The presence of cavities and cracks, which are inherent in sintered materials, are known to have effect on the mechanical properties of materials. Changes in microstructure, such as growth of microcracks from pores, cause changes in the overall compliance of the material. In order to study these effects, we develop three dimensional constitutive equations for porous, brittle solids based on the damage mechanics of elastic materials containing spherical pores and cracks. For homogeneous deformation modes, the microcrack growth causes nonlinearities in the stress-strain relations. Failure criteri afor discontinuous bifurcations, loss of uniqueness, and localizations are examined for the developed nonlinear constitutive relations. A study of the computed compressive strength of such materials is presented in which moderate levels of lateral stresses are applied for biaxial stress states.
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