Micromechanics and homogenization of inelastic composite materials with growing cracks

Abstract

A homogenization scheme is employed to derive the effective constitutive equations of an elastoplastic composite system with growing damage. The homogenization procedure followed herein is based on the thermodynamics of dissipative media. It is shown that when damage consists of sharps microcracks the macroscopic constitutive behavior is that of a so-called generalized standard material. The latter is a general dissipative medium whose constitutive equations are completely characterized by a single scalar convex potential function of the chosen state variables and whose evolution is completely characterized by a single convex dissipation potential function of the thermodynamic forces conjugate to the chosen internal state variables. The analysis presented is valid under the assumption that the evolution of the representative volume element at hand is unique and stable. The results of the theoretical analysis are then employed for formulating an approximate method for practically deriving the macroscopic constitutive equations. Computer software development for the application of said method is currently ongoing. A simple example of the numerical results obtained so far is presented.