Damage Theory Based on Composite Mechanics

Abstract

A new theory of composite damage mechanics is developed. A material with damage is considered as a composite comprised of two different phases (called matrix and inclusion). Both phases are linearly elastic isotropic materials. The matrix is considered as the intact material, and the inclusion is the damaged material. Three different composite models, Voigt (parallel), Reuss (serial), and generalized self-consistent (spherical), are introduced for three types of damage distributions. These composite models are usually used for initial tangential modulus of a composite material, here we use them for secant modulus of a distressed material. Since the parallel and the serial models represent the upper and lower bounds for stiffness of materials, the composite damage theory obtains the upper and lower bounds for postpeak stress and the level of damage for the material beyond the elastic limit. The spherical model is in between the two bounds. Depending on the “elastic limit” of the inclusion, the theory can be used to describe elastic perfectly plastic behavior, strain hardening, and strain softening. Two different degradations, the linear and exponential degradations of the stress–strain response curve are introduced. The two degradation models are used in two different failure surfaces, i.e., Tresca and Mohr–Coulomb failure surfaces, to predict the postpeak behavior of distressed material.