P.B. Winter et al., MITlaos User Manual
Contents
1. Figure 12 Save panel The edit box at the top of this panel allows the user to choose the beginning of the save file names When the figures and data files are saved each of their names will begin with the text in this box and an appropriate suffix will be added to distinguish each file This provides a simple way to group related files together For example when saving a JPEG image called Figurel a setting located beneath the Customize Figure Saving Options button if the text the Beginning of save file name box is TestSample42 then the final save file would be called TestSample42 Figure l jpg NOTE The saved files figures and data files will always be located in the same folder as the initial input data file The Save Data Files checkbox This box must be checked to save any data files The Save Figures checkbox This box must be checked to save any image files Details regarding the Customize Data File Saving Options and Customize Figure Saving Options buttons are discussed in the following two subsections Customize Data File Saving Options button 14 When the Customize Data File Saving Options button is clicked the datasaveGUI window opens allowing the user to specify the layout and format of the saved data files Figure 13 datasaveGUI_MITlaos _ Raw and Reconstructed Data Add Suffix to Save File Name Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column2. button in the Data Input panel to browse and select the file to analyze Figure 3 Select the file then click Open and the filename and directory information will automatically be entered into the MITlaos main window Pick a Data File Look in S ampleD ataFiles e m ce Eg 2 E CPyCL omega00p30 gam03p1600 1cycle vRate txt txt EG E CPyCL omega00p30 gam03p1600 1cycle vStrain txt txt My Recent CPyCL omega00p30 gam03p1600 dat Documents E CPyCL omega00p30 gam03p1600 VEParameters txt 2 GiesekusSimulation omega01p00 gam05p000 dat m SlugSlime omega03p00 Run31 dat Desktop My Documents My Computer E i l My Network File name rt O Places Files of type MATLAB files l Cancel Figure 3 Choose Data Window Preview Data button Optional The Preview Data button uses a function called Import Wizard to preview the selected data file This can be used to quickly look at the contents of the selected input file The Import Wizard is shown in Figure 4 A WARNING Import Wizard must only be used for previewing data Press Cancel when finished using the wizard DO NOT click Next Import Wizard Sle x Select Column Separator s Number of text header lines iy 3 f046e 07 3 foo4e 06 8 1210e 06 1 1958e 05 1 5694e 05 0 13250 1 9412e 05 0 15693 0 17651 2 0 19738 3 0963e 05 0 21617 3 5167e 05 0 23556 0 24664 4 958e 05
3. 4 8694e 05 4 7 112e 05 Figure 4 Import Wizard only used to preview data In Figure 4 the box on the left shows the raw contents of the chosen data file The grid on the right shows how MITlaos will load the file In the example shown in Figure 4 MITlaos automatically cuts off the top rows of text containing the headers and units and reads only the numerical data below them Note that the values of Torque are being read properly however the numerical value is so small that Import Wizard rounds to O in the display WARNING Any options changed using The Import Wizard will NOT be changed in MITlaos Import wizard is for previewing purposes only If MITlaos does not properly read the input file then the input file layout must be modified outside of MITlaos File Name edit box The File Name edit box displays the name of the chosen data input file Using the Choose Data button will automatically fill in this box however the user may also manually type the name of the data file into this box if desired Path Name edit box The Path Name edit box displays the directory of chosen input file As with the File Name edit box the Choose Data button can be used to automatically fill in this box The user also has the option to type the pathname of the data file into this box Input Variables Panel The Input Variables panel allows the user to specify all the information MITlaos requir
