Micromechanics-based constitutive model for alumina incorporating the effect of confinement

A micromechanics-based constitutive model is developed to predict the mechanical behaviour of alumina under quasi-static loading, with particular emphasis on the effect of confining pressure and microstructural features. To capture the micro-mechanical response, finite element simulations are performed on a representative volume element (RVE) containing pre-existing cracks, subjected to various confining pressures ranging from 0 to 800 MPa. Computational homogenisation is used to derive the macroscopic stress-strain behaviour. The model incorporates a crack propagation criterion based on the strain energy release rate, and the degradation of material properties is quantified using the Unified Mechanics Theory (UMT). According to this framework, the entropy generated during crack evolution is transformed into a degradation parameter termed the Thermodynamic State Index (TSI). The effective modulus and strain energy release rate are key inputs for the constitutive formulation. The model successfully predicts the stress-strain response of alumina under varying levels of confinement, demonstrating its potential applicability to other brittle materials where confinement plays a critical role.