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Nonlinear Analysis: Viscoelastic Material Analysis © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Objectives Module 4 – Viscoelastic Materials Page 2 The objective of this module is to provide an introduction to the theory and methods used in the analysis of components containing materials described by viscoelastic material models. © 2011 Autodesk Topics covered include models based on elastic and viscous mechanical elements; Representation of relaxation data in the form of a Prony series; Instantaneous and long term relaxation moduli; Data required by Autodesk Simulation Multiphysics to perform a viscoelastic analysis; and Results from a Mechanical Event Simulation Analysis with Nonlinear Material Models. Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Viscoelasticity Module 4 – Viscoelastic Materials Page 3 Viscoelasticity is concerned with describing elastic materials that exhibit strain rate or time dependent response to applied stress. Viscoelastic materials exhibit hysteresis, creep, and relaxation. Polymers often exhibit viscoelastic properties. © 2011 Autodesk Linear Viscoelasticity The relaxation and creep functions are a function only of time. Nonlinear Viscoelasticity The relaxation and creep functions are a function of both time and stress or strain. Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Time Dependent Responses Module 4 – Viscoelastic Materials Page 4 Polymers respond differently to different types of time dependent loading. Instantaneous elasticity Creep under constant stress Relaxation under constant strain Instantaneous recovery followed by delayed recovery and permanent set W. N. Findley, Lai, J.S., Onaran, K., Creep and Relaxation of Nonlinear Viscoelastic Materials, Dover, 1989, pp.50. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Relaxation Modulus Module 4 – Viscoelastic Materials Page 5 When subjected to a constant strain, the stress in polymers will relax (i.e. stress will decrease to a steady state value). Relaxation Curves for a Linear Viscoelastic Material 0.009 0.008 In a linear viscoelastic material the relaxation is proportional to the applied strain. 0.007 0.006 Stress 0.005 0.004 2 times 2 times 0.003 0.002 2 times 2 times 0.001 The relaxation modulus is defined as: Tension Shear t o © 2011 Autodesk E t t o 0 0 1 2 3 4 5 6 Tim e, sec. G t Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Creep Compliance Module 4 – Viscoelastic Materials Page 6 When subjected to constant stress, polymers will creep (i.e. strain will continue to increase to a steady state value). Creep Curves for a Linear Viscoelastic Material Creep Curves If the creep response is proportional to the applied stress, the material is “linear”. The creep compliance is defined by: t o © 2011 Autodesk 0.4 0.35 2 times 0.3 Strain, in/in 0.45 J t Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. 2 times 0.25 0.2 0.15 2 times 2 times 0.1 0.05 0 0 1 2 3 4 5 6 Tim e, sec. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Sinusoidal Response Module 4 – Viscoelastic Materials Page 7 When subjected to a sinusoidally varying stress there will be a phase angle between the stress and strain. This phase angle creates the hysteresis seen in cyclic stressstrain curves. o cos t o cos t t The phase angle can be related to the damping of the material. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. T 2 www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Mechanical Element Analogs Module 4 – Viscoelastic Materials Page 8 Mechanical elements provide a means to construct potential viscoelastic material models. Elastic Element – Stress is proportional to strain. E E Viscous Element – Stress is proportional to strain rate. The proportionality constant is called viscosity due to its similarity to a Newtonian fluid. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. d dt www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Maxwell Model Module 4 – Viscoelastic Materials Page 9 The Maxwell model uses a spring and dashpot in series. Derivation of Governing Equation The Maxwell model doesn’t match creep response well. 1 E It predicts a linear change in stress versus time for the creep response. 2 E1 1 2 2 1 2 Combining yields Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. Units are seconds E © 2011 Autodesk 1 E E www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Kelvin Model Module 4 – Viscoelastic Materials Page 10 The Kelvin model uses a spring Derivation of Governing Equation and dashpot in parallel. 1 2 The Kelvin model doesn’t match relaxation data. E 1 E 2 1 2 It doesn’t exhibit time dependent relaxation. E © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. 