Polymer Viscoplasticity
Use the Polymer Viscoplasticity subnode to define the viscoplastic properties of rubber, elastomer, and thermoplastic materials. This material model is available in the Solid Mechanics interface and can be used together with Hyperelastic Material.
See also Polymer Viscoplasticity in the Structural Mechanics Theory chapter.
Viscoplasticity Model
Use this section to define the viscoplastic properties of the material.
Select a Material model — Bergstrom–Boyce, Bergstrom–Bischoff, Parallel network, or User defined. Then follow the instructions below.
Bergstrom–Boyce
The rheology of the Bergstrom–Boyce model adds a spring-dashpot network in parallel to the Hyperelastic Material.
Enter the Energy factor βv to describe the stiffness of the spring element in the network. The default value is 1.2, which means that at infinitesimal deformations the shear modulus of the network is 1.2 times the equivalent shear modulus of the Hyperelastic Material.
Enter the settings for the nonlinear dashpot:
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Viscoplastic rate coefficient A.
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Flow resistance σres.
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Stress exponent n.
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Cutoff stress σco.
Select the hardening model from the Isotropic hardening model list.
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Select None if the material undergoes viscoplastic deformation without hardening.
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For Strain hardening enter a value or expression for the strain exponent c.
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For User defined enter a value or expression for the hardening function. Write any expression in terms of the viscoplastic strain in the h(λvpe) field.
Select the Stiffness used in stationary studies — Long-term or Instantaneous. With Long-term the damper is assumed to be fully relaxed, whereas with Instantaneous the damper is assumed to be rigid.
Bergstrom–Bischoff
The rheology of the Bergstrom–Bischoff model consists of two spring-dashpot networks added in parallel to a Hyperelastic Material.
Enter the Viscoplastic rate coefficient A.
Enter the settings for the nonlinear dashpot in the first network:
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Energy factor βv1.
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Flow resistance σ1,res.
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Stress exponent n1.
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Pressure hardening coefficient a1.
Enter the settings for the nonlinear dashpot in the second network:
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Initial energy factor βv,i.
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Final energy factor βv,f.
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Energy factor evolution coefficient α.
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Flow resistance σ2,res.
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Stress exponent n2.
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Pressure hardening coefficient a2.
Select the Stiffness used in stationary studies — Long-term or Instantaneous. With Long-term all dampers are assumed to be fully relaxed, whereas with Instantaneous all dampers are assumed to be rigid.
Parallel Network
The rheology of the Parallel Network model consists of one or more spring-dashpot networks added in parallel to a Hyperelastic Material.
Select a Material model for the spring — From parent, Neo-Hookean, Mooney–Rivlin, Yeoh, Ogden, Arruda–Boyce, or Gent.
For From parent, enter the Energy factor βv to describe the stiffness of the spring element in the network. The default value is 1.2, which means that at infinitesimal deformations the shear modulus of the network is 1.2 times the equivalent shear modulus of the parent Hyperelastic Material.
For the other options, enter the settings as described in Neo-Hookean, Mooney–Rivlin, Two Parameters, Yeoh, Ogden, Arruda–Boyce, or Gent.
Enter the settings for the nonlinear dashpot:
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Viscoplastic rate coefficient A.
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Flow resistance σres.
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Stress exponent n.
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Cutoff stress σco.
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Pressure hardening coefficient a.
Select the hardening model from the Isotropic hardening model list.
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Select None if the material undergoes viscoplastic deformation without hardening.
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For Strain hardening (default) enter a value or expression for the strain exponent c.
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For User defined enter a value or expression for the hardening function. Write any expression in terms of the viscoplastic strain in the h(λvpe) field.
Select the Stiffness used in stationary studies — Long-term or Instantaneous. With Long-term all dampers are assumed to be fully relaxed, whereas with Instantaneous all dampers are assumed to be rigid.
Additional Network
When the Parallel Network model is selected, it is possible to add Additional Network subnodes to the Polymer Viscoplasticity node.
Enter the Energy factor βv to describe the stiffness of the spring element in the additional network. The default value is 1.2, which means that at infinitesimal deformations the shear modulus of the network is 1.2 times the equivalent shear modulus of the parent Parallel Network.
The settings for the additional nonlinear dashpot are the same as described for the Parallel Network model.
User Defined
The rheology of the User defined model consists of one spring-dashpot network added in parallel to a Hyperelastic Material.
Enter the Energy factor βv to describe the stiffness of the spring element in the network. The default value is 1.2, which means that at infinitesimal deformations the shear modulus of the network is 1.2 times the equivalent shear modulus of the parent Hyperelastic Material.
For User defined enter a value or expression for the Equivalent viscoplastic rate. Write any expression in terms of stress tensor components or its invariants in the λvp field.
Select the Stiffness used in stationary studies — Long-term or Instantaneous. With Long-term the damper is assumed to be fully relaxed, whereas with Instantaneous the damper is assumed to be rigid.
Thermal Effects
Select a thermal function g(T) — None, Arrhenius, Power law, or User defined, which acts as a multiplier for the viscoplastic rate.
Arrhenius
For Arrhenius, enter the following setting:
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Reference temperature Tref. The default value is 293.15 K.
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Activation energy Q. The default is 0 J/mol.
Power law
For Power law, enter the following setting:
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Reference temperature Tref. The default value is 293.15 K.
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Temperature exponent m. The default is 0.
User defined
For User defined, enter an expression for g(T) as a function of temperature T or other variables in the model.
Time Stepping
Select a Method — Automatic, Backward Euler, or Domain ODEs.
Automatic
The Automatic method corresponds to the backward Euler method with predefined settings for the Newton loop used to solve the local equations.
Backward Euler
For the Backward Euler method, enter the following settings:
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Maximum number of local iterations. To determine the maximum number of iteration in the Newton loop when solving the local viscoplasticity equations.
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Absolute tolerance. To check the convergence of the local viscoplasticity equations based on the step size in the Newton loop.
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Relative tolerance. To check the convergence of the local viscoplasticity equations based on the step size in the Newton loop. The final tolerance is computed based on the current solution of the local variable and the entered value.
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Residual tolerance. To check the convergence of the local viscoplasticity equations based on the residual of each equation.
If both a step size and residual convergence check is requested, it is sufficient that either of the conditions are fulfilled. Setting either the Absolute tolerance and Relative tolerance or the Residual tolerance to zero ignores the corresponding convergence check. An error is returned if all are set to zero.
Domain ODEs
No settings are needed for the Domain ODEs method. However, this method adds degrees-of-freedom that are solved as part of the general solver sequence. The scaling of these fields can affect the convergence of the overall solution.
Advanced
For a 2D geometry, enable Include out-of-plane strains to solve for all components of the viscoplastic strain tensor. By default, COMSOL assumes that the out-of-plane components are zero.
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
To compute the energy dissipation caused by viscoplasticity, enable the Calculate dissipated energy check box in the Energy Dissipation section of the parent Hyperelastic Material node.
Location in User Interface
Context Menus
Solid Mechanics>Hyperelastic Material>Polymer Viscoplasticity
Ribbon
Physics tab with Hyperelastic Material node selected in the model tree:
Attributes>Polymer Viscoplasticity