A viscoelastic damage model with applications to stable and unstable fracturing

A viscoelastic damage rheology model is presented that provides a generalization of Maxwell viscoelasticity to a non-linear continuum mechanics framework incorporating material degradation and recovery, transition from stable to unstable fracturing and gradual accumulation of non-reversible deformation. The model is a further development of the damage rheology framework of Lyakhovsky et al. for evolving effective elasticity. The framework provides a quantitative treatment for macroscopic effects of evolving distributed cracking with local density represented by an intensive state variable. The formulation, