Use the Pressure-Dependent Plasticity 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 www.comsol.com/products/specifications/.

Use this section to define the plastic properties of the material. Select a plasticity model — Drucker–Prager, Elliptic, Foam, or Parabolic.

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

Select the Plastic potential Qp related to the flow rule — Associated or Nonassociated.

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.

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 Plastic potential is set to Nonassociated, 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.

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 From Material, or given as a User defined value. It is also possible to set a parameter to Exclude, 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 Octahedral section Γ(θ) — Circular, Gudehus, or Lagioia–Panteghini.

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

When Plastic potential is set to Nonassociated, 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 From Material, or assigned a User defined value. It is also possible to set a parameter to Exclude, in which case that term in the nonassociated potential is explicitly removed.

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 From Material, or given a User defined value. It is also possible to Exclude a parameter, in which case that term is explicitly removed from the yield function.

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

When Plastic potential is set to Nonassociated, 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 From Material, or given a User defined value. It is also possible to set a parameter to Exclude, 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.

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.

The default values are taken From material, but optionally a User defined input can be entered.

Foam plasticity uses a nonassociated flow rule where the plastic potential is an ellipse defined by a single parameter, the plastic Poisson’s ratio 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 From material, a User defined input, or From default suggestion. The default suggestion corresponds to νp = 0, which is common for many structural foams.

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

By selecting Hardening function, 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 From material, or given by a User defined 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 Hardening function, uniaxial data, 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 From material, or given by a User defined input. In the latter case, enter an expression where the variable for εpa is named using the scheme <physics>.epea.

The default setting is None. Select Implicit Gradient to add nonlocal regularization to the equivalent plastic strain. Then, enter values or expressions for:

To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog, and it is available with the Implicit gradient nonlocal plasticity model.

Select the shape function for the Nonlocal equivalent plastic strain εpe,nl — Automatic, Linear, Quadratic Lagrange, Quadratic serendipity, Cubic Lagrange, Cubic serendipity, Quartic Lagrange, Quartic serendipity, or Quintic Lagrange. The available options depend on the 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.

Select the Smoothing of plastic potential — Automatic, Manual tuning, or User defined to control how much the smoothed plastic potential deviates from the original potential.

When Manual tuning or User defined is selected, enter the Edge smoothing parameter β when using Mohr–Coulomb plastic potential. The default value is β = 0.99.

When Manual tuning is selected, enter a value for the Vertex smoothing multiplier fv. This multiplier scales the amount of smoothing at the apex given by the Automatic option.

The User defined option allows full control of the smoothing by entering a value for the Vertex smoothing parameter σv,off. A typical value would be around 10% of the initial cohesion for soil models.

Select the Local method to solve the plasticity problem — Automatic, Backward Euler, or Backward Euler, damped. When Backward Euler or Backward Euler, damped 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:

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

Physics tab with Linear Elastic Material, Nonlinear Elastic Material, or Hyperelastic Material node selected in the model tree: