Va. Lubarda et D. Krajcinovic, SOME FUNDAMENTAL ISSUES IN RATE THEORY OF DAMAGE-ELASTOPLASTICITY, International journal of plasticity, 11(7), 1995, pp. 763-797
The paper elaborates on some fundamental constitutive issues in the ra
te theory of damage-elastoplasticity. The analysis combines the consti
tutive theories of elastoplastic and progressively damaged solids. Aft
er defining needed kinematic and kinetic preliminaries, the anisotropi
c elastic response is analyzed by introducing a set of damage tensors
which represent material degradation and induced elastic anisotropy. D
ecomposition of the rate of stress and deformation tensors into their
elastic and inelastic parts is then defined in a manner analogous to t
he corresponding decomposition used in large-deformation elastoplastic
ity theory. The procedure is further developed to partition the inelas
tic stress and strain rates into the damage and plastic parts, which t
akes into account the physics of these deformation processes. The ener
gy dissipation rate is derived and the thermodynamic forces conjugate
to elastic stiffness and compliance tensors are identified, based on a
thermodynamic analysis of isothermal deformation process. The damage
potentials for the corresponding fluxes are introduced and the constit
utive expressions for the damage stress and strain rates are establish
ed. The concept of a damage surface is used to define the onset and ev
olution of damage. A constitutive analysis for inelastic stress and st
rain rates is then presented. The inelastic potential function and the
yield surface are introduced. A dual formulation is constructed in bo
th the stress and strain spaces. The two limiting cases, one involving
plasticity without damage, and the other involving damage without pla
sticity, are deduced from the developed and more general constitutive
framework of damage-elastoplasticity.