Va. Lubarda et D. Krajcinovic, CONSTITUTIVE STRUCTURE OF RATE THEORY OF DAMAGE IN BRITTLE ELASTIC SOLIDS, Applied mathematics and computation, 67(1-3), 1995, pp. 81-101
This paper presents a rate-type constitutive analysis applicable to br
ittle elastic materials whose elastic properties degrade in the course
of deformation due to evolution of many microcracks. Thermodynamic an
alysis is used to identify the appropriate damage tensors and their co
njugate forces (affinities). It is shown that the introduced damage po
tentials are dual: for the damage fluxes in the space of affinities, a
nd for the damage strain and stress rates in the corresponding stress
and strain spaces. Rate constitutive equations are derived, providing
explicit representations of the tangent stiffness and compliance tenso
rs. General results are specialized in the case of some simple, physic
ally appealing choices of damage functions, analogous to those used in
other damage and pressure-dependent plasticity models.