The Elastoplastic Soil Material feature is used to model stress–strain relationships that are nonlinear even at infinitesimal strains. It is available in the Solid Mechanics interface. This material model requires the Geomechanics Module (see www.comsol.com/products/specifications/). Elastoplastic Soil Material is available for 3D, 2D, and 2D axisymmetry.

By adding the following subnodes to the Elastoplastic Soil Material node you can incorporate other effects:

Add an External Stress node in case you need to define a pore pressure in a porous soil. The Pore pressure pA is user defined by default. The default value is 1 atm, but you can change it to another value or expression for the pore fluid pressure. If there are other physics interfaces (like Darcy’s Law) in the model that make a pressure variable available, such variables will be available in the list.

The Global coordinate system is selected by default. The Coordinate system list contains all applicable coordinate systems in the component. The coordinate system is used for interpreting directions of orthotropic and anisotropic material data and when stresses or strains are presented in a local system. The coordinate system must have orthonormal coordinate axes, and be defined in the material frame. Many of the possible subnodes inherit the coordinate system settings.

Select a Material model from the list: Modified Cam-clay, Modified structured Cam-clay, Extended Barcelona basic, Hardening soil, or Hardening soil small strain.

All elastoplastic soil models have density as an input. The default Density ρ uses values From material. For User defined enter a custom value or expression.

If the material has a temperature dependent density or other material property, and From material is selected, the Volume reference temperature list will appear in the Model Input section. As a default, the value of Tref is obtained from a Common model input. You can also select User defined to enter a value or an expression for the reference temperature locally.

Select the Octahedral section — Circular, Mohr–Coulomb, or Matsuoka–Nakai. The shape of the yield function in the Octahedral Plane is generally circular, but it can be made a function of the Lode angle θ. See Octahedral Section for details.

When the octahedral section is Mohr–Coulomb, the slope of the critical state line, M, is computed from the friction angle ϕ.

When the octahedral section is Circular or Matsuoka–Nakai, select how the slope of the critical state line, M, is computed — From material, Match to Mohr–Coulomb criterion, or User defined. See Mohr–Coulomb Criterion and Matsuoka–Nakai Criterion for details.

Select the Plastic potential Qp related to the flow rule — Associated, Nonassociated, or McDowell–Hau.

When Nonassociated is selected in the Plastic potential list, the dilatation angle ψ replaces the friction angle ϕ in the plastic potential Qp. The default value for the Dilatation angle ψ is taken From material.

When McDowell–Hau is selected in the Plastic potential list, the default for the Plastic potential shape parameter ζ is taken From material.

Select how the Equivalent plastic strain εpe is computed — Associated, von Mises, or User defined. Enter a User defined value in the hp field as needed. See Hardening Rule for details.

From the Specify list select how to specify the elastic property for the material — Poisson’s ratio or Shear modulus. Then, depending on the selection, enter a value or select from the applicable list to use the value From material or enter a User defined value or expression.

The defaults for the Swelling index κ, Compression index λ, Friction angle ϕ, and Initial void ratio e0 are taken From material. For User defined enter other values or expressions.

Select how the Slope of critical state line, M, is computed — From material, Match to Mohr–Coulomb criterion, or User defined. See Mohr–Coulomb Criterion for details.

When Nonassociated is selected in the Plastic potential list, select how the Slope of critical state line for plastic potential, MQ, is computed — From material, Match to Mohr–Coulomb criterion, or User defined. Enter the Dilatation angle ψ to define the nonassociated plastic potential Qp.

Enter a value or an expression for the Reference pressure pref and the Preconsolidation pressure pc0.

From the Specify list select how to specify the elastic property for the material — Poisson’s ratio or Shear modulus. Then, depending on the selection, enter a value or select from the applicable list to use the value From material or enter a User defined value or expression.

The defaults for the Swelling index for structured clay κs, Compression index for destructured clay λd, Friction angle ϕ, Initial structure strength pb0, Destructuring index for volumetric deformation dv, Destructuring index for shear deformation ds, Plastic deviatoric strain at failure efp, Initial void ratio for structured clay e0, and Additional void ratio at preconsolidation pressure Δec0 are taken From material. For User defined enter other values or expressions.

