the stress strain law

the yield function

(208) |

loading-unloading conditions

(209) |

evolution law for plastic strain

(210) |

the incremental definition of cumulated plastic strain

(211) |

the law governing the evolution of the damage variable

e | (212) |

and the hardening law

e | (213) |

In the equations above, is the effective stress tensor,

normalized such that Tr

(215) |

where , and . Here, , and are elastic constants characterizing the compact (poreless) material, is the volume fraction of solid phase and and are dimensionless exponents.

Similar relations as for the stiffness tensor are also postulated for the components of a fourth-order tensor
** that is used in the yield condition. The yield condition is divided into tensile and compressive parts. Tensor
**** is different in each part of the effective stress space. This tensor is denoted
**** in tensile part, characterized by
and
**** in compressive part, characterized by
, where
**

(216) |

(217) |

In the equation above is uniaxial yield stress along the -th principal axis of orthotropy, is the shear yield stress in the plane of orthotropy and is the so-called interaction coefficient, and are dimensionless exponents and parameters with subscript

(218) |

The model description and parameters are summarized in Tab. 46.

2018-01-02