penalty Students may DROP any class without penalty or permission during the FIRST TEN calendar days of the term Wednesday Wednesday August 31 2011 Withdrawal from Full Term Length Classes Students may WITHDRAW from classes without professor s permission until Friday October 21 2011 Please note that a W will appear on the transcript and tuition will be charged Refer to Class Schedule Tuition and Fees for tuition information Withdrawal from Session II See the web page for details www sa utah edu regist calendar datesDeadlines Fall2011 htm Withdrawals after October 21st will only be granted due to compelling nonacademic emergencies A petition and supporting documentation must be submitted to the Dean s Office 1610 Warnock Engineering Building or University College 450 SSB if you are a pre major Petitions must be received before the last day of classes before finals week Adding Classes Please read carefully All classes mus
5. e giving expected or desired trends where data are incomplete or not available Case study application classical linear and power law isotropic hardening of von Mises theory contrasted with kinematic hardening showing identical results in loading but differences in unloading Guest Lecturer Ali Sadeghirad research associate developing a simplified plasticity model for Uintah Homework Implement power law hardening into the von Mises plasticity model via two approaches isotropic hardening and kinematic hardening Week 10 Nov 1 amp 3 Computational algorithms for classical small strain intrinsic elastic anisotropy Homework Implementation of a small strain transversely isotropic elasticity model with functional testing under simple loading such as confirming an anisotropic stress resulting from isotropic strain verification testing against analytical solutions for a limiting case valid for large deformations thus showing validation limits of such models Week 11 Nov 8 amp 10 Continued validation critique of plasticity models revealing the need for pressure dependent strength and apparent non associativity The difference between a desired realistic instability and an anomalous unrealistic instability illustrated via the Sandler Rubin instability for non associated flow rules Algorithms for nonassociated plasticity Homework Implement a non associated linear Drucker Prager plasticity model and devise a way without being
6. he code is applying the model as advertised in its user s manual and how to quantitatively assess the mathematical and physical believability of the solution The related but fundamentally different discipline of Materials Science aims to reveal the underlying microscale physical mechanisms such as grain structure dislocation density etc that give rise to the relationships observed in the laboratory Stated differently constitutive equations predict what happens whereas materials science explains why it happens Materials Science plays an essential role in revealing appropriate definitions of and relationships between macroscale state variables As such even though this course focuses on the implementation and testing of the final equations themselves the reasoning behind the equations whether based on empirical observations or microscale or atomistic considerations is essential to check the predictions and to assess if the equations are being used within their applicability domains Working from a premise that aside from user input typos the largest source of error in typical engineering finite element simulations is modeling uncertainty in the constitutive equations this course surveys a small selection of common constitutive models as a means of illustrating principles of verification which is evidence that the equations are solved correctly and validation which is evidence that the equations are realistic Students will w
7. is course as they are listed in the syllabus for this special topics course especially computing and continuum _ I understand that I am expected to turn in homework that is professional in appearance and easy to understand by including the following information for each problem 1 problem statement 2 solution with words explaining each equation and 3 discussion of the result I understand that some homework assignments will require computer programming with math software of my choosing Mathematica Maple Matlab Python etc I understand that all email communication will be sent to my university email address ul23456 utah edu and that it is my responsibility to ensure that that messages sent to my university email address will reach me OPTIONAL What I hope to learn from this class Grads list areas of research that you hope will be emphasized in classroom examples and applications OPTIONAL What I hope will NOT be part of this class are there topics in the current course plan that you would prefer to drop in favor of something else Name Signature Date
8. ith student performance 1 2 3 4 5 COMMENTS 9 I believe that my knowledge of this subject will significantly help my professional career 1 2 3 4 5 COMMENTS 10 I student am happy with the effort Ihave put into this course to date 1 2 3 4 5 COMMENTS 11 I student am happy with my performance in this course to date 1 2 3 4 5 COMMENTS If I could change one thing about this course and of course if I could justify the change to the taxpayers who subsidize this public institution it would be IS THIS SURVEY MISSING ANY IMPORTANT AREA FOR FEEDBACK Please include additional comments concerns or suggestions on the back of this page ME EN 7960 Special topics COMPUTATIONAL CONSTITUTIVE MODELING Student information amp affirmation sheet Student s Full Name print legibly Name I prefer to go by UID I certify that _ Ihave been given the course information syllabus which includes instructor contact information prerequisite requirements course objectives evaluation methods grading policy course description important dates tentative topics list and the College of Engineering Guidelines _ I understand the course objectives that are listed in the syllabus _ I understand that the instructor retains the right to revise the syllabus with the proviso that students retain a right to reasonable notice of changes I have satisfied the pre requisites for taking th
9. mphasis is on elastic and inelastic geometric and material nonlinearity as it pertains to selecting and properly using finite element and similar codes Required Textbook A Anandarajah Computational Methods in Elasticity and Plasticity Solids and Porous Media Springer 2010 ISBN 1441963782 685 pages I 119 Free supplemental Textbook Schreyer H L Mechanics of Inelastic Continuum Course Notes as of 2007 Electronic copy will be provided Optional books J C Simo and T J R Hughes Computational Inelasticity Springer Verlag New York 1998 ISBN 0 0378 97520 9 392 pages Ellis H Dill Continuum Mechanics Elasticity Plasticity Viscoelasticity CRC Press 2006 ISBN 10 0849397790 ISBN 13 978 0849397790 Grading H Homework 90 F Final Exam Thurs December 15 3 30 5 30 pm 30 TOTAL 120 minus 20 from lowest 100 Formula SCORE 90H 30F 20L 100 where L min H F This formula allows your better score to dominate your grade while still requiring completion of homework and a final exam The score is assigned a letter grade according to the following table 0 59 60 62 63 66 67 69 70 72 73 76 77 79 80 82 83 86 87 89 90 92 93 96 97 100 E D D W CI C Ct B B Bei A A A The instructor reserves the right to lower the score required for any letter grade There is no curve Course Objectives By the end of this course you are expected t
10. ning of a stand alone driver program using any computing language approved by the student s advisor that takes a piecewise linear specification of deformation an F table as input and computes key kinematical quantities Jacobian polar decomposition logarithmic strain etc as output displayed as graphs Week 2 Aug 30 amp Sep 1 Review of continuum stress definitions Review of 3D linear isotropic elasticity classical Hooke s law contrasted with linear isotropic Newtonian viscosity Homework Extend the stand alone driver to implement Hooke s law and test it under axial tension and compression using two different models 1 Kirchhoff stress with logarithmic strain and 2 Second Piola Kirchhoff stress with Lagrange strain the latter will be exposed to be flawed since it will predict the unacceptable result that only a finite stress is required to compress the material down to zero volume Week 3 Sep 6 amp 8 Incremental rate forms of constitutive models and the use of linearization to solve nonlinear equations Continuum strain energy Time integration schemes and subcycling in constitutive models Homework Modify the stand alone Hooke s law model to be written in rate form that is integrated through time using an explicit time integrator Apply it to a closed path in strain to demonstrate strain energy conservation Week 4 Sep 13 amp 15 Review of classical thermoelasticity and algorithms large and small def
11. o 1 Understand and be able to design single element benchmark problems that test basic principles frame indifference thermodynamic admissibility basis insensitivity etc that apply to any material model 2 Write a single element kinematics model driver capable of computing key quantities strain strain rate deformation gradient polar decomposition Jacobian etc that are typically used as input variables sent to computational constitutive models 3 Implement stand alone computer code for several classical constitutive models Hooke s law Linear Drucker Prager nonhardening and hardening plasticity orthotropic composite elasticity viscoelasticity thermoelasticity porosity etc and test them using the single element driver 4 Be able to summarize seminal contributions in the literature and summarize current active research in computational constitutive modeling Homework Policies As this is an advanced course homework assignments will involve open ended questions such as estimation exercises and asking the students to come up with their own ideas for testing models Turned in homework should be written at an advanced professional level to be expected in any 7000 level course In particular a homework problem will be given a grade of zero if it is incoherent or if it fails to include the following information Problem Statement What is given and what is sought Solution word explanations must accompany each equation
12. or audit classes Brannon at Seattle ballistics conference Last day to withdraw from classes Fall break Brannon at Barcelona Particles conference Thanksgiving break Last day to reverse CR NC option Last lecture Mon August 22 Sun August 28 Wed August 31 Tues September 6 Thurs Sept 22 Fri October 21 Tues amp Thurs October 11 amp 13 Tues amp Thurs October 25 amp 27 Thurs November 24 Fri December 2 Thurs December 8 Comprehensive final exam Grades Available Thurs December 15 3 30 5 30 pm Tues Dec 28 NOTICES The above dates are provided only for convenience For official dates refer to the 2009 academic calendar at http www sa utah edu regist calendar datesDeadlines Fall201 1 htm The instructor retains the right to revise this syllabus with the proviso that students retain a right to reasonable notice of changes The following COE guidelines are available at the COE website http www coe utah edu current undergrad policies_appeals php COLLEGE OF ENGINEERING GUIDELINES http www coe utah edu Appeals Procedures See the Code of Student Rights and Responsibilities located in the Class Schedule or on the UoftU Web site for more details Appeals of Grades and other Academic Actions If a student believes that an academic action is arbitrary or capricious he she should discuss the action with the involved faculty member and attempt to resolve If unable to
13. ormations Homework revise the Hooke s law model to now take the temperature rate as input in addition to strain rate and confirm that the governing equations predict analytical solutions for thermal expansion Also implement and test a classical large deformation hyper elasticity model e g Mooney Rivlin Week 5 Sep 20 amp 22 Setting up and running constitutive model verification problems and data fitting methods in an FEM code guest lecturer Steve Maas Lead developer of the University of Utah s FEbio code Homework verification tests using the FEBio code at the CADE lab and fitting of an FEbio model to actual test data Week 6 Sep 27 amp 29 Review of basis change equations and basis invariance requirements of constitutive models Review of superimposed rotation and objective rates theory and algorithms Review of frame indifference in the context of hyperelasticity and hypoelasticity Homework Apply the stand alone driver to check for consistency of Hooke s law under basis change Apply the stand alone driver to reproduce the famous Dienes and others oscillating stress with Jaumann rate in hypoelasticity contrasted with hyperelasticity Perform a literature search of recent within the last five years journal articles to assess the degree to which objective rates continue to be the subject of research Week 7 Oct 4 amp 6 Introduction to computational plasticity non hardening von Mises classical radial re
14. resolve the student may appeal the action in accordance with the following procedure 1 Appeal to Department Chair in writing within 40 business days chair must notify student of a decision within 15 days If faculty member or student disagrees with decision then Appeal to Academic Appeals Committee see hetp www coe utah edu current undergrad appeal php for members of committee See IH Section D Code of Student Rights and Responsibilities for details on Academic Appeals Committee hearings Americans with Disabilities Act ADA The University of Utah seeks to provide equal access to its programs services and activities for people with disabilities If you need accommodations in a class reasonable prior notice needs to be given to the instructor and to the Center for Disability Services 162 Olpin Union 581 5020 V TDD to make arrangements for accommodations All written information in a course can be made available in alternative format with prior notification to the Center for Disability Services Repeating Courses When a College of Engineering class is taken more than once only the grade for the second attempt is counted Grades of W I or V on the student s record count as having taken the class Some departments enforce these guidelines for other courses as well e g calculus physics See an advisor or departmental handbook Students should note that anyone who takes a required class twice and does not hav
