Some fundamental issues in rate theory of damage-elastoplasticity

Abstract

Abstract The paper elaborates on some fundamental constitutive issues in the rate theory of damage-elastoplasticity. The analysis combines the constitutive theories of elastoplastic and progressively damaged solids. After defining needed kinematic and kinetic preliminaries, the anisotropic elastic response is analyzed by introducing a set of damage tensors which represent material degradation and induced elastic anisotropy. Decomposition of the rate of stress and deformation tensors into their elastic and inelastic parts is then defined in a manner analogous to the corresponding decomposition used in large-deformation elastoplasdcity theory. The procedure is further developed to partition the inelastic stress and strain rates into the damage and plastic parts, which takes into account the physics of these deformation processes. The energy 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 constitutive expressions for the damage stress and strain rates are established. The concept of a damage surface is used to define the onset and evolution of damage. A constitutive analysis for inelastic stress and strain rates is then presented. The inelastic potential function and the yield surface are introduced. A dual formulation is constructed in both the stress and strain spaces. The two limiting cases, one involving plasticity without damage, and the other involving damage without plasticity, are deduced from the developed and more general constitutive framework of damage-elastoplasticity.