where cðtÞ is the mean crack radius, and No is the initial crack number
density per solid angle. In the current model, No is kept as a
material constant, and the damage in the material is reflected
through the evolution of cðtÞ.
In the DCA model, the total strain rate _e is decomposed into the
contributions from the matrix (uncracked solid) and from the response
(open, shear, and growth) of microcracks. Here, to include
plastic deformation, the decomposition is modified as (Dienes
et al., 2006)