SOME FUNDAMENTAL ISSUES IN RATE THEORY OF DAMAGE-ELASTOPLASTICITY

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.