4. If the data was collected as torque instead of stress click on the Convert Torque box to the left of the word Stress Similar changes will occur allowing the user to specify a conversion factor between torque and stress Use the appropriate conversion factor such that stress is in units of Pascals according to the equation t Pa FT Note that torque may be reported in various units but F must be chosen to give stress in units of Pascals These conversion factors depend on T the type and size of geometry being used cone plate plate plate etc Values for conversion factors may be found in rheology textbooks and may sometime be given by the geometry manufacturer Data Windowing MITIlaos can analyze all or part of the time series data contained in the input file There are two large buttons titled Select Part of Data and Use Full Data Set that allow the user to choose between these options see Figure 5 To the right of these buttons are three boxes which display the starting point ending point and number of cycles chosen from the dataset These boxes will be empty if no data range has yet been chosen NOTE At least one complete cycle must be selected for the analysis to work properly To analyze the full time series data set press the Use Full Data Set button The full dataset will be trimmed to an integer number of complete cycles this is necessary for analysis and the boxes to the right of the
5. OR On Selecting The Data Range The stress response reaches a steady state when the stress amplitudes of each cycle are equal and the shape of the cycle repeats itself In Figure 7 steady state is reached after the first peak which is slightly smaller than the others For best analysis include only cycles that have reached equilibrium Example Incorrect column settings To illustrate a possible mistake with the settings of the Input Variables panel a sample picture is included here Figure 8 in which the columns for the data have been incorrectly assigned As shown in Figure 8 a straight line running through the graph is an immediate indication that something is wrong since both stress and strain should be oscillating In this example the time column was incorrectly specified as the strain column Stress Strain arb 500 1000 1500 2000 2500 3000 3500 4000 Index Figure 8 Data Set with Incorrectly Specified Columns 10 Example Multiple strain amplitudes in one data file Figure 9 shows an example of more advanced data processing that can be done with MITlaos This shows the data collected from a waveform test combined with a stepwise increases in amplitude 6 cycles at each strain amplitude The decreasing stress amplitudes after each step show that the system has not reached equilibrium MITlaos can not accurately process this entire set of data Figure 9 due to the changing strain amplitude However the data can manually b
6. Portland ME Paper BS9 2006 Ewoldt R H A E Hosoi and G H McKinley Rheological Fingerprinting of Complex Fluids using Large Amplitude Oscillatory Shear LAOS Flows Nordic Rheology Conference Stavanger Norway Annual Transactions of the Nordic Society of Rheology pp 3 8 2007a Ewoldt R H A E Hosoi and G H McKinley in preparation 2007b 21
7. The Stress Filtering Smoothing panel allows the user to change two options involved in this Fourier reconstruction Figure 10 Stress Filtering Smoothing The Highest Harmonic ta consider i gis in stress reconstruction View FT Spectrum of Stress TE Points per Quarter Cycle in Fourier Transform reconstruction 300 zueTestst parae U0 Juan Figure 10 Stress Filtering Smoothing panel The first editable setting is the value for n the highest odd harmonic used in stress reconstruction i e n where is the oscillatory test frequency The maximum available value for n labeled as n max is displayed as well this indicates the Nyquist frequency The value of n max is limited by the number of data points per cycle and will be displayed as soon as a data range is chosen see data windowing Although n max is the maximum possible value for n it is common to use a lower n value than this Choosing a lower n will limit the number of harmonics used in the Fourier Transform FT reconstruction If n is too low the stress will be overly ssmoothed and less accurate However if n is too high random noise may be incorporated into the smoothed stress For help on choosing the appropriate value for n click the View FT Spectrum of Stress button see below The second editable setting is the Points per Quarter Cycle PPQC in Fourier Transform reconstruction This value indicates the number of
