Porous Plasticity
Use the Porous Plasticity subnode to define the properties of a plasticity model for a porous material.
The Porous Plasticity 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.
When a Porous Plasticity or Elastoplastic Soil Material node is present, a Volumetric Plastic Strain plot is available under Result Templates
For Porous Plasticity, also a Current Void Volume Fraction plot is available under Result Templates.
Porous Plasticity Model
Use this section to define the plastic properties of the porous material.
Material Model
Select the Material model for the porous plasticity criterion — Shima–Oyane, Gurson, Gurson–Tvergaard–Needleman, Fleck–Kuhn–McMeeking, FKM–GTN, or Capped Drucker–Prager.
Shima–Oyane
For Shima–Oyane enter the following data:
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Initial yield stress σys0.
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Shima–Oyane parameter α.
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Shima–Oyane parameter γ.
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Shima–Oyane parameter m.
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Initial void volume fraction f0.
Gurson
For Gurson enter the following data:
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Initial yield stress σys0.
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Initial void volume fraction f0.
Gurson–Tvergaard–Needleman
For Gurson–Tvergaard–Needleman enter the following data:
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Initial yield stress σys0.
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Tvergaard correction coefficient q1.
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Tvergaard correction coefficient q2.
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Tvergaard correction coefficient q3.
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Initial void volume fraction f0.
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Select an Effective void volume fraction — Bilinear, Asymptotic, or User defined.
For Bilinear and Asymptotic, enter the following data:
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Critical void volume fraction fc.
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Failure void volume fraction ff.
For User defined, enter the effective void volume fraction as a function of for example the void volume fraction, variable <phys>.f.
Fleck–Kuhn–McMeeking
For Fleck–Kuhn–McMeeking enter the following data:
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Initial yield stress σys0.
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Initial void volume fraction f0.
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Maximum void volume fraction fmax.
FKM–GTN
For FKM–GTN enter the following data:
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Initial yield stress σys0.
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Tvergaard correction coefficient q1.
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Tvergaard correction coefficient q2.
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Tvergaard correction coefficient q3.
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Initial void volume fraction f0.
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Maximum void volume fraction fmax.
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Void volume fraction cutoff for GTN model fGTN.
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Void volume fraction cutoff for FKM model fFKM.
Capped Drucker–Prager
For Capped Drucker–Prager enter the following data:
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Initial yield stress σys0.
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Select the Plastic potential Qp related to the flow rule — Associated or Nonassociated.
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Select how the Equivalent plastic strain εpe is computed — Associated, von Mises, or User defined. Enter a User defined expression in the hp field as needed. See Hardening Rule for details.
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Yield function parameter a1
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When Plastic potential is set to Nonassociated, the Potential parameter a1Q.
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Initial void volume fraction f0.
The material properties use values From material (default) or User defined.
See also Porous Plasticity in the Structural Mechanics Theory chapter.
Void Nucleation and Growth
It is possible to Include void nucleation in tension or Include void growth in shear by selecting the corresponding checkbox. See the section Void Nucleation and Growth for details.
When Include void nucleation in tension is selected, enter the Void volume fraction of nucleating voids, the Standard deviation for void nucleation, and the Mean strain for void nucleation. For each property use the value From material or enter a User defined value or expression.
When Include void growth in shear is selected, enter the Void growth rate parameter. Use the value From material or enter a User defined value or expression.
Isotropic Hardening
Select the type of linear or nonlinear isotropic hardening model from the Isotropic hardening model list.
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Select Perfectly plastic (ideal plasticity) if the material can undergo plastic deformation without any increase in yield stress. When Capped Drucker–Prager is selected, enter values or expressions to define the semi-axes of the cap under Elliptic cap parameter pa and Elliptic cap parameter pb.
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For Linear the default Isotropic tangent modulus ETiso uses values From material (if it exists) or User defined. 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 Ludwik from the list to model nonlinear isotropic hardening. The flow stress (yield level) σfm 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 Power law isotropic hardening, the Hardening exponent n uses the value From material (if it exists) or User defined. 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.
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For Hardening function, the isotropic Hardening function σh(εpm) uses values From material or User defined. The flow stress (yield level) σfm is modified as
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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 User defined 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.
