Nonlinear Analysis Viscoelastic Material Analysis 2011 Autodesk Freely

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Nonlinear Analysis: Viscoelastic Material Analysis © 2011 Autodesk Freely licensed for use by educational

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 § Page 2 The objective of this module

Section 3 – Nonlinear Analysis Objectives § Page 2 The objective of this module is to provide an introduction to theory and methods used in the analysis of components containing materials described by viscoelastic material models. § § § © 2011 Autodesk Module 4 – Viscoelastic Materials 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 § Viscoelasticity is concerned with describing elastic materials

Section 3 – Nonlinear Analysis Viscoelasticity § 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 Module 4 – Viscoelastic Materials Page 3 § 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

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 § § When subjected to a constant

Section 3 – Nonlinear Analysis Relaxation Modulus § § When subjected to a constant strain, the stress in polymers will relax (i. e. stress will decrease to a steady state value). In a linear viscoelastic material the relaxation is proportional to the applied strain. Module 4 – Viscoelastic Materials Page 5 Relaxation Curves for a Linear Viscoelastic Material 2 times § 2 times The relaxation modulus is defined as: Tension Shear © 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 Creep Compliance § § § When subjected to constant

Section 3 – Nonlinear Analysis Creep Compliance § § § When subjected to constant stress, polymers will creep (i. e. strain will continue to increase to a steady state value). If the creep response is proportional to the applied stress, the material is “linear”. The creep compliance is defined by: © 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. Module 4 – Viscoelastic Materials Page 6 Creep Curves for a Linear Viscoelastic Material 2 times www. autodesk. com/edcommunity 2 times Education Community

Section 3 – Nonlinear Analysis Sinusoidal Response § When subjected to a sinusoidally varying

Section 3 – Nonlinear Analysis Sinusoidal Response § 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. Module 4 – Viscoelastic Materials Page 7 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. www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Mechanical Element Analogs Module 4 – Viscoelastic Materials Page

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. 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. www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Maxwell Model § The Maxwell model uses a spring

Section 3 – Nonlinear Analysis Maxwell Model § The Maxwell model uses a spring and dashpot in series. Module 4 – Viscoelastic Materials Page 9 Derivation of Governing Equation § The Maxwell model doesn’t match creep response well. § It predicts a linear change in stress versus time for the creep response. © 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. Combining yields Units are seconds www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Kelvin Model § The Kelvin model uses a spring

Section 3 – Nonlinear Analysis Kelvin Model § The Kelvin model uses a spring Module 4 – Viscoelastic Materials Page 10 Derivation of Governing Equation and dashpot in parallel. § The Kelvin model doesn’t match relaxation data. § It doesn’t exhibit time dependent 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. www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Standard Linear Solid – Governing Equations § The Standard

Section 3 – Nonlinear Analysis Standard Linear Solid – Governing Equations § 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 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. Module 4 – Viscoelastic Materials Page 11 Derivation of Governing Equation Elastic Arm Maxwell Arm Characteristic Time www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Standard Linear Solid – Laplace Domain Module 4 –

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. Time Domain Laplace Domain The overscore indicates the Laplace transform of the variable. Elastic Arm Maxwell Arm Governing Equation in Laplace Domain © 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 Standard Linear Solid – Relaxation Equations § § §

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 At infinite time the stress relaxes to a steady state value of © 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. Unit Step Function Substitution into the governing equation yields Taking the inverse Laplace transform yields www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Standard Linear Solid – Relaxation Plot § The relaxation

Section 3 – Nonlinear Analysis Standard Linear Solid – Relaxation Plot § The relaxation modulus, E(t), is shown in the figure. § The values chosen for the parameters Er, Em, and t are for demonstration purposes only. § The stress relaxes to a steady state value controlled by the parameter Er. © 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. Module 4 – Viscoelastic Materials Page 14 www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Standard Linear Solid – Creep Equations § § The

Section 3 – Nonlinear Analysis Standard Linear Solid – Creep Equations § § The creep behavior is obtained by finding the response to a step change in stress. At time t=0, there is an instantaneous stress response equal to Module 4 – Viscoelastic Materials Page 15 Substitution into the governing equation yields Taking the inverse Laplace transform yields § At infinite time the strain grows to a steady state value of © 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 Standard Linear Solid – Creep Plot § The creep

Section 3 – Nonlinear Analysis Standard Linear Solid – Creep Plot § The creep compliance modulus, J(t), is shown in the figure. § The values chosen for the parameters Er, Em, and t are for demonstration purposes only. § The strain creeps to a steady state value controlled by the parameter Cr. § 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. Module 4 – Viscoelastic Materials Page 16 www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Standard Linear Solid - Summary Module 4 – Viscoelastic

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. ü Instantaneous elastic strain when stress applied; ü Under constant stress, strain creeps towards a limit; ü Under constant strain, stress relaxes towards a limit; ü When stress is removed, instantaneous elastic recovery, followed by gradual recovery to zero strain; ü 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

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. § It consists of a linear spring in parallel with a series of springs and dashpots (Maxwell elements). Relaxation Modulus Relaxation Time © 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. 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 Page 19 § is