1 www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Standard Linear Solid – Governing Equations Module 4 – Viscoelastic Materials Page 11 The Standard Linear Solid model is a threeparameter model that contains a Maxwell Arm in parallel with an elastic arm. Laplace transforms will be used to develop relaxation and creep constitutive equations. © 2011 Autodesk Derivation of Governing Equation 1 2 2 1 Elastic Arm 1 E r Em Er Maxwell Arm 2 Em 2 Characteristic Time Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. Em www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Standard Linear Solid – Laplace Domain Module 4 – Viscoelastic Materials Page 12 It is easier to determine the governing equation in the Laplace domain than in the time domain. Laplace Domain Time Domain 1 2 Elastic Arm Maxwell Arm 1 s E r s 1 E r 2 Em 2 s s E r E m s 1 © 2011 Autodesk s 1 s 2 s The overscore indicates the Laplace transform of the variable. s s 2 s E m s 1 Governing Equation in s Laplace Domain Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Standard Linear Solid – Relaxation Equations Module 4 – Viscoelastic Materials Page 13 The relaxation behavior is obtained by finding the response to a step change in strain. At time t=0, there is an instantaneous stress response equal to 0 E r E m 0 At infinite time the stress relaxes to a steady state value of E r © 2011 Autodesk 0 Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. t 0 u t s u t Unit Step 0 Function s Substitution into the governing equation yields s s E r E m s 1 0 s Taking the inverse Laplace transform yields t t E r E m e www.autodesk.com/edcommunity 0 Education Community Section 3 – Nonlinear Analysis Standard Linear Solid – Relaxation Plot Module 4 – Viscoelastic Materials Page 14 The relaxation modulus, E(t), is shown in the figure. The values chosen for the parameters Er, Em, and are for demonstration purposes only. The stress relaxes to a steady state value controlled by the parameter Er. © 2011 Autodesk t 0 E t E r E m e t 25 E r 10 20 Stress E m 10 15 1 10 5 0 0 Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. 1 2 3 4 5 6 Tim e, sec. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Standard Linear Solid – Creep Equations Module 4 – Viscoelastic Materials Page 15 t 0 u t The creep behavior is obtained by finding the response to a step change in stress. s At time t=0, there is an instantaneous stress response equal to At infinite time the strain grows to a steady state value of C r 0 © 2011 Autodesk s Substitution into the governing equation yields s Er Em s s s 1 0 0 C g 0 0 Taking the inverse Laplace transform yields t t C g C r C g 1 e c Cg Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. 1 Er Em Cr 1 Er www.autodesk.com/edcommunity c 0 Cr Cg Education Community Section 3 – Nonlinear Analysis Module 4 – Viscoelastic Materials Standard Linear Solid – Creep Plot Page 16 The creep compliance modulus, J(t), is shown in the figure. The values chosen for the parameters Er, Em, and are for demonstration purposes only. t t J t C g C r C g 1 e c 0 Cg 1 Er Em Cr 1 Er c Cr Cg 0.120000 0.100000 The strain creeps to a steady state value controlled by the parameter Cr. 0.080000 in/in 0.060000 0.040000 E r 10 0.020000 E m 10 1 0.000000 Since Cg is greater than Cr the characteristic creep time is slower than that for relaxation. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. 0 2 4 6 Tim e, sec. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Standard Linear Solid - Summary Module 4 – Viscoelastic Materials Page 17 The Standard Linear Solid more accurately represents the response of real materials than does the Maxwell or Kelvin models. Instantaneous elastic strain when stress applied; Under constant stress, strain creeps towards a limit; Under constant strain, stress relaxes towards a limit; When stress is removed, instantaneous elastic recovery, followed by gradual recovery to zero strain; Two time constants One for relaxation under constant strain One for creep/recovery under constant stress (Relaxation is quicker than creep) © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Wiechert Model Module 4 – Viscoelastic Materials Page 18 The Wiechert model is a generalization of the Standard Linear Solid model and can be used to model the viscoelastic response of many materials. G It consists of a linear spring in parallel with a series of springs and dashpots (Maxwell elements). t G t 0 G t G i © 2011 Autodesk i Ei n Gie t i Relaxation Modulus i 1 Relaxation Time Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. The shear relaxation modulus is used from this point forward since Simulation expects data for the shear relaxation modulus to be entered. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Module 4 – Viscoelastic Materials G 0 and G Page 19 is the value of G(t) at time equal to zero. G0 Relaxation function versus time 25 It is the instantaneous shear modulus. is the value of G(t) at time equal to infinity. G G0 20 Stress 15 G 10 5 0 0 It is the final or fully relaxed shear modulus. 1 2 3 4 5 6 Tim e, sec. n G0 G G i i 1 © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Weichert Model – Multiple Relaxation Times Module 4 – Viscoelastic Materials Page 20 The Wiechert model can accurately model the response characteristics of real materials because it can include as many relaxation times and corresponding moduli as needed. In the figure, five Maxwell elements are used to fit the experimental data. Each Maxwell element has a relaxation modulus and corresponding relaxation time constant. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. Example Relaxation Data for a Real Material 1 2 3 4 n www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Prony Series Module 4 – Viscoelastic Materials Page 21 The challenge in describing a material by the Weichert model is to find the coefficients, Gi and relaxation times, i, of the Prony Series. G t G n Ge t i i i 1 Prony Series Specialized optimization algorithms are used to determine the best set of moduli, Gi, and relaxation times, i , that match experimental data. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Alternate Forms Module 4 – Viscoelastic Materials Page 22 This form of the equation is used when the relaxation properties are specified in terms of the long term modulus, G . G t G n Gie n i 1 G t G n Ge G i i 1 t i i n G G0 Gi i 1 i 1 t i G t G 0 G t G 0 This form of the equation is used when the relaxation properties are specified in terms of the instantaneous modulus, G0. n i 1 n i 1 © 2011 Autodesk i e i G0 G t i 1 G t G 1 n Gie t i t i Gi 1 e Gie t i i 1 t n i G t G 0 1 i 1 e i 1 Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. n www.autodesk.com/edcommunity n i 1 i 1 Education Community Autodesk Simulation Multiphysics Material Data Screen Section 3 – Nonlinear Analysis Module 4 – Viscoelastic Materials Page 23 The instantaneous form of the relaxation modulus equation is used. t n G t G 0 1 i 1 e i i 1 (Mooney-Rivlin) Defines the instantaneous shear modulus G 0 2 C 10 C 01 First Constant © 2011 Autodesk Second Constant Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Volumetric Relaxation Data Module 4 – Viscoelastic Materials Page 24 Unless the “Independent Volumetric/Deviatoric Relaxation” box is checked, the relaxation data will be applied to both the deviatoric (shear) and volumetric material properties. Many polymers are nearly incompressible and remain so (i.e. no relaxation of the volumetric properties). Zeros have been added for the volumetric Prony series data. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Example - Sandwich Problem Module 4 – Viscoelastic Materials Page 25 Elastomeric adhesives are commonly used as vibration dampers. The hysteresis associated with elastomers provides natural damping. A sandwich type construction where the elastomer is placed between two stiff materials is shown in the figure. Locating the elastomer in the middle exposes it to the highest shear stresses. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. Section of Sandwich Beam 6061-T6 Aluminum 1/16 in 1/32 in 1/16 in 6061-T6 Aluminum ISR 70-03 Industrial Adhesive www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Example – 2D Model Module 4 – Viscoelastic Materials Page 26 The beam is modeled using a 2D plane strain representation. A 3D representation would require elements in the thickness direction. The plane strain representation is acceptable since there will be little stress variation through the thickness direction. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. Thickness Direction www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Example – Beam Geometry Module 4 – Viscoelastic Materials Page 27 The dynamic response of the cantilevered sandwich beam will be computed. The beam is ½ inch wide and 12 inches long. The top and bottom plates are made from 1/16 inch thick 6061T6 aluminum. The adhesive layer (shown in blue) is 1/32 inch thick. © 2011 Autodesk Portion of the Inventor model of the sandwich beam. Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Loads and Boundary Conditions Module 4 – Viscoelastic Materials Page 28 The displacements at one end of the beam are fixed to simulate a clamped condition. The other end is exposed to a step force of 1 lbs. Displacement Constraints © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. 1 lb divided among 21 nodes www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis FEA Model Module 4 – Viscoelastic Materials Page 29 A nonlinear dynamic analysis will be performed using the MES with Nonlinear Material Models analysis type. The 2D elements will allow the analysis to run much quicker than if 3D elements were used. Section of Sandwich Beam 6061-T6 Aluminum 1/16 in 1/32 in 1/16 in 6061-T6 Aluminum Simson 70-03 Industrial Adhesive Mesh absolute element size is 1/64th of an inch. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Element Definition: Adhesive Module 4 – Viscoelastic Materials Page 30 A viscoelastic Mooney-Rivlin Material is selected. This will give a nonlinear stressstrain relationship with a linear viscoelastic response. The plane strain option is selected. The mid-side nodes option is selected. By default, this is a large displacement analysis. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Example – Material Properties Module 4 – Viscoelastic Materials Page 31 Tension relaxation properties for ISR 70-03 adhesive are given in the referenced document. E 4 . 