Cap Model
Use this section the enter data for the compression cap when the Capped Drucker–Prager material model is selected.
elect the Cap model — Elliptic, or Planar.
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For Elliptic, enter the Initial pressure limit pc0 and the Initial ellipse centroid pcc0. The ellipse aspect ratio is then derived from the intersection of the ellipse with the criterion defined in the parent node.
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For Planar, enter the Initial pressure limit pc0.
Select the Hardening model — Perfectly plastic (no hardening), Exponential, or Hardening function.
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When Exponential is selected from the list, the default Hardening modulus Kc and the Maximum volumetric plastic strain εpvol,max are taken From material.
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When Hardening function is selected from the list, the default Hardening modulus pch and the Maximum volumetric plastic strain εpvol,max are taken From material.
Select the Hardening variable — Volumetric plastic strain, Equivalent plastic strain, or User defined.
See also Compression Cap in the Structural Mechanics Theory chapter.
Nonlocal Plasticity Model
Nonlocal plasticity can be used to facilitate for example the modeling of material softening. Typical examples that involve material softening are finite strain plasticity and soil plasticity. In these situations, standard (local) plasticity calculations reveal a mesh fineness and topology dependence, where a mesh refinement fails to produce a physically sound solution. Nonlocal plasticity adds regularization to the equivalent plastic strain, thereby stabilizing the solution.
Select None, or Implicit Gradient. By selecting Implicit Gradient, regularization can be added to the equivalent plastic strain or to the void volume fraction. These two hardening variables describe different mechanisms and therefore often require different model parameters.
If Equivalent matrix plastic strain is selected, enter values for the:
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Length scale, matrix plastic strain, lint,m.
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Nonlocal coupling modulus, Hnl, which can be seen as a penalization of the difference between the local and nonlocal equivalent matrix plastic strain. A larger value will force the local equivalent matrix plastic strain to be closer to the nonlocal variable.
If Void volume fraction is selected, enter a value for the Length scale, void volume fraction, 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.
For the Capped Drucker–Prager material model, enter values for the
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Length scale lint,e
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Nonlocal coupling modulus, Hnl, which can be seen as a penalization of the difference between the local and nonlocal equivalent plastic strain. A larger value will force the local equivalent plastic strain to be closer to the nonlocal variable.
See also Nonlocal Plasticity in the Structural Mechanics Theory chapter.
Discretization
This section is available with the Implicit gradient nonlocal plasticity model. Select the shape function for the Nonlocal equivalent matrix plastic strain εpm,nl, the Nonlocal void volume fraction fnl, and Nonlocal equivalent plastic strain εpe,nl— Automatic, Linear, Quadratic Lagrange, Quadratic serendipity, Cubic Lagrange, Cubic serendipity, Quartic Lagrange, Quartic serendipity, or Quintic Lagrange. The options available depends on the chosen order of the displacement field.
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog.
Advanced
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog.
Enter the Maximum damage, which defines the residual stiffness of the model. The default value is 0.995.
Select the Local method to solve the plasticity problem — Automatic or Backward Euler. When Backward Euler is selected, it is possible to specify the maximum number of iterations and the relative tolerance used to solve the local plasticity equations. Enter the following settings:
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Maximum number of local iterations. 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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Relative tolerance. 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.
For the Capped Drucker–Prager model, see the settings in the Advanced section for Pressure-Dependent Plasticity and Cap and Cutoff.
See also the Numerical Integration Algorithm section in the Structural Mechanics Theory chapter.
To compute the energy dissipation caused by porous compaction, enable the Calculate dissipated energy checkbox in the Energy Dissipation section of the parent Linear Elastic Material or Nonlinear Elastic Material node.
Location in User Interface
Context Menus
Solid Mechanics > Linear Elastic Material > Porous Plasticity
Solid Mechanics > Nonlinear Elastic Material > Porous Plasticity
Solid Mechanics > Hyperelastic Material > Porous Plasticity
Ribbon
Physics tab with Linear Elastic Material, Nonlinear Elastic Material, or Hyperelastic Material node selected in the model tree:
Attributes > Porous Plasticity