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

The objective of this paper is to develop simple but comprehensive constitu tive equations that model a number of physical phenomena exhibited by dry p orous geological materials and metals. For geological materials the equatio ns model: porous compaction; porous dilation due to distortional deformatio n and tensile failure; shear enhanced compaction; pressure hardening of the yield strength; damage of the yield strength due to distortional deformati on and porosity changes; and dependence of the yield strength on the Lode a ngle. For metals the equations model: hardening of the yield strength due t o plastic deformation; pressure and temperature dependence of the yield str ength, and damage due to nucleation of porosity during tensile failure. The equations are valid for large deformations and the elastic response is hyp erelastic in the sense that the stress is related to a derivative of the He lmholtz free energy. Also, the equations are viscoplastic with rate depende nce occurring in both the evolution equations of porosity and elastic disto rtional deformations. Moreover, formulas are presented for robust numerical integration of the evolution equations at the element level that can be ea sily implemented into standard computer programs for dynamic response of ma terials. (C) 2000 Elsevier Science Ltd. All rights reserved.