CONSTITUTIVE MODELS FOR POROUS MATERIALS WITH EVOLVING MICROSTRUCTURE

A constitutive model is developed for the effective behavior of nonlinear porous materials which is capable of accounting, approximately, for the evolution of the material's microstructure under large quasi-static deformations. The model is formulated in terms of an effective potential function for the porous material, which depends on appropriate variables characterizing the state of the microstructure, together with evolution equations for these state variables. For the special case of triaxial loading of an initially isotropic porous material, the appropriate state variables are the porosity and the aspect ratios of the typical void; they serve respectively to characterize the evolution of the size and shape of the pores. The implications of the model are studied in the context of two specific examples: axisymmetric and plane strain loading conditions. It is found that the porosity acts as a hardening mechanism when the material is subjected to boundary conditions resulting in overall hydrostatic compression, and as a softening mechanism for overall hydrostatic tension. On the other hand, the change in shape of the voids is found to have a more subtle influence on the overall behavior of the porous material. Thus the change in shape of the voids has a direct effect which may range from strong softening during void collapse to slight hardening during void elongation, but it also has an indirect effect through its concomitant effect on the evolution of the porosity, which may actually be quite significant. Because of the complex interplay between these hardening-softening mechanisms, the new model is found to yield significantly different predictions, in particular for the onset of localization, than the well-known model of Gurson, which neglects the change in shape of the voids, especially, for low-triaxiality loading conditions. The model, in its present form, is not meant to be used for high-triaxialities for which the Gurson and other associated models are considered to be quite accurate.