Select how the Slope of critical state line, M, is computed — From material, Match to Mohr–Coulomb criterion, or User defined. See Mohr–Coulomb Criterion for details.

When Nonassociated is selected in the Plastic potential list, select how the Slope of critical state line for plastic potential, MQ, is computed — From material, Match to Mohr–Coulomb criterion, or User defined. Enter the Dilatation angle ψ to define the nonassociated plastic potential Qp.

Enter a value or an expression for the Reference pressure pref and the Preconsolidation pressure pc0.

From the Specify list select how to specify the elastic property for the material — Poisson’s ratio or Shear modulus. Then, depending on the selection, enter a value or select from the applicable list to use the value From material or enter a User defined value or expression.

The defaults for the Swelling index at saturation κ0, Swelling index for changes in suction κs, Compression index at saturation λ0, Compression index for changes in suction λs, Friction angle ϕ, Weight parameter w, Soil stiffness parameter m, Plastic potential smoothing parameter b, Tension to suction ratio k, Initial yield value for suction sy0, and Initial void ratio e0 are taken From material. For User defined enter other values or expressions.

Select how the Slope of critical state line, M, is computed — From material, Match to Mohr–Coulomb criterion, or User defined. See Mohr–Coulomb Criterion for details.

When Nonassociated is selected in the Plastic potential list, select how the Slope of critical state line for plastic potential, MQ, is computed — From material, Match to Mohr–Coulomb criterion, or User defined. Enter the Dilatation angle ψ to define the nonassociated plastic potential Qp.

Enter a value or an expression for the Initial suction s0, Suction s, Reference pressure pref, and Preconsolidation pressure pc0.

Select the Mobilized dilatancy angle ψm — Soreide, Rowe, Modified Rowe, Wehnert, or User defined. See Mobilized Dilatancy Angle for details.

The Reference initial stiffness for primary loading Eiref, Reference stiffness for unloading and reloading Eurref, Poisson’s ratio ν, Stress exponent m, Cohesion c, Friction angle ϕ, and Initial void ratio e0 are taken From material. For User defined enter other values or expressions.

Select how the Slope of critical state line, M, is computed — From material, Match to Mohr–Coulomb criterion, or User defined. See Mohr–Coulomb Criterion for details.

When Nonassociated is selected in the Plastic potential list, select how the Slope of critical state line for plastic potential, MQ, is computed — From material, Match to Mohr–Coulomb criterion, or User defined. Enter the Dilatation angle ψ to define the nonassociated plastic potential Qp.

Enter a value or an expression for the Failure ratio Rf and the Reference pressure pref.

Activate the Dilatancy cutoff if needed. Enter a value or an expression for the Maximum void ratio emax and the Initial volumetric strain εvol0.

If required, add a Cap and Cutoff subnode.

Select the Mobilized dilatancy angle ψm — Soreide, Rowe, Modified Rowe, Wehnert, or User defined. See Mobilized Dilatancy Angle for details.

The defaults for the Reference initial stiffness for primary loading Eiref, Reference stiffness for unloading and reloading Eurref, Small strain shear modulus G0, Poisson’s ratio ν, Reference shear strain γref, Stress exponent m, Cohesion c, Friction angle ϕ, and Initial void ratio e0 are taken From material. For User defined enter other values or expressions.

Select how the Slope of critical state line, M, is computed — From material, Match to Mohr–Coulomb criterion, or User defined. See Mohr–Coulomb Criterion for details.

When Nonassociated is selected in the Plastic potential list, select how the Slope of critical state line for plastic potential, MQ, is computed — From material, Match to Mohr–Coulomb criterion, or User defined. Enter the Dilatation angle ψ to define the nonassociated plastic potential Qp.

Enter a value or an expression for the Failure ratio Rf and the Reference pressure pref.

Activate the Dilatancy cutoff if needed. Enter a value or an expression for the Maximum void ratio emax and the Initial volumetric strain εvol0.

If required, add a Cap and Cutoff subnode.

In case of cyclic loading the load reversal points are automatically detected, but in many cases these are known a priori. The Load Reversal Points section enables to set the load reversal points manually based on user defined expressions.

From the list select how to specify the load reversal points — Automatic, None, or User defined. For User defined enter a Boolean expression to fulfill the reversal point for each component of the strain tensor.

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

Select a Formulation — From study step, Total Lagrangian, or Geometrically linear to set the kinematics of the deformation and the definition of strain. When From study step is selected, the study step controls the kinematics and the strain definition.

When From study step is selected, a total Lagrangian formulation for large strains is used when the Include geometric nonlinearity checkbox is selected in the study step. If the checkbox is not selected, the formulation is geometrically linear, with a small strain formulation.

To have full control of the formulation, select either Total Lagrangian, or Geometrically linear. When Total Lagrangian is selected, the physics will force the Include geometric nonlinearity checkbox in all study steps.

Select a Strain decomposition — Automatic, Additive, Logarithmic, or Multiplicative to decide how the inelastic deformations are treated. This option is not available when the formulation is set to Geometrically linear.

The Strain decomposition input is only visible for material models that support both additive and multiplicative decomposition of the deformation gradient.

Only the additive decomposition of strains is available for the Hardening Soil Small Strain model.

Select how to compute the energy dissipated by Creep, Plasticity, Viscoplasticity, or other dissipative processes.

Select how to Store dissipation — From physics interface, Individual contributions, Total, Domain ODEs (legacy), or Off.

Use From physics interface to treat the dissipative processes as specified in the settings of the physics interface, see for instance Energy Dissipation in the Solid Mechanics interface.

Use Individual contributions to treat each dissipative process independently. Selecting this option gives a more flexible implementation for problems where dissipation occurs at different time scales, and you want to distinguish each phenomenon separately.

Use Total to accumulate all the dissipative processes into one common variable.

Use Domain ODEs to accumulate the dissipative processes into ODE variables instead of internal state variables.

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.

Select the Reduced integration checkbox to reduce the number of integration points used for the weak contribution in the material. Reduced integration give faster computations at the element level and help mitigate locking issues. However, reduced integration may also introduce numerical instabilities, which then require an additional stabilization term.

By default, the Reduced integration checkbox is cleared, except in interfaces designed for explicit dynamic analysis, where it is always selected.

Select a method for Hourglass stabilization — Automatic, Energy sampling, Hessian, Flanagan–Belytschko, Manual, or None to be used in combination with the reduced integration scheme.

The Automatic option selects the stabilization method and its properties based on the physics interface, space dimension, shape function type and order of the displacement field, and the study type.

For the Energy sampling, Hessian, and Flanagan–Belytschko methods, the hourglass stiffness can be scaled by specifying a stiffness multiplier fstb. This multiplier can be an expression of any parameter or variable in the model. This multiplier can be expressed as any parameter or variable in the model. However, to maintain computational efficiency, avoid expensive definitions such as nonlocal coupling operators.

For the hourglass stabilization methods, the stiffness is automatically adjusted during the solution process using an internal multiplier. This accounts for the effect of inelastic deformations, such as damage and plasticity. This correction can be disabled by setting Inelastic deformations to Ignore. Ignoring inelastic deformations may be necessary for scenarios like cyclic loading, where the hourglass stiffness could become too small during unloading. Alternatively, adjust the value for the Minimum stiffness multiplier., which acts as a lower bound for the hourglass stiffness, which is applied in addition to any expression entered for fstb.

For the Energy sampling method, the default stabilization uses an isotropic linear elastic potential. Set the Energy Sampling Potential to Hyperelastic for large deformations. When selected, a neo-Hookean potential is used for nonlinear strains, while linear strains use the linear elastic potential.

The Hessian method evaluates a weak contribution using the reduced integration order. For hexahedral mesh elements, this approach may not suppress all hourglass modes. In most cases, non-stabilized modes are suppressed by constraints adjacent to the domain, but if they are not, select Use full integration to increase the integration order of the stabilization equations to suppress all modes. The higher integration order will increase the computational cost of the stabilization method.

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.

Select the Hardening function offset — Automatic or User defined to control how much the smoothed potential at the apex deviates from the original plastic potential. The Automatic option does not apply any smoothing. Select User defined to enter a value. See Apex Smoothing for details.

Physics tab with Solid Mechanics selected: