Soil Plasticity
In the Soil Plasticity subnode you define the properties for modeling materials exhibiting soil behavior. Soil Plasticity can be used together with Linear Elastic Material, Nonlinear Elastic Material, and Hyperelastic Material. It is available with the Geomechanics Module. Soil Plasticity is available for 3D, 2D, and 2D axisymmetry.
When a Soil Plasticity node is present, an Equivalent Plastic Strain plot is available under Result Templates.
The failure criteria are described in the Structural Mechanics Theory chapter:
•
Drucker–Prager Criterion
•
Mohr–Coulomb Criterion
•
Matsuoka–Nakai Criterion
•
Lade–Duncan Criterion.
Soil Plasticity
Select the Failure criterion — Drucker–Prager, Mohr–Coulomb, Matsuoka–Nakai, or Lade–Duncan.
Plastic Potential
Select the Plastic potential Qp related to the flow rule — Associated, Nonassociated, or Drucker–Prager.
Equivalent Plastic Strain
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.
Drucker–Prager
In the standard Drucker–Prager formulation, the material parameters are given in terms of the coefficients α and k. Often, material data is expressed by the cohesion c and friction angle ϕ used in the Mohr–Coulomb criterion.
Select Match to Mohr–Coulomb — Compressive meridian, Tensile meridian, Inscribe (plane strain), Uniaxial (plane stress), Biaxial (plane stress), or User defined. The default values for the Initial cohesion c0 and Friction angle ϕ are taken From material. For User defined, the values for the Drucker–Prager parameters k0 and α and are taken From material.
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. If not matched to the Mohr–Coulomb criterion, parameter αQ defines the nonassociated plastic potential. It is by default taken From material.
If required, add a Cap and Cutoff subnode.
Mohr–Coulomb
When Associated is selected in the Plastic potential list, the default values for the Initial cohesion c0 and Friction angle ϕ and are taken From material.
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 is taken From material.
When Drucker–Prager is selected in the Plastic potential list, a Drucker–Prager plastic potential with a dilatation angle ψ replaces the Mohr–Coulomb potential. Select the Dilatation angle — From material, From friction angle, or User defined.
If required, add a Cap and Cutoff subnode.
Matsuoka–Nakai
Select Match to Mohr–Coulomb — Compressive meridian or User defined. The default values for the Initial cohesion c0 and Friction angle ϕ are taken From material. For User defined, the values for the Drucker–Prager parameters k0 and α and are taken From material.
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 is taken From material.
When Drucker–Prager is selected in the Plastic potential list, a Drucker–Prager plastic potential with a dilatation angle ψ replaces the Matsuoka–Nakai potential. Select the Dilatation angle — From material, From friction angle, or User defined.
If not matched to the Mohr–Coulomb criterion, parameter αQ defines the nonassociated plastic potential. It is by default taken From material.
If required, add a Cap and Cutoff subnode.
Lade–Duncan
Select Match to Mohr–Coulomb — Compressive meridian or User defined. The default values for the Initial cohesion c0 and Friction angle ϕ are taken From material. For User defined, the values for the Drucker–Prager parameters k0 and α and are taken From material.
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 is taken From material.
When Drucker–Prager is selected in the Plastic potential list, a Drucker–Prager plastic potential with a dilatation angle ψ replaces the Lade–Duncan potential. Select the Dilatation angle — From material, From friction angle, or User defined.
If not matched to the Mohr–Coulomb criterion, parameter αQ defines the nonassociated plastic potential. It is by default taken From material.
If required, add a Cap and Cutoff subnode.
Isotropic Hardening
For all failure criteria, select the type of hardening model from the Isotropic hardening model list. See Isotropic Hardening for details.
•
Select Perfectly plastic (ideal plasticity) if the material can undergo plastic deformation without any change in cohesion.
•
For Hardening function, the isotropic Hardening function ch(εpe) uses values From material or User defined. The cohesion is modified as
When Match to Mohr–Coulomb is set to User defined, the isotropic Hardening Function kh(εpe) directly specifies the evolution of the strength parameter k as
-
The above definitions imply that the hardening functions in the Material node must be zero at zero plastic strain. For example, c = c0 when εpe = 0. With this option it is possible to enter any nonlinear curve. The hardening function can depend on more variables than the equivalent plastic strain, for example the temperature. Select User defined to enter any function of the equivalent plastic strain εpe. The variable is named using the scheme <physics>.epe, for example, solid.epe.
See also Pressure-Dependent and Soil Plasticity 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.
The default is None. Select Implicit Gradient to add nonlocal regularization to the equivalent plastic strain. Enter a value for the:
•
Length scale, lint. The length scale should not exceed the maximum element size of the mesh.
•
Nonlocal coupling modulus, 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.
Discretization
This section 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.
•
Deep Excavation: Application Library path Geomechanics_Module/Soil/deep_excavation
•
Flexible and Smooth Strip Footing on a Stratum of Clay: Application Library path Geomechanics_Module/Soil/flexible_footing
Advanced
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog.
The plastic potential of soil plasticity models include a vertex where it intersects the hydrostatic axis. To improve robustness of the plasticity algorithm, smoothing is applied to remove these singularities.
Select the Smoothing of plastic potential — Automatic, Manual tuning, or User defined to control how much the smooth plastic potential deviates from the unsmoothed potential. When Manual tuning is selected, enter a value for the Vertex smoothing multiplier fv. This multiplier scales the amount of smoothing for the Automatic option. The User defined option allows full control of the smoothing by entering a value for the Vertex smoothing parameter σv,off.
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:
•
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.
•
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.
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.
See also the Numerical Integration Algorithm section in the Structural Mechanics Theory chapter.
Location in User Interface
Context Menus
Solid Mechanics > Linear Elastic Material > Soil Plasticity
Solid Mechanics > Nonlinear Elastic Material > Soil Plasticity
Solid Mechanics > Hyperelastic Material > Soil Plasticity
Ribbon
Physics tab with Linear Elastic Material, Nonlinear Elastic Material, or Hyperelastic Material node selected in the model tree:
Attributes > Soil plasticity