Effects of multiscale substructures on the effective behavior and field statistics of porous materials

Abstract

This work investigates the effects of multiscale substructure on the mechanical response of porous materials. First, we consider porous materials consisting of two populations of cylindrical pores embedded in an incompressible anisotropic viscous matrix and obtain analytical estimates for the overall response and field statistics under plane-strain loading in transverse plane. We demonstrate that the effective bulk viscosity of three-scale porous materials is lower compared to that of two-scale porous materials, whereas the effective shear viscosity remains unaffected. However, the stress and strain-rate fields become substantially more heterogeneous because of the multiscale substructure, with the enhancement increasing with the anisotropy of the viscous matrix, the total pore volume fraction, and the relative volume fraction of large and small pores. Next, we consider porous polycrystals in which the pores of two populations are distributed in a polycrystalline material composed of anisotropic viscous grains. Depending on the relative sizes of the pores to the grains, three types of porous polycrystals are considered: porous polycrystals containing intergranular pores and voids; porous polycrystals with porous grains and intergranular pores; and porous polycrystals with porous grains and voids. As before, the overall deviatoric response remains largely independent of the relative sizes of pores and grains, but the polycrystals containing porous grains show a softer dilatational response than the other two types of porous polycrystals. Moreover, the polycrystals consisting of intragranular pores exhibit substantially more heterogeneity of the stress and strain-rate fields, compared to polycrystals containing only voids or intergranular pores. While this work focuses on multiscale porous viscous materials, the framework to derive the overall response and field statistics is quite general and, with an appropriate linearization scheme, it can be extended to multiscale porous viscoplastic materials. In this work, however, we considered porous materials with anisotropic viscous phases and focused on uncovering the effects of multiscale substructures, which are found to significantly influence the field statistics of porous materials with strongly anisotropic phases.