Section 3 – Nonlinear Analysis Module 4 – Viscoelastic Materials Page 19 § is the value of G(t) at time equal to zero. § It is the instantaneous shear modulus. § is the value of G(t) at time equal to infinity. § It is the final or fully relaxed shear modulus. © 2011 Autodesk Relaxation function versus 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. www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Weichert Model – Multiple Relaxation Times § The Wiechert

Section 3 – Nonlinear Analysis Weichert Model – Multiple Relaxation Times § 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. Module 4 – Viscoelastic Materials Page 20 Example Relaxation Data for a Real Material t 1 t 2 t 3 t 4 tn www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Prony Series § § The challenge in describing a

Section 3 – Nonlinear Analysis Prony Series § § The challenge in describing a material by the Weichert model is to find the coefficients, Gi and relaxation times, ti, of the Prony Series. Module 4 – Viscoelastic Materials Page 21 Prony Series Specialized optimization algorithms are used to determine the best set of moduli, Gi, and relaxation times, ti , 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

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, . This form of the equation is used when the relaxation properties are specified in terms of the instantaneous modulus, G 0. © 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

Autodesk Simulation Multiphysics Material Data Screen Section 3 – Nonlinear Analysis Module 4 –

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. Defines the instantaneous shear modulus First Constant © 2011 Autodesk (Mooney-Rivlin) 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 § Unless the “Independent Volumetric/Deviatoric Relaxation”

Section 3 – Nonlinear Analysis Volumetric Relaxation Data § 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. Module 4 – Viscoelastic Materials Page 24 www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Example - Sandwich Problem Elastomeric adhesives are commonly used

Section 3 – Nonlinear Analysis Example - Sandwich Problem 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. Module 4 – Viscoelastic Materials Page 25 § © 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 -T 6 Aluminum 1/16 in 1/32 in 1/16 in 6061 -T 6 Aluminum ISR 70 -03 Industrial Adhesive www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Example – 2 D Model § The beam is

Section 3 – Nonlinear Analysis Example – 2 D Model § The beam is modeled using a 2 D plane strain representation. § A 3 D 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. Module 4 – Viscoelastic Materials Page 26 Thickness Direction www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Example – Beam Geometry § The dynamic response of

Section 3 – Nonlinear Analysis Example – Beam Geometry § 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 6061 T 6 aluminum. § The adhesive layer (shown in blue) is 1/32 inch thick. © 2011 Autodesk Module 4 – Viscoelastic Materials Page 27 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

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 § § A nonlinear dynamic analysis will

Section 3 – Nonlinear Analysis FEA Model § § A nonlinear dynamic analysis will be performed using the MES with Nonlinear Material Models analysis type. The 2 D elements will allow the analysis to run much quicker than if 3 D elements were used. Module 4 – Viscoelastic Materials Page 29 Section of Sandwich Beam 6061 -T 6 Aluminum 1/16 in 1/32 in 1/16 in 6061 -T 6 Aluminum Simson 70 -03 Industrial Adhesive Mesh absolute element size is 1/64 th 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 –

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 Page 31 Tension relaxation properties

Section 3 – Nonlinear Analysis Example – Material Properties Page 31 Tension relaxation properties for ISR 70 -03 adhesive are given in the referenced document. Mpa Sec. Relaxation Modulus 20 Extension Relaxation Moduls [Mpa] § Module 4 – Viscoelastic Materials 1 E-05 18 16 14 12 10 8 6 4 2 1 E-04 1 E-03 1 E-02 1 E-01 0 1 E+01 1 E+02 1 E+03 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. © 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 - Shear Relaxation Properties The relaxation properties given

Section 3 – Nonlinear Analysis Example - Shear Relaxation Properties 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. Module 4 – Viscoelastic Materials Page 32 § § Shear Relaxation Data Mpa Sec. 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. www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Example - Instantaneous Form § The shear relaxation data

Section 3 – Nonlinear Analysis Example - Instantaneous Form § The shear relaxation data will be entered into the Simulation Prony series table using the instantaneous option. © 2011 Autodesk Module 4 – Viscoelastic Materials Page 33 Instantaneous Shear Modulus Relaxation Data 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. Sec. www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Example - Mooney-Rivlin Properties § The adhesive will be

Section 3 – Nonlinear Analysis Example - Mooney-Rivlin Properties § 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 C 10/C 01 will be set equal to 4. © 2011 Autodesk Module 4 – Viscoelastic Materials Page 34 These two equations lead to constants of C 10 = 396. 4 psi and C 01 = 99. 1 psi. 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

Section 3 – Nonlinear Analysis Example - Bulk Modulus Module 4 – Viscoelastic Materials Page 35 The bulk modulus will be approximated from the equation For an incompressible material n=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 § The alpha constants

Section 3 – Nonlinear Analysis Example - Prony Series Data § 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, G 0. § 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. Module 4 – Viscoelastic Materials Page 36 www. autodesk. com/edcommunity Education Community

Section 3 – Nonlinear Analysis Parameters § § § Module 4 – Viscoelastic Materials

Section 3 – Nonlinear 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 § The plot shows the computed

Section 3 – Nonlinear Analysis Example - Results § The plot shows the computed displacement history for the tip of the cantilever. Module 4 – Viscoelastic Materials Page 38 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

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