Extended Drucker-Prager

The Drucker-Prager material model, also known as the Extended Drucker-Prager model, is an elastic-plastic constitutive behavior commonly used to model frictional materials.

The model requires the definition of a yield behavior and a hardening mechanism. It also supports optional rate dependence and creep behavior.

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Extended Drucker-Prager Models

Drucker-Prager models:

  • are used to model materials in which the compressive yield strength is greater than the tensile yield strength, such as those commonly found in granular-like soils and rock, composites and polymeric materials;
  • allow a material to harden or soften isotropically;
  • generally allow for volume change with inelastic behavior: the flow rule, defining the inelastic straining, allows simultaneous inelastic dilation (volume increase) and inelastic shearing;
  • can include creep in implicit analysis if the material exhibits long-term inelastic deformations;
  • can be defined to be sensitive to the rate of straining, as is often the case in polymeric materials (see Rate-Dependent Hardening Options);
  • can be used with either the elastic material model or, in implicit analysis if creep is not defined, the porous elastic material model;
  • can be used with an equation of state model to describe the hydrodynamic response of the material in an explicit time integration simulation;
  • can be used with the models of progressive damage and failure to specify different damage initiation criteria and damage evolution laws that allow for the progressive degradation of the material stiffness and the removal of elements from the mesh; and
  • are intended to simulate material response under essentially monotonic loading.

Drucker-Prager plasticity must be used with the Drucker-Prager hardening option. An optional Drucker-Prager creep behavior is available for implicit analyses.

You can define the flow potential eccentricity, ϵ . The eccentricity is a small positive number that defines the rate at which the hyperbolic flow potential approaches its asymptote. If a linear yield criteria is used ϵ is only used if Drucker-Prager creep is included.

The yield criteria for this class of models are based on the shape of the yield surface in the meridional (p-t) plane. The yield surface can have a linear form, a hyperbolic form, or a general exponent form:

  • Linear: Specify the linear yield criterion.
  • Hyperbolic: Specify the hyperbolic yield criterion.
  • Exponent Form: Specify the exponent form yield criterion.

Parameters for the Linear Shear Criterion

Input Data Description
Friction Angle Material angle of friction, β , in the p–t plane.
Flow Stress Ratio K , the ratio of the flow stress in triaxial tension to the flow stress in triaxial compression. If creep material behavior is included, K must be set to 1.0.
Dilation Angle Dilation angle, ψ , in the p-t plane.
Use temperature-dependent data Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.

Parameters for the Hyperbolic Shear Criterion

Input Data Description
Friction Angle Material angle of friction, β , in the p–t plane.
Initial Hydrostatic Tension K , the ratio of the flow stress in triaxial tension to the flow stress in triaxial compression. If creep material behavior is included, K must be set to 1.0.
Dilation Angle Dilation angle, ψ , at high confining pressure in the p–q plane.
Use temperature-dependent data Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.

Parameters for the Exponent Form Shear Criterion

Input Data Description
a Material constant.
b Exponent b. To ensure a convex yield surface, b 1
Dilation Angle Dilation angle, ψ , at high confining pressure in the p–q plane.
Use temperature-dependent data Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.