15. rite their own stand alone constitutive model driver which will be compared with single element testing of finite element models that purport to implement the same equations Considerable emphasis is placed on exposing applicability limits of constitutive models ME EN 7960 Special topics COMPUTATIONAL CONSTITUTIVE MODELING Fall 2011 Tues amp Thurs 03 40 PM 05 00 PM WEB 1460 3 credit hours Course materials and assignments distributed online Instructor Rebecca Brannon 2134 MEB email via course server Cell 801 662 8340 use judiciously Office hours Tues amp Thurs 5 00 6 00pm or by appointment or drop in if instructor is available Course description in catalog 7960 Special Topics 1 to 3 Prerequisites Graduate Standing OR Instructor Consent Contemporary problems in Mechanical Engineering Course description and prerequisites for this topics course 7960 Computational Constitutive Modeling 3 Prerequisites Continuum Mechanics ME EN 6530 PDEs MATH 3150 Finite Element Analysis ME EN 6510 computer programming in any language such as Matlab C Python FORTRAN etc numerical methods OR permission of instructor granted if similar courses have been taken under different names Broad theoretical and practical aspects of materials modeling illustrated through development and testing via stand alone driver and single element FEM simulations of algorithms for various commonly used material models E
16. t be added within two wecks of the beginning of the semester deadline September 5th Late adds will be allowed September 6 9th requiring only the instructor s signature Any request to add a class after September 9th will require signatures from the instructor department and dean and need to be accompanied by a petition letter to the Dean s office A 50 FEE WILL BE ASSESSED BY THE REGISTRAR S OFFICE FOR ADDING CLASSES AFTER September 9th STUDENT SURVEY This form will be handed out two or three times during the semester Instructions Circle the number corresponding to your response l strongly disagree 2 disagree 3 neutral 4 agree 5 strongly agree 1 The pace at which the course is proceeding is appropriate 1 2 3 4 5 COMMENTS 2 The prerequisites for this course are reasonable 1 2 3 4 5 COMMENTS 3 I student know the prerequisite material well enough to focus on new material 1 2 3 4 5 COMMENTS 4 The instructor s use of class time is effective in helping me understand the material covered 12 3 4 5 COMMENTS 5 The textbook and or lecture notes are useful for learning the material covered 1 2 3 4 5 COMMENTS 6 Homework problems are assigned in proper quantities and are of proper difficulty 1 2 3 4 5 COMMENTS 7 The first midterm exam was a fair representation of subjects covered and was graded fairly 1 2 3 4 5 COMMENTS 8 The instructor is respectful when pointing out issues or problems w
17. told how to verify that the nonassociative feature does reduce dilatation in uniaxial strain loading Week 12 Nov 15 amp 17 Softening plasticity smeared damage and decohesion models aleatory uncertainty scale effects etc Methods for assessing rate of convergence with respect to spatial mesh resolution Homework Literature review to find published simulations of damage that show signs of spurious mesh dependencies Week 13 Nov 22 only Porous and granular media stable and unstable behaviors Stable pore crushing model experimental evidence of nonlocal deformation SEM images of compaction bands and shear band localization Introduction to principles of material stability Guest Lecture Michael Homel Homework cap plasticity feature in the model driver limited to pure hydrostatic loading for tractability Week 14 Nov 29 amp Dec 1 Unresolved research problems in Computational Solid Mechanics e g mesh dependence scale effects aleatory uncertainty spurious instabilities Homework none Thanksgiving treat Week 15 Dec 6 amp 8 Viscoelasticity materials with memory Deborah number etc and viscoplasticity overstress models for high rate loading Homework analytical solutions to viscoelastic models Addition of overstress to the plasticity model driver Important dates First lecture Last day to register without a permission code Last day to drop delete classes Last day to register elect CR NC
18. turn algorithm Principles of constitutive model verification testing with emphasis on the method of manufactured solutions MMS Guest Lecturer Krishna KC Kamojjala who is a PhD student experienced with deriving analytical solutions to idealized plasticity problems testing for frame indifference and deriving body forces and tractions for the MMS Homework reproduce analytical results for pure shear followed by uniaxial strain Week 8 Oct 18 amp 20 Isomorphic projections of 6D stress space onto 2D meridional or octahedral planes Tangent stiffness tensors in fourth order form and in reduced matrix form using Mandel components as a preferred alternative to Voigt components Intro to anisotropy orthotropy and transverse isotropy Reducing 3D constitutive models to simpler forms for verification testing Homework Non computing mathematics practice with Mandel and Voigt components Reduction to pure axisymmetric loading of an isotropic model down to a 2x2 system again using Mandel components Self study introduction to isomorphic stress and strain invariants and their relationships to more conventional invariants such as octahedral shear stress mean stress von Mises equivalent stress etc Week 9 Oct 25 amp 27 Validation testing contrasted with verification testing leading to the need to introduce internal variables in constitutive models Methods to develop evolution theories to match available experimental data whil
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