Viscoplasticity

Use the subnode to define the viscoplastic properties of the material model. This material model is available in the Solid Mechanics, Layered Shell, Shell, and Membrane interfaces, and can be used together with , , and .

The Nonlinear Structural Material Module is required for this material model.


	See also Creep and Viscoplasticity in the Structural Mechanics Theory chapter.

Shell Properties

This section is only present when is used as a subnode to:

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in the Layered Shell interface. See the documentation for the Viscoplasticity node in the Layered Shell chapter.

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in the Shell interface. See the documentation for the Viscoplasticity node in the Shell and Plate chapter.

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in the Membrane interface. See the documentation for the Viscoplasticity node in the Membrane chapter.

Viscoplasticity Model

Select a — , , or . Then follow the instructions as below.

Anand

For enter the following data:

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ξ.

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s0.

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sinit.

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h0.

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Each of the material properties can either be defined obtained or as . 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 enter the following settings:

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σref. The default is 1 MPa.

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Yield Function F

The defines the limit of the elastic regime F(σ, σys) ≤ 0.

Select a criterion — , , , or .

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The default is with associate plastic potential.

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Select to use a Tresca yield criterion. The plastic potential can be an or nonassociated flow rule with the stress as plastic potential.

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Select to use Hill’s criterion. For from the list select either the σys0ij or F, G, H, L, M, and N. The default for either selection uses values (if it exists) or . The principal directions of orthotropy are inherited from the coordinate system selection in the parent feature.

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For enter a different value or expression. In the φ(σ) field write any expression in terms of the stress tensor components or its invariants.

For also select the Q related to the flow rule — , , or (nonassociated). Enter a value in the Q field as needed.

Initial Yield Stress

The default σys0 uses values andrepresents the stress level where viscoplastic deformation starts.

Isotropic Hardening Model

Select the type of linear or nonlinear isotropic hardening model from the list.

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Select (ideal viscoplasticity) if the material can undergo viscoplastic deformation without any increase in yield stress.

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For the default ETiso uses values (if it exists) or . The yield level σys is modified as hardening occurs, and it is related to the equivalent viscoplastic strain εvpe as

with

For the linear isotropic hardening model, the yield stress increases proportionally to the equivalent viscoplastic strain εvpe. The Young’s modulus E is taken from the elastic material properties.

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Select from the list to model nonlinear isotropic hardening. The yield level σys is modified by the power-law

the k and the n use values (if it exists) or .

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Select from the list to model strain rate dependent hardening. The k, n,

, and C use values (if it exists) or .

Select a — , , or .

For , enter the Tref, the Tm, and the , m.

For , enter the f(Th), the Tref, and the Tm. The softening function f(Th) typically depends on the built-in variable for the normalized homologous temperature Th, and has the properties f(0) = 0 and f(1) = 1. The variable is named using the scheme <physics>.<elasticTag>.<viscoplasticTag>.Th (for example solid.lemm1.vpl1.Th).

The yield stress and hardening function for the Johnson–Cook model is given by

In the case of power law softening,

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For nonlinear isotropic hardening, the ε0 and the n use values (if it exists) or . The yield level σys is modified by the power-law

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Select from the list to model nonlinear isotropic hardening. The yield level σys is modified by the exponential law

the σsat and the β use values (if it exists) or .

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For nonlinear isotropic hardening, the σ∝, the m, and the n use values (if it exists) or . The yield level σys is increased by the exponential law

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For , the isotropic σh(εvpe) uses values or . The yield level σys is modified as

This definition implies that the hardening function σh(εvpe) in the Material node must be zero at zero viscoplastic strain. In other words, σys = σys0 when εvpe = 0. With this option it is possible to enter any nonlinear isotropic hardening curve. The hardening function can depend on more variables than the equivalent viscoplastic strain, for example the temperature. Select to enter any function of the equivalent viscoplastic strain εvpe. The variable is named using the scheme <physics>.evpe, for example, solid.evpe.

Kinematic Hardening Model

Select the type of kinematic hardening model from the list.

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Select when the material can undergo viscoplastic deformation without a shift in the yield surface.

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If is selected as the , the default Ek uses values . 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 is selected from the list, the default Ck and γk use values . 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 is selected from the list, the default C0 uses values . Add branches as needed to solve N rate equations for the back stresses:

For each row, enter Ci (the hardening modulus of the branch i) in the column and γi (the hardening parameter of the branch i) in the column.

Use the button (

) and the button (

) to add or delete a row in the table. Use the button (

) and the 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 enter the following settings:

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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

Ribbon

Physics tab with , , or node selected in the model tree: