Mechanical and numerical modeling of a porous elastic–viscoplastic material with tensile failure

The objective of this paper is to develop simple but comprehensive constitutive equations that model a number of physical phenomena exhibited by dry porous geological materials and metals. For geological materials the equations model: porous compaction; porous dilation due to distortional deformation and tensile failure; shear enhanced compaction; pressure hardening of the yield strength; damage of the yield strength due to distortional deformation and porosity changes; and dependence of the yield strength on the Lode angle. For metals the equations model: hardening of the yield strength due to plastic deformation; pressure and temperature dependence of the yield strength, and damage due to nucleation of porosity during tensile failure. The equations are valid for large deformations and the elastic response is hyperelastic in the sense that the stress is related to a derivative of the Helmholtz free energy. Also, the equations are viscoplastic with rate dependence occurring in both the evolution equations of porosity and elastic distortional deformations. Moreover, formulas are presented for robust numerical integration of the evolution equations at the element level that can be easily implemented into standard computer programs for dynamic response of materials. #