8. data points included in the reconstructed stress signal A smaller number of points will decrease the resolution of the reconstruction and a higher number of points will increase the file size The default value is currently 300 PPQC which is likely adequate to capture most nonlinearities No limit is placed on size of the reconstructed Fourier Transform other than the operator s ability to store the resulting data Note that a smoothed stress signal with a large PPQC value will likely represent a higher time resolution than is actually contained in the smoothed signal since harmonics greater than n have been omitted 12 View FT Spectrum of Stress button Clicking the View FT Spectrum of Stress button opens the FTHamonicGUI window Figure 11 This window displays the Fourier Transform FT power spectrum of the raw stress signal and provides the user with information to choose the appropriate value for n FT harmonicGUI_MITlaos Full FT Spectrum Instructions data for higher harmonics overflows My ad a Select Choose Highest Harmonic and then click in the graph to choose the highest odd harmonic you would like to consider for filtering smoothing Normalized Power and calculations 10 n Harmonic order o Figure 11 FTharmonicGUI window The FT spectrum will typically show a series of decreasing peaks that eventually fall into the noise floor at higher frequencies note that a singl
9. 7 Column 8 v Filet 1cycle vStrain txt Strain S v Stress w Elast Str w Empty v Include a header with calculated variables 7 File 2 1cycle vRate txt Strain v Stress vy isco St v Empty v Include a header with calculated variables File 3 Se This creates a file containing the calculated viscoelastic parameters v File arranged in a row with header labels 7 Files VEParameters di ith header label Figure 13 datasaveGUI window The check boxes labeled File 1 File 2 etc determine if each save will be saved File 1 File 2 and File 3 are intended to contain columns of time series data the layout of which can be modified by using the dropdown menus associated with each file File 4 has a fixed format since it contains the calculated viscoelastic parameters All data files will be saved with the extension txt The layout File 1 will be determined by the box immediately to the right of the File 1 checkbox The window shown in Figure 13 indicates here that File 1 File 2 and File 4 will all be saved Since the File 3 checkbox is unchecked it will not be saved and none of its information is displayed in the window The edit boxes underneath the header Add Suffix to Save File Name will determine the last part of the name this file is saved as Note that th
10. GUT WiN OW ee EO EA eeseteanie Dt 9 Figure 8 Data Set with Incorrectly Specified Columns sssesrerssssssssssssssssssesereerreesssssssssssssesereerees 10 Figure 9 Data Set with a Stepwise Increase in Amplitude sssssessssssessssssssssssesereerreessssssssssssresereerees 11 Figure 10 Stress Filtering Smoothing panel essssssssssssssssssssssssereeeerreersssssssssssssserererreereeeeesesssssssses 12 Feaie Mes ell Boreva cc ternule Oi Op ia abate le eE E O A E 13 Pearce yi em OF Hao Uk temtn cree ra ram ine es ak naT PONDS E Hem rt ne Reem Ie 14 Ri caui cow Koper leks nus 700 lake velo eeeter eran an meee or nen e Smee CEILS NN OAT ne ewe ne 15 Preure 14s retire save Cr UT at ClO enis AE A E N 16 Feuer Maria roe cai DUON Siete tae E ae i rd ENEE dates nates 17 Figure 16 Definitions of alternative viscoelastic moduli a minimum strain modulus G and large strain modulus G b minimum rate dynamic viscosity 7 and large rate dynamic viscosity m e ieure reproduced from Ewoldt etal ZOOTI iscsi ties oan ENEE 18 Figure 17 The first few odd Chebyshev polynomials of the first kind ssssssssssssseserrrssssssssssssssssesees 19 Introduction This manual describes the use of MITlaos MATLAB version for analyzing rheological properties in large amplitude oscillatory shear LAOS In addition to calculating standard viscoelastic parameters such as G G MITlaos calculates additional parameters for interpreting nonlinear vi
