This model is an extension of the Drucker-Prager model that takes into account effects associated with granular materials such as powders, soil and sand. In addition to pressure hardening, the model also represents density hardening and variations in the shear modulus with density.

The yield stress is made up of two components, one dependent on the density and one dependent on the pressure,

where σ_{y}, σ_{p} and σ_{ρ} denote the total yield stress,
the pressure yield stress and the density yield stress respectively.

The unload/reload slope is defined by the shear modulus which is defined as a function of the zero pressure density of the material.

**Note:** The yield stress is defined by a yield stress - pressure
and a yield stress - density curve with up to 10 points in each curve.

The shear modulus is defined by a shear modulus - density curve with up to 10 points.

All three curves must be defined.

This model can only be applied to solid bodies.

**Table 123: Input Data**

Name | Symbol | Units | Notes |
---|---|---|---|

Yield Stress vs Pressure | Stress | Tabular data | |

Yield Stress vs Density | Stress and Density | Tabular data | |

Shear Modulus vs Density | Stress and Density | Tabular data |

Custom results variables available for this model:

Name | Description | Solids | Shells | Beams |
---|---|---|---|---|

EFF_PL_STN | Effective Plastic Strain | Yes | No | No |

PRESSURE | Pressure | Yes | No | No |

DENSITY | Density | Yes | No | No |