Porous Plasticity

Use the subnode to define the properties of a plasticity model for a porous material.

The node is only available with some COMSOL products (see https://www.comsol.com/products/specifications/). The material model is available for 3D, 2D, and 2D axisymmetry.

Porous Plasticity Model

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

Formulation

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

Material Model

Select the for the porous plasticity criterion — , , , , , or .

Shima–Oyane

For enter the following data:

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σys0.

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α.

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γ.

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f0.

Gurson

For enter the following data:

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σys0.

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f0.

Gurson–Tvergaard–Needleman

For enter the following data:

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σys0.

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q1.

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q2.

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q3.

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f0.

•

Select an — , , or .

For and , enter the following data:

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fc.

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ff.

For , enter the effective void volume fraction as a function of for example the void volume fraction, variable <phys>.f.

Fleck–Kuhn–McMeeking

For enter the following data:

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σys0.

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f0.

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fmax.

FKM–GTN

For enter the following data:

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σys0.

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q1.

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q2.

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q3.

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f0.

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fmax.

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fGTN.

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fFKM.

Capped Drucker–Prager

For enter the following data:

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α.

•

f0.

The material properties use values (default) or .


	See also Porous Plasticity, Elliptic Cap, and Elliptic Cap With Hardening in the Structural Mechanics Theory chapter.

Void Growth

It is possible to or by selecting the corresponding check box. See the section Void Growth for details.

When is selected, enter the , the , and the . For each property use the value or enter a value or expression.

When is selected, enter the . Use the value or enter a value or expression.

Isotropic Hardening Model

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

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Select (ideal plasticity) if the material can undergo plastic deformation without any increase in yield stress. When is selected, enter values or expressions to define the semi-axes of the cap under pa and pb.

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For the default ETiso uses values (if it exists) or . The flow stress (yield level) σfm is modified as hardening occurs, and it is related to the equivalent plastic strain in the porous matrix εpm as

with

For the linear isotropic hardening model, the flow stress (yield stress) increases proportionally to the equivalent plastic strain in the porous matrix εpm. 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 flow stress (yield level) σfm is modified by the power-law

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

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For isotropic hardening, the n uses the value (if it exists) or . The flow stress (yield level) σfm is modified by the power-law

for

The Young’s modulus E is taken from the elastic material properties.

•

For , the isotropic σh(εpm) uses values or . The flow stress (yield level) σfm is modified as

This definition implies that the hardening function σh(εpm) in the Material node must be zero at zero plastic strain. In other words, σfm = σys0 when εpm = 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 in the porous matrix, for example the temperature. Select to enter any function of the equivalent plastic strain εpm. The variable is named using the scheme <physics>.<elasticTag>.<plasticTag>.epm, for example, solid.lemm1.popl1.epm.

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For hardening, the cap in the model evolves with the volumetric strain. Since the volumetric plastic strain εpvol is negative in compression, the limit pressure pb in the cap increases from pb0 as hardening evolves

The Kiso, the εpvol,max and the R use values (if it exists) or . Enter a value or expression to define the initial semi-axis of the ellipse under the pb0

Nonlocal Plasticity Model

In this section, nonlocal regularization can be added to the porous plasticity model. Select , or . By selecting , regularization can added the equivalent matrix plastic strain and the void volume fraction. These two hardening variables describe different mechanisms and therefore often require different model parameters.

If is selected, enter values for the:

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, lint,m.

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, Hnl, which can be seen as a penalization of the difference between the local and nonlocal equivalent matrix plastic strains. A larger value will force the local equivalent matrix plastic strain to be closer to the nonlocal variable.

If is selected, enter a value for the , lint,f.

The two length scales lint,m and lint,f can be chosen independent of each other, but should not exceed the mesh size. It is also not recommended to define them as functions of the mesh size.


	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 εpm,nl and the fnl — , , , , , or . The options available depends on the chosen order of the displacement field.

To display this section, click the button (

) and select in the dialog box.

Advanced

Enter the , which defines the residual stiffness of the model. The default value is 0.995.

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.


	To compute the energy dissipation caused by porous compaction, enable the Calculate dissipated energy check box in the Energy Dissipation section of the parent material node (Linear Elastic Material or Nonlinear Elastic Material).

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