Macroscopic Modeling of Porous Nonassociated Frictional Materials

Abstract

The aim of this work is to propose a macroscopic plastic model for “Porous nonassociated Drucker-Prager”-type materials, using homogenization techniques and the hollow sphere model proposed by Gurson (J Eng Mater Technol 99:2–15, 1977) for von Mises solid matrix. In the first part, we determine analytically the plastic limit state of a hollow sphere with a Drucker-Prager matrix and subjected to hydrostatic loading. For the associated case, the collapse is complete with a unique regime. For the nonassociated cases, we consider weaker solutions (partial collapse and regime change). Nevertheless, we show that the collapse is complete and exhibits a single regime. Consequently, the collapse stress field and the limit load do not depend on the value of the dilation angle, as confirmed by numerical simulations. This result has been already obtained by Maghous et al. (Eur J Mech A, Solids 28:179–188, 2009) by means of a modified second moduli approach. In Gurson’s footsteps, Guo et al. (J Mech Phys Solids 56:2188–2212, 2008) proposed a macroscopic model for porous solid with pressure-sensitive dilatant matrix obeying to the normality law (associated material). The second part of the paper is a first attempt to extend Guo’s model to the nonassociated materials. Using the concept of bipotential, we proposed a two-fields variational approach to deduce a macroscopic model.