Viscoplasticity
Use the Viscoplasticity subnode to define the viscoplastic properties of the material model. This material model is available in the Solid Mechanics and Membrane interfaces, and can be used together with Linear Elastic Material and Nonlinear Elastic Material.
The Nonlinear Structural Material Module is required for this material model.
See also Creep and Viscoplasticity in the Structural Mechanics Theory chapter.
Layer Selection
This section is only present in the in the Layered Shell interface, where it is described in the documentation for the Viscoplasticity node.
Viscoplasticity Model
Select a Viscoplasticity model — Anand, Chaboche, or Perzyna. Then follow the instructions as below.
Anand
For Anand enter the following data:
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Creep rate coefficient A.
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Creep activation energy Q.
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Multiplier of stress ξ.
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Stress sensitivity m.
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Deformation resistance saturation coefficient s0.
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Deformation resistance initial value sinit.
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Hardening constant h0.
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Hardening sensitivity a.
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Deformation resistance sensitivity n.
Each of the material properties can either be defined obtained From material, or as User defined. In the latter case, enter a value or an expression.
Viscoplastic Creep in Solder Joints: Application Library path Nonlinear_Structural_Materials_Module/Viscoplasticity/viscoplastic_solder_joints
Chaboche
For Chaboche enter the following settings:
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Viscoplastic rate coefficient A.
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Reference creep stress σref. The default is 1 MPa.
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Stress exponent n.
Yield Function F
The Yield function F defines the limit of the elastic regime F(σ, σys) ≤ 0.
Select a Yield function F criterion — von Mises stress, Tresca stress, Hill orthotropic plasticity, or User defined.
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The default is von Mises stress with associate plastic potential.
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Select Tresca stress to use a Tresca yield criterion. The plastic potential can be an Associated or non associated flow rule with the von Mises stress as plastic potential.
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Select Hill orthotropic plasticity to use Hill’s criterion. For Hill orthotropic plasticity from the Specify list select either the Initial tensile and shear yield stresses σys0ij or Hill’s coefficients F, G, H, L, M, and N. The default for either selection uses values From material (if it exists) or User defined. The principal directions of orthotropy are inherited from the coordinate system selection in the parent feature.
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For User defined enter a different value or expression. In the φ(σ) field write any expression in terms of the stress tensor components or its invariants.
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For User defined also select the Plastic potential Q related to the flow rule — Associated (the default), von Mises, or User defined (non associated). Enter a User defined value in the Q field as needed.
Initial Yield Stress
The default Initial yield stress σys0 uses values From material and represents the stress level where viscoplastic deformation starts.
Isotropic Hardening Model
Select the type of linear or nonlinear isotropic hardening model from the Isotropic hardening model list.
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Select Perfectly plastic (ideal viscoplasticity) if the material can undergo viscoplastic deformation without any increase in yield stress.
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For Linear the default Isotropic tangent modulus ETiso uses values From material (if it exists) or User defined. The yield level σys is modified as hardening occurs, and it is related to the effective viscoplastic strain εvpe as
with
For the linear isotropic hardening model, the yield stress increases proportionally to the effective viscoplastic strain εvpe. The Young’s modulus E is taken from the elastic material properties.
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Select Ludwik from the list to model nonlinear isotropic hardening. The yield level σys is modified by the power-law
the Strength coefficient k and the Hardening exponent n use values From material (if it exists) or User defined.
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For Swift nonlinear isotropic hardening, the Reference strain ε0 and the Hardening exponent n use values From material (if it exists) or User defined. The yield level σys is modified by the power-law
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Select Voce from the list to model nonlinear isotropic hardening. The yield level σys is modified by the exponential law
the Saturation flow stress σsat and the Saturation exponent β use values From material (if it exists) or User defined.
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For Hockett-Sherby nonlinear isotropic hardening, the Steady-state flow stress σ∝, the Saturation coefficient m, and the Saturation exponent n use values From material (if it exists) or User defined. The yield level σys is increased by the exponential law
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For User defined isotropic hardening the Hardening function σh(εvpe) uses values From material. The yield level σys is modified as
This definition implies that the hardening function σh(εvpe) must be zero at zero viscoplastic strain. In other words, σys = σys0 when εvpe = 0. With this option it is possible to fit nonlinear hardening curves. The hardening function can depend on more variables than the effective viscoplastic strain, for example the temperature.
Kinematic Hardening Model
Select the type of kinematic hardening model from the Kinematic hardening model list.
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Select No kinematic hardening when the material can undergo viscoplastic deformation without a shift in the yield surface.
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If Linear is selected as the Kinematic hardening model, the default Kinematic tangent modulus Ek uses values From material. This parameter is used to calculate the back stress σb as:
with
This is Prager’s linear kinematic hardening model, so the back stress σb is collinear to the viscoplastic strain tensor εvp.
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If Armstrong-Frederick is selected from the list, the default Kinematic hardening modulus Ck and Kinematic hardening parameter γk use values From material. These parameters are used to calculate the back stress σb from the rate equation
This is Armstrong-Frederik nonlinear kinematic hardening model.
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When Chaboche is selected from the Kinematic hardening model list, the default Kinematic hardening modulus C0 uses values From material. Add branches as needed to solve N rate equations for the back stresses:
For each Branch row, enter Ci (the hardening modulus of the branch i) in the Hardening modulus (Pa) column and γi (the hardening parameter of the branch i) in the Hardening parameter (1) column.
Use the Add button () and the Delete button () to add or delete a row in the table. Use the Load from file button () and the Save to file button () to load and store data for the branches in a text file with three space-separated columns (from left to right): the branch number, the hardening modulus for that branch, and the hardening parameter for that branch.
The total back stress σb is then computed from the sum
Perzyna
For Perzyna enter the following settings:
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Viscoplastic rate coefficient A.
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Reference creep stress σref. The default is 1 MPa.
The other settings are the same as for Chaboche.
To compute the energy dissipation caused by viscoplasticity, enable the Calculate dissipated energy check box in the Energy Dissipation section of the parent material node (Linear Elastic Material or Nonlinear Elastic Material).
Location in User Interface
Context Menus
 Solid Mechanics>Linear Elastic Material>Viscoplasticity
 Solid Mechanics>Nonlinear Elastic Material>Viscoplasticity
 Layered Shell>Linear Elastic Material>Viscoplasticity
 Membrane>Linear Elastic Material>Viscoplasticity
 Membrane>Nonlinear Elastic Material>Viscoplasticity
Ribbon
Physics tab with Linear Elastic Material or Nonlinear Elastic Material node selected in the model tree:
Attributes>Viscoplasticity