Plasticity

Use the subnode to define the properties for modeling elastoplastic materials. This material model is available in the Solid Mechanics, Shell, Layered Shell, Membrane and Truss interfaces, and can be used together with Linear Elastic Material, Nonlinear Elastic Material, and Hyperelastic Material.

The Nonlinear Structural Materials Module or the Geomechanics Module are required for this material model, and the available options depend on the used products. For details, see https://www.comsol.com/products/specifications/.


	See also Elastoplastic Materials 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 Plasticity node in the Layered Shell chapter.

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

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

Plasticity Model

Use this section to define the plastic properties of the material.

Formulation

Select or to apply either an additive or multiplicative decomposition between elastic and plastic strains.

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When using plasticity together with a hyperelastic material, only the option is available.

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When using plasticity in the Shell, Membrane and Truss interfaces, only the option is available.

Equivalent Stress

The defines the limit of the elastic regime, F(σe, σys) ≤ 0, and sets the onset for plastic deformation. Changing the equivalent stress measure allows to specify different yield criteria. See Defining the Yield Criterion for details.

Select the — , , , or to define the yield criterion.

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The default is criterion with associate plastic potential.

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

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Select to use Hill’s criterion. 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 node. See Expressions for the Coefficients F, G, H, L, M, N for details.

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For enter a value or expression for the equivalent stress. Write any expression in terms of the stress tensor components or its invariants in the φ(σ) field.

Initial Yield Stress

For all yield criteria, the default σys0 uses values andrepresents the stress level where plastic deformation starts.

Plastic Potential

Select the Qp related to the flow rule — , , or (non associated). Enter a value in the Qp field as needed.

Isotropic Hardening Model

For all yield criteria, select the type of linear or nonlinear isotropic hardening model from the list. See Isotropic Hardening for details.

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Select (ideal plasticity) if the material can undergo plastic 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 plastic strain εpe as

with

For the linear isotropic hardening model, the yield stress increases proportionally to the equivalent plastic strain εpe. 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 have the properties f(0) = 0 and f(1) = 1. The variable is named using the scheme <physics>.<elasticTag>.<plasticTag>.Th, for example, solid.lemm1.plsty1.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

Typically, the reference strain equals the onset of plasticity, ε0 = σys0/E.

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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(εpe) uses values or . The yield level σys is modified as

This definition implies that the hardening function σh(εpe) in the Material node must be zero at zero plastic strain. In other words, σys = σys0 when εpe = 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 plastic strain, for example the temperature. Select to enter any function of the equivalent plastic strain εpe. The variable is named using the scheme <physics>.epe, for example, solid.epe.

Kinematic Hardening Model

For all yield criteria, select the type of kinematic hardening model (not available for hyperelastic materials) from the list. See Kinematic Hardening for details.

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Select (when either ideal plasticity or an isotropic hardening model is selected as isotropic hardening model) if it is a material that can undergo plastic 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 plasticity occurs:

with

This is Prager’s linear kinematic hardening model, so the back stress σb is collinear to the plastic strain tensor εp.

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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–Frederick nonlinear kinematic hardening model. Replacing the variable for the back strain instead of the back stress

gives the rate for the back strain

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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:

or equivalently, solve N rate equations for the back strain such as

The total back stress σb is then computed from the sum of the branches

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.


	To compute the energy dissipation caused by plasticity, enable the Calculate dissipated energy check box in the Energy Dissipation section of the parent material node.

Nonlocal Plasticity Model

The default is . Select to add nonlocal regularization to the equivalent plastic strain. Enter a value for the:

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, lint. The length scale should not exceed the maximum element size of the mesh.

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, Hnl. This stiffness is the penalization of the difference between the local and nonlocal variables. A larger value enforces the equivalent plastic strain εpe to be closer to the nonlocal equivalent plastic strain εpe,nl.


	See also Nonlocal Plasticity in the Structural Mechanics Theory chapter.

Discretization

This section is available with the nonlocal plasticity model. Select the shape function for the εpe,nl — , , , , , or . The available options depend on the order of the displacement field.

To display this section, click the button (

) and select in the dialog box.

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Sheet Metal Forming: Application Library path

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For an example of , see Necking of an Elastoplastic Metal Bar: Application Library path .

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For an example of strain rate dependent plasticity, see Tensile Test with Strain Rate Dependent Plasticity: Application Library path

Advanced

It is possible to specify the maximum number of iterations and the relative tolerance used to solve the plastic flow rule. Enter the following settings:

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. To determine the maximum number of iteration in the Newton loop when solving the local plasticity equations. The default value is 25 iterations.

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. To check the convergence of the local plasticity 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. The default value is 1e-6.

To display this section, click the button (

) and select in the dialog box.


	See also Numerical Solution of the Elastoplastic Conditions in the Structural Mechanics Theory chapter.

Location in User Interface

Context Menus

Ribbon

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