11. MITlaos User Manual Version 2 1 Beta for MATLAB User manual creator User manual editor MITlaos creator MITIlaos GUI master MITlaos supervisor Peter Winter Randy H Ewoldt Randy H Ewoldt Peter Winter Gareth H McKinley Hatsopoulos Microfluids Laboratory Department of Mechanical Engineering Massachusetts Institute of Technology MITlaos mit edu Table of Contents Introduction eGR aaah IEE SOIIS E EIET N E E EE E TEIE E E EE SE S EE I E EE N E T EI E I EE EES E OIEI TE 3 Introduction OIER PIO IESE TOT EOS E A E EE ES E EE EI E TTT TE SOL CTO E E E EE E T E EE E A EEE LE 3 Installation of MTITlaos ISIE ETE E N IEEE E EISE EE EERE TE E ES S E TE EE E E TEE S S SE TE 3 unning XOS WER VIAA ANA vase tates a vig ces aia A ate ae colts al mai aie geld anu ee Reeve celal ne ENE A OAAS TEAR Structure of Input Data File OEE EEE P EE E S E OTT E E EE E STINE E REE SR E E E N T E 3 Running the Program PELOTON E SSE N E N E ES E TE E T E TE EEEE T E E EETRIS EE ESE E EE AR 3 M i W i d W Ov rview aln Inao CTVICW sasesana aE Te Peer ETL Ne Eee CTT RT MONT A Ie RET Che TEE ee Tee PON Te eT Ee wee ee CTO TAT OE rae eee a Data Input Panel ISTE EE SOOT ORNL E ES OT ETT OE OE OTTO LOTT ET TOOT Tee Oe STN Oe Lee OTT OTTO NOSE PORE TS CeO T EAA EES 5 Input V ariables Panel EOP Oe HTS OTL LY eee TON TT Te POOR TIO DER Te TT CIO OT COI IST EEE E eC NT TLE OO eC ITNT eee re tress Fi tering moot INE FAMELA EAEE EEEE ETAETA EAEE EEEE EEA
12. TSS SSS Save Panel OPPER E EEEE RA TS S ENE EEDE T IE S E EN E IIE R O E EEIE E EERE EEA 14 Main Buttons REA EENE E EARE EEE E E ES ENR A NES E E Tee N TOE EE EEIE S IE ENEN EA 1 enalx A eTinitions o onlinear Viscoelastic Farameters oo BY SKAAAAALAAYAAY NYA A NAYA ABEL EWEARE YO LOJZ he SAUEAWIW CINY A CAR UAE ER UD ILU 6H HH HH HHH HHH HH HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH HS ternative Viscoelastic odu ORE eee PONTE Tyee OTe TET IT Te CPCS UU ON TCC TOUT T Fy eMC TOE NEw POT NT OTT 1scoelastic epysne Ges Mt Gs Sy WES ee mene E E E Oa IT CMD Bae DUD Tr wn eee BO T HE EN ene N ine Acknowledgements LEE OE ESO TE TOT TESOL TOOT CT ITT TE ORME COPE ST OL TOOT SOOO LOT OT Ee CONT eT O Te he oI A TOU EIN Z 1 References EEEE TA E E I E IEE ETTIR E E NE TTT E IEE E ET E SE N E E E E E E EE E IIN TEE 21 Table of Figures Figure 1 The MITlaos main window arrows added to show the standard order of completion 4 Foarte 2 Data PUE ane eene T ES 5 Fure o Choose Daa WW Ii OW eetatsicsnce teat ea an ET A TE 5 Figure 4 Import Wizard only used to preview data ssssssesessessssssssseeresssssssrererssssssrrerresessssrrrreresss 6 Picaro Se nput Vira eS pane benseen Ea E T E E 7 Figure 6 Input Variables panel with Convert Displacement and Convert Torque options selected and the Time column input turned on ssssssssssssssssssssseeeeerersssssssssssssssrereeoreresesssssssserereree 8 PIOUS Te Process Par Data
13. ber of Cycles Selected 4 Stress Filtering Smoothing 4 7 i The Highest Harmonic to consider L j n fmaxj k Points per Quarter Cycle in Fourier Transform reconstruction suggested range 100 1000 Figure 1 The MITlaos main window arrows added to show the standard order of completion The MITlaos main window is broken into separate panels which look like boxes that group together related information MITlaos was designed for filling out the information in one panel and then moving to the next one The typical order for using MITlaos is to complete the Data Input panel and then the Input Variables panel the Stress Filtering Smoothing panel optional the Save Panel optional and then to press the Process Analyze Data button The black arrows in Figure 1 show the progression across the main MITlaos window This User Manual will also follow this order Data Input Panel The Data Input panel lets the user select and preview the data file MITlaos will analyze To select the data file either click the Choose Data button or type the filename and its directory into the File Name and Path Name boxes see Figure 2 Data Input Choose Data File Name SlugSlime omega03p00 Run31 dat Preview Data Path Name C Documents and Settings 4ll Users Documernts MITlaos SampleDataFiles Figure 2 Data Input Panel Choose Data button Press the Choose Data
14. button will immediately display how much data will be included for analysis 8 Windowing the data is required if the time series data contain transients or if several strain amplitudes or frequencies are contained within the same data In these cases only part of the data should be used for each analysis Press the Select Part of Data button and a new window will open called processPartDataGUI which allows the user to select which portion of the time series to include for analysis ProcessPartDataGUI Stress and strain are plotted against time or arbitrary time in the ProcessPartDataGUI Figure 7 Since MITlaos is designed to analyze a viscoelastic system response to a sinusoidal strain input the strain signal should appear as a sine wave and the stress response should oscillate with the same period note that stress should simply be a shifted sine wave in the linear viscoelastic regime By looking at this stress and strain signals the user should be able to determine which portion of the data should be analyzed ProcessPartDataGUI_MITlaos Instructions Select Choose Range and then click twice on the figure to determine the range of data to be analyzed The points you have selected will be displayed in the edit boxes Within the Stress Strain arb selected range the data will be cut further in order to contain an integer number of cycles First Point 58 redo first point Choose Range Second Po
15. e windowed to analyze one strain amplitude at a time This data set could then be used to separately analyze four different strain amplitudes Note however that for best results it is recommended that the analysis can be carried out on a system that has reached steady state Stress Strain arb 25 Time 5 Figure 9 Data Set with a Stepwise Increase in Amplitude Example data files are included with the distribution of MITlaos in the subfolder MITlaos subfunctions_MITlaos A document in the same subfolder describes these example data files 11 NOTE The following 2 sections Stress Filtering Smoothing panel and Save panel are OPTIONAL steps Default values for these settings are provided when MITIaos is initialized However these settings are not optimal for all data Stress Filtering Smoothing Panel Stress signals are smoothed with the help of a Fourier Transform FT The raw stress signal is first decomposed into Fourier components A linear viscoelastic response should have only one frequency component in its Fourier spectrum whereas a nonlinear viscoelastic response will also contain higher harmonics The smoothed stress signal is then reconstructed using only the odd integer harmonics of the Fourier spectrum since all other harmonics are the consequence of noise unsteady oscillations or systematic bias This FT filtering technique eliminates noise and also aids in calculating nonlinear viscoelastic parameters
16. e beginning of each save file name will be identical and can be changed in the Main Window under the Save Panel In Figure 13 File 1 will be saved under a name ending with lcyclevStrain txt Files 1 3 have selectable round circles labeled Include a header with calculated variables located under the save file name edit boxes When this option is selected a 23 line header will be printed in the file which specifies all the calculated viscoelastic parameters of the processed data The Column drop down menus to the right allow the choice of time series data to be saved in each column The drop down menu underneath the words Column 1 and to the right of File 2 will change the first column saved in the second file Up to eight different columns can be specified for each save file File 4 is permanently set to create a save file containing all the calculated viscoelastic parameters and contains two rows of text The first row includes a text description for each parameter and the second row contains the numerical values for each parameter This layout was chosen so that other programs could be written to easily access these viscoelastic parameters 15 NOTE If the Save Data Files checkbox in the main window is not checked none of these files will be saved regardless of what options are chosen Customize Figure Saving Options button The Customize Figure Saving Options button opens the figuresav
17. e peak at n 1 is required for a linear viscoelastic response Any data signal will have such a noise threshold For Figure 11 the signal to noise ratio for the first harmonic is of the order S N 107 An appropriate value for n the highest harmonic to use in reconstruction is typically a value which is above the noise threshold yet high enough to capture the viscoelastic nonlinearities To select the desired n value click the Choose Highest Harmonic button The pointer will turn into a set of crosshairs Next click on the graph at the desired 7 value typically near the last big peak that stands out above the noise threshold note that the vertical location of the crosshairs is irrelevant When the graph is clicked once the value of n will automatically be rounded to the nearest odd integer and displayed in the box below the graph The user may also manually type the desired value of n into this box 13 Save Panel The Save Panel allows the user to select all the options for saving the analyzed data as figures and or data files No files will be saved until the Process Analyze Data button is clicked which is located at the bottom of the main window The data will be saved at the completion of the analysis Save Panel Beginning of save file name suffixes willbe added for each saved file Slugslime amegalspO00 Runst Save Data Files Customize Data File Saving Options Save Figures Customize Figure Saving Options
18. eGUI window Figure 14 The check boxes on the left allow the choice of which figures to save The dropdown menus underneath the header Image Format allow the choice of saving each figure as JPEG or TIFF format The edit boxes underneath the header Suffix to Append to File Name will determine the last part of the name for each file Note that the beginning of each save file name will be identical and can be changed in the Main Window under the Save panel As prescribed in Figure 14 the overview plot will be saved under a name ending with Fig Overview JPEG figuresaveGUI_MITlaos Figures to Save Image Format Suffix to Append to File Name Save Overview Plot JPEG v Fig_Overview Save Elastic Lissajous Stress vs Strain TIFF Fig_LissElastic Save Viscous Lissajous Stress vs Strain Rate TIFF Fig_Liss Viscous FiterPerfromance Figure 14 figuresaveGUI window NOTE If the Save Figures checkbox in the main window is not checked none of these figures will be saved regardless of the selected options 16 Main Buttons Once all of the details are specified the analysis is initialized by clicking the Process Analyze Data button at the lower right corner of the MITlaos main window Figure 15 Figure 15 Main Program Buttons Exit Quits MITlaos and closes main window Process Analyzes Data This analyzes the selected data using the chosen analys
19. es for loading the data It asks three separate questions e At what oscillatory frequency was the sample tested e Which columns in the data file contain which variables e What portion of the time series data should be analyzed Input Variables Frequency rads Column Units O TE airain F Convert Stress O Yes No Time Mote Include time vector if data are not already evenly spaced Which part of your data would you like to process Ending Point 4 Number of Cycles selected le Figure 5 Input Variables panel Frequency edit box In the Frequency box enter the oscillatory strain frequency used to test the sample in units of rad s This input is necessary to run the analysis It is suggested that the user include the frequency in the input filename as a convenient reference Column Specification Since different kinds of rheometers have different formats for saving data MITlaos is flexible in how it can read raw data To change which column in the data file is read as strain click on the dropdown menu to the right of the word Strain and underneath the heading Column If 2 is chosen from the dropdown menu the second column in the input data file will be read as strain Similarly one can select which column is read as Stress and which column is read as Time To make the Time column options visible the user must first select the Yes box to the left of the word Time If t
20. he input datafile has headers labeling the columns it is possible to see them with the Preview Data button in the Data Input panel to see which column contains which variable NOTE Different columns must be selected for each variable Strain and Stress are the two variables required by MITlaos Time is an additional variable that can be incorporated into the analysis if necessary If the data was NOT collected at equally spaced time intervals then it is important to include time as an input If time is not included MITlaos will assume the data points are equally spaced in time It is recommended to NOT include time if data are evenly spaced In order to input displacement instead of strain click on the Convert Displacement checkbox to the left of the word Strain A box allowing the input of a conversion factor will appear to the right of Units and the word Strain will be changed to Displacement Figure 6 Use the appropriate conversion factor such that strain is wnitless i e not in terms of percent according to the equation y F O Input Variables Frequency radisy Conversion Colurairy Factor Displacement P ke Yl 7 1 Conwert ae q 3 PaF T F 1 Oves Ono Time Mote Include time vector if data are not alreadty evenly spaced Figure 6 Input Variables panel with Convert Displacement and Convert Torque options selected and the Time column input turned on
21. int 297 redo second point Starting Point After Data Trimming 7 Ending Point After Data Trimming of Cycles Figure 7 ProcessPartDataGUI window Click the Choose Range button on the bottom left of the window to select the desired portion of data to analyze The cursor will immediately change to a cross hair which will be used for selecting the limiting points of the desired range Move the cross hair over the graph and click once at the beginning and once at the end of the desired data range note that the vertical position of the crosshairs is irrelevant The two chosen points will be displayed in the First Point and Second Point edit boxes If desired the user may choose to manually type the location of the chosen points into the edit boxes The chosen data range will be further trimmed to be an integer number of cycles The new limits of the data to be processed will be displayed in the Starting Point After Data Trimming and Ending Point After Data Trimming boxes The bottom box shows the total number of complete cycles that will be used in data analysis An integer number of cycles is required for proper processing It is possible to redo either of the endpoints of the initially selected data range To redo one point but leave the other point as is click Redo First Point or Redo Second Point and then click on the graph When satisfied with the selected data range click
22. is options and saves the specified figures and data files Figures chosen for saving will also be displayed on screen for viewing Note that inputs in the MITlaos main window are only reset if MITlaos is closed and re opened This allows the user to 1 Tweak processing parameters and quickly reprocess the data with the Process Analyze Data button 2 Select a different input data file while keeping the same processing parameters This allows for quick subsequent processing of multiple data files 17 Appendix A Definitions of Nonlinear Viscoelastic Parameters Alternative Viscoelastic Moduli Since G G are arbitrary and insufficient with nonlinear viscoelasticity MITlaos uses two alternative ways to quantify elastic and viscous moduli of a complex material All measures reduce to the linear moduli in the limit of small strain amplitude but represent different approximations of the first order viscoelastic response Different alternative moduli can be compared to quantify the type of nonlinearity see below Mathematical and graphical definitions of the elastic and viscous alternative moduli are given in Figure 16a and Figure 16b respectively 800 800 600 600 T 7 amp 400 400 B 200 H 200 d 200 8 200 u a 400 400 600 600 800 L 800 L 3 2 4 0 141 2 3 10 5 0 5 10 Shear Strain Strain Rate s Figure 16 Definitions of alternative viscoelastic moduli a minimum strain modulus G a
23. nd large strain modulus G b minimum rate dynamic viscosity 7 and large rate dynamic viscosity 7 Figure reproduced from Ewoldt et al 2007b The alternative viscoelastic moduli determined for a given equilibrium oscillatory response can be compared to indicate the nature of the viscoelastic nonlinearity as summarized below gt l strain stiffening gt l shear thickening 1 Ny G Gy lt l strain softening linear elastic linear viscous lt 1 shear thinning 18 Viscoelastic Chebyshev Coefficients For a strain controlled oscillatory shear test the nonlinear stress response is commonly decomposed as a Fourier series shown below in two possible forms n odd t 0 7 gt G 0 7 sinnat G a 7 cosnat n odd t 0 7 Dd m 0 7 sinnat 7 7 cosnat arguments Cho et al 2005 The total stress can be decomposed into elastic and viscous stresses by using symmetry o x o y 7 o 7 7 5 elastic y m O VV _ O Pay x fs Oo jee viscous y 7 7 Building upon the work of Cho et al 2005 we suggest an additional orthogonal decomposition of the elastic and viscous stresses using Chebyshev polynomials of the first kind see also Figure 17 J gt e o 0 7 T x n odd gt v OY T 7 n odd Figure 17 The first few odd Chebyshev polynomials of the first kind 19 The elastic and viscous Cheb
24. scoelastic behavior Brief definitions and interpretation of these nonlinear viscoelastic parameters are given in Appendix A For detailed information regarding definitions and interpretation please refer to Cho et al 2005 Ewoldt et al 2006 and Ewoldt et al 2007a Installation of MITlaos MITlaos is currently distributed as a ZIP folder which contains multiple subfolders and multiple MATLAB subfunctions Installation is done by unzipping and saving the MITlaos folder to any location on the local hard drive Although any location is acceptable a convenient location for the MITlaos folder is MATLAB work MITlaos WARNING Do not modify the contents of the MITlaos folder Please contact MITlaos mit edu regarding installation problems Running MITlaos with MATLAB Structure of Input Data File MITIlaos requires a text based ASCII data file which contains columns of data Header information is typically tolerated by the program At a minimum time series data for strain or displacement and stress or torque are required Additionally a data column of time may be included if data are sampled at uneven intervals NOTE MITIaos is flexible regarding the arrangement of columns in the data input file The user will specify which column contains strain stress and time optional Running the Program Once MITIlaos is installed and the data input file is of the proper form MITlaos can be initialized with the following
25. sequence 1 Open MATLAB 2 Change the current working directory to the MITIlaos folder e g MATLAB work MITlaos This folder should contain MITlaos m 3 Type MITlaos at the command prompt to start the program Main Window Overview The MITlaos program consists of one main window Figure 1 and several side windows The main window shows all the necessary steps for analyzing sets of data Several buttons in the main window open side windows that provides the user with more information and with more options to customize the data analysis MITlaos MITlaos Using Fourier Transform Rheology Chebyshev Decomposition and Alternative Moduli to gain physical insight with Large Amplitude Oscillatory Shear L403 Data Input Choose Data File Name CPyCL omega00p30 gam03p1 600 dat Fath Name C Documents and SettingsiAll Users Documents MiTlaosiSampleDataFilesi Input Variables 4 Save Panel Frequency rad s 3 Beginning of save file name ree Units suffixes will be added for each saved file o nee Strain v Unities CPyCL omega00p30 gam03p1 600 o Convert Stress Torque Save Data Files Customize Data File Saving Options O Yes No Time Note Include time vector if data are not already evenly spaced Which part of your data would you like to process Save Figures Customize Figure Saving Options Select Part of Data Starting Point Ending Point Uen Ful Data Sat Num
26. yshev coefficients are related to the oft calculated Fourier Transform coefficients as n 1 e G 1 2 G Va 11 60 n odd A positive third order contribution results in higher stress at maximum strain or strain rate than represented by the first order contribution alone Thus the sign of the third order coefficients suggest a physical interpretation of stiffening softening and thickening thinning and are directly related to the Fourier coefficients The interpretation of these parameters is summarized below gt 0 strain stiffening 0 lt 0 strain softening 20 G linear elastic v gt 0 shear thickening 0 lt 0 linear viscous O ase shear thinning Acknowledgements Special thanks to Dr Trevor Shen Kuan Ne for helpful discussions and feedback regarding MITIlaos development The development of MITlaos was supported in part by a gift from Procter amp Gamble Cincinnati OH R H Ewoldt gratefully acknowledges the National Science Foundation Graduate Research Fellowship Program for funding References Cho K S K H Ahn and S J Lee A geometrical interpretation of large amplitude oscillatory shear response J Rheol 49 3 747 758 2005 Ewoldt R H A E Hosoi and G H McKinley Rheological fingerprinting of pedal mucus from terrestrial gastropods snails and slugs using large amplitude oscillatory shear LAOS experiments 78th Annual Meeting of The Society of Rheology
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