101 Mpa 1 Mpa Sec. 0 . 378 1 . 60 x10 2 0 . 427 2 . 91 x10 3 0 . 523 9 . 965 4 0 . 773 4 . 14 x10 5 1 . 014 2 . 01 x10 6 1 . 521 1 . 68 x10 7 2 . 501 2 . 44 x10 8 3 . 364 4 . 82 x10 9 5 . 904 9 . 83 x10 © 2011 Autodesk 3 2 1 2 3 4 5 6 E t E 9 Eie t i i 1 Relaxation Modulus 20 Extension Relaxation Moduls [Mpa] 1.E-06 18 16 14 12 10 8 6 4 2 1.E-04 1.E-02 0 1.E+00 1.E+02 Log(time) [sec] Reference Garcia-Barruetabena, J., et al, Experimental Characterization and Modelization of the Relaxation and Complex Moduli of a Flexible Adhesive, Materials and Design, 32 (2011) 2783-2796. Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Example - Shear Relaxation Properties Module 4 – Viscoelastic Materials Page 32 The relaxation properties given on the previous slide are for tension. Simulation expects shear relaxation properties. Poisson’s ratio for an incompressible material is 0.5. G E 2 1 E 3 The shear relaxation data is obtained by dividing the tension data by three. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. Shear Relaxation Data G 1 . 367 Mpa Mpa Sec. 1 0 . 126 1 . 60 x10 2 0 . 142 2 . 91 x10 3 0 . 174 9 . 965 4 0 . 258 4 . 14 x10 5 0 . 338 2 . 01 x10 6 0 . 507 1 . 68 x10 7 0 . 834 2 . 44 x10 8 1 . 121 4 . 82 x10 9 1 . 968 9 . 83 x10 3 2 1 2 3 4 5 6 www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Example - Instantaneous Form Module 4 – Viscoelastic Materials Page 33 The shear relaxation data will be entered into the Simulation Prony series table using the instantaneous option. Instantaneous Shear Modulus Relaxation Data G 0 6 . 835 Mpa 991 . psi n G0 G G i 6 . 835 MPa Sec. 1 0 . 01843 1 . 60 x10 2 0 . 02082 2 . 91 x10 3 0 . 02550 9 . 965 4 0 . 03770 4 . 14 x10 5 0 . 04945 2 . 01 x10 6 0 . 07417 1 . 68 x10 7 0 . 1220 2 . 44 x10 8 0 . 1640 4 . 82 x10 9 0 . 2879 9 . 83 x10 3 2 i 1 n G t G 0 1 i 1 e i i 1 t © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity 1 2 3 4 5 6 Education Community Section 3 – Nonlinear Analysis Example - Mooney-Rivlin Properties Module 4 – Viscoelastic Materials Page 34 The adhesive will be modeled using a hyperelastic material model in conjunction with linear viscoelasticity. The Mooney-Rivlin hyperelastic material model will be used. These constants are normally obtained from the slope and yintercept of a Mooney curve. As an approximation, the ratio of C10/C01 will be set equal to 4. G 0 2 C 10 C 01 941 ps i © 2011 Autodesk C 10 These two equations lead to constants of C10 = 396.4 psi and C01 = 99.1 psi. 4 C 01 Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Example - Bulk Modulus Module 4 – Viscoelastic Materials Page 35 The bulk modulus will be approximated from the equation 2 G 0 1 3 1 2 For an incompressible material =0.5, and the bulk modulus is infinite. A Poisson’s ratio of 0.499 will be assumed, which results in a bulk modulus of approximately 496,000 psi. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Example - Prony Series Data Module 4 – Viscoelastic Materials Page 36 The alpha constants and relaxation times are entered in the Prony series table for the Deviatoric Relaxation data. Note the alpha constants are nondimensional since they have been normalized by the instantaneous shear modulus, G0. Assuming that there is no relaxation of the bulk modulus, the volumetric relaxation data will be set to zeros. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Analysis Parameters Module 4 – Viscoelastic Materials Page 37 The response will be computed for 1 second (Event Duration). The response will be captured at 500 time points. This gives an initial time step of 0.002 seconds. Autodesk Simulation Multiphysics will automatically adjust the time step as needed. The multiplier in the Load Curve table is set to 1 at the beginning and end of the event. This will result in the loads being applied as a step input. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Example - Results Module 4 – Viscoelastic Materials Page 38 The plot shows the computed displacement history for the tip of the cantilever. Computed displacement history at the tip of the cantilever. The peak displacement is approximately twice the steady state response which is consistent with the step response of a linear system. The effect of the damping in the adhesive layer is very evident. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Section 3 – Nonlinear Analysis Module Summary Module 4 – Viscoelastic Materials Page 39 An introduction to viscoelastic materials has been provided to help explain the parameters and information required by Autodesk Simulation Multiphysics software. Shear relaxation data is needed to define the deviatoric material properties. Volumetric relaxation data can also be entered and used during the analysis. Autodesk Simulation Multiphysics software provides the ability to couple nonlinear hyperelastic material models with linear viscoelastic models. Although the material is defined in terms of relaxation data, the creep and dynamic response can also be computed. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community