Thermo-mechanical constitutive equations for brittle porous materials

Abstract
The behavior and failure of a brittle material is significantly influenced by the existence of inhomogeneities such as pores and cracks. The proposed constitutive equations model the coupled micro-mechanical response of these inhomogeneities through evolution equations for scalar measures of porosity, and a "density" function of randomly oriented penny-shaped cracks. A specific form for the Helmholtz free energy is proposed which incorporates the known Mie-Grüneisen constitutive equation for the nonporous solid. The resulting thermo-mechanical constitutive equations are valid for large deformations and the elastic response is hyperelastic in the sense that the stress is related to a derivative of the Helmholtz free energy. These equations allow for the simulation of the following physical phenomena exhibited by brittle materials : (1) High compressive strength compared with much lower tensile strength ; (2) Inelastic deformation due to growth and nucleation of cracks and pores, instead of dislocation dynamics associated with metal plasticity ; (3) Degradation of elastic moduli due to damage accumulation ; and (4) Bulking of the material during compressive loading due to fragment mismatch. The main features of the model are demonstrated by simulation of plate impact experiment on AD85 ceramic. The theoretical predictions of the model are in good agreement with the experimental data.