Recent micromechanically inspired phenomenological theories using internal state variable (ISV) representations of damage have been used to predict the thermomechanical behavior of microcracked solids. These models do not, in an explicit manner, account for distributions of microcracks in a representative volume element (RVE) and have been used successfully only to determine the effective moduli of damaged solids. It has been demonstrated that while the distribution and interaction of damage entities within an RVE generally have a minor effect on the effective moduli, it has a significant effect on the evolution of damage and failure at the macroscale. Damage evolution rates, in general, cannot be described adequately by such theories because of their inability to account for interactions between damage entities in an arbitrary distribution.
Key issues pertaining to the development of viable damage evolution equations using a continuum damage mechanics approach are addressed. In particular, limitations associated with the use of ISVs that can be expressed either in terms of macroscopically measurable quantities or through a spatial average of the geometric features of individual damage entities are discussed. Numerical simulations of evolving crack systems in two-dimensional perfectly brittle solids indicate that “effective stress” models may have difficulty in characterizing damage evolution in brittle microcracked solids when the damage consists of cracks of variable size or spatial distributions. An argument for implementing ISVs based on higher-order moments of the damage distribution within an RVE is presented.