COMSOL 6.3 - Pressure-Dependent Plasticity

Use the subnode to define the properties for modeling materials where the yielding and failure depends on pressure. This material model is available in the Solid Mechanics interface, and can be used together with Linear Elastic Material, Nonlinear Elastic Material, and Hyperelastic Material.

The Nonlinear Structural Materials Module is required. For details, see https://www.comsol.com/products/specifications/.

	When a Pressure-Dependent Plasticity node is present, an Equivalent Plastic Strain plot is available under Result Templates.

	See also Pressure-Dependent and Soil Plasticity in the Structural Mechanics Theory chapter.

Use this section to define the plastic properties of the material. Select a plasticity model — , , , or .

The Drucker–Prager, Elliptic, and Parabolic options are generic plasticity models intended for pressure sensitive materials. These models share the following common settings:

The default σys0 uses values and represents the von Mises stress where plastic deformation starts given zero pressure.

Select the Qp related to the flow rule — or .

Select how the εpe is computed — , , or . Enter a expression in the hp field as needed. See Hardening Rule for details.

Select the type of linear or nonlinear isotropic hardening model. See Isotropic Hardening for details.

For the Drucker–Prager plasticity model, the yield function is defined by two parameters, the initial yield stress σys0 at zero pressure, and a parameter a1 that controls the pressure dependency.

When is set to , an additional parameter a1Q is used to define the pressure dependency of the plastic potential independently of the yield function.

The Drucker–Prager model can be combined with a Cap and Cutoff if needed.

See Drucker–Prager Criterion in the Structural Mechanics Theory chapter for details.

The yield function of the elliptic plasticity model can be modified by specifying parameters b1, b2, and b3. This set of parameters defines the shape of the ellipse in the Meridional Plane through the function

where σm is the mean stress. Each parameter can be taken , or given as a value. It is also possible to set a parameter to , in which case that term of the function is explicitly removed.

In addition, the shape of the yield function in the Octahedral Plane can be controlled by setting the Γ(θ) — , , or .

See Octahedral Section in the Structural Mechanics Theory chapter for details.

When is set to , an additional set of parameters b1Q, b2Q, and b3Q can be specified. This set of parameters defines the shape of the plastic potential in the Meridional Plane independently from the yield function. Each parameter can either be taken , or assigned a value. It is also possible to set a parameter to , in which case that term in the nonassociated potential is explicitly removed.

The shape of the plastic potential is assumed to be circular in the octahedral plane. See Elliptic Criterion in the Structural Mechanics Theory chapter for details.

The yield function of the parabolic plasticity model can be modified by specifying the parameters a1, a2, a3, and a4. The set of parameters defines the shape of the parabola in the Meridional Plane by the function

where σm is the mean stress. Each parameter can be taken , or given a value. It is also possible to set a parameter to , in which case that term is explicitly removed.

In addition, the shape of the yield function in the Octahedral Plane can be controlled by setting Γ(θ) — , , or . See Octahedral Section in the Structural Mechanics Theory chapter for details.

When is set to , an additional set of parameters a1Q, a2Q, a3Q, and a4Q can be specified. This set of parameters defines the shape of the plastic potential in the meridional plane independently from the yield function. Each parameter can either be taken , or given a value. It is also possible to set a parameter to , in which case that term of the function is explicitly removed. The shape of the plastic potential is assumed to be circular in the Octahedral Plane.

The parabolic plasticity model can be combined with a Cap and Cutoff if needed.

See Parabolic Criterion in the Structural Mechanics Theory chapter for details

The Foam plasticity model is a specialized version of the Elliptic model often used for the analysis of structural foam and other materials with a cellular structure. The material model is set up to make it straightforward to specify the anisotropic strength of foams when loaded in tension and compression. In addition, a volumetric hardening model can be included to account for the compaction of the foam during plastic deformation.

Define the initial shape of the elliptic yield function by specifying the following parameters:

The default values are taken , but optionally a input can be entered.

Foam plasticity uses a nonassociative flow rule where the plastic potential is an ellipse defined by a single parameter, the νp. It is identified as the ratio of longitudinal to transverse plastic strain, that is, the value of νp controls to amount of volumetric plastic deformation when loading is not on the hydrostatic axis, such as in uniaxial compression. The value of νp can be taken , a input, or . The default suggestion corresponds to νp = 0, which is common for many structural foams.

	The Plastic Poisson’s ratio νp must be defined between −1 and 0.5.

A can be added to the Foam plasticity model by entering a hardening function. When is selected no hardening occurs. Note that the yield stress in hydrostatic tension, pt, is always treated as constant during plastic deformation.

By selecting , it is possible to define the variation of the compressive hydrostatic yield stress by specifying a function pch with respect to the accumulated volumetric plastic strain, εpv. The variable εpv is positive in compression and it increases monotonically. The total hydrostatic yield stress is then given by

The function pch can either be taken , or given by a input. In the latter case, enter an expression where the variable for εpv is named using the scheme <physics>.epev.

Alternatively, it is possible to specify evolution of the uniaxial compressive yield stress. When , is selected, define the variation of the uniaxial compressive yield stress by specifying a function σuch with respect to the accumulated axial plastic strain, εpa. The axial plastic strain is here estimated as εpa = εpv/(1 − 2νp), and the total uniaxial compressive yield stress is then given by

The function σuch can either be taken , or given by a input. In the latter case, enter an expression where the variable for εpa is named using the scheme <physics>.epea.

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

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.

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

•

, 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.

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.

To display this section, click the button (

) and select in the dialog.

The plastic potential may include vertices where it intersects the hydrostatic axis. To improve robustness of the plasticity method, smoothing is applied to remove these singularities. If visible, select the — , , or , to control how much the smooth plastic potential deviates from the original plastic potential. When is selected, enter a value for the fv. This multiplier scales the amount of smoothing of the option. The option allows full control of the smoothing by entering a value for the σv,off.

Select the to solve the plasticity problem — , , or .

When or 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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. 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.

When the method is selected, the Newton’s method is enhanced by line search iterations. Using this method can improve the robustness of the plasticity problem when the plastic potential or hardening model are highly nonlinear. When selected, it is possible to specify the . The default value is 4 iterations.

For a 2D geometry, enable to solve for all components of the plastic strain tensor. By default, it is assumed that the out-of-plane components are zero.