where Cm is the compliance tensor of the matrix, DðcÞ is the damage
tensor, and _ ep is the plastic strain rate, which is to be defined later.
The plastic deformation considered in the current work refers to
deformation that cannot be recovered upon removal of the stress
on the material. For a crystalline solid, the physical (micromechanical)
origin of such deformation is the movement of dislocations
(slip) on the slip planes in the material. Deformation mechanisms
such as mechanical twinning and phase transformation are not
considered.
If the matrix is modeled by linear isotropic elasticity, then the
compliance tensor Cm of the matrix can be written as