Porous Plasticity

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

Porous Plasticity Model

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

Plasticity Model

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

Yield Function F

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

Select a 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.

•

f0.

Gurson

For enter the following data:

•

σys0.

•

f0.

Gurson–Tvergaard–Needleman

For enter the following data:

•

σys0.

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q1.

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q2.

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f0.

•

fc.

•

ff.

Fleck–Kuhn–McMeeking

For enter the following data:

•

σys0.

•

f0.

•

fmax.

FKM–GTN

For enter the following data:

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σys0.

•

q1.

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q2.

•

f0.

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fmax.

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fGTN.

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fFKM.

Capped Drucker–Prager

For enter the following data:

•

α.

•

f0.

The material properties use values (default) or .

Void Growth

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

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.

•

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.

•

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.


	See also Porous Plasticity, Elliptic Cap, and Elliptic Cap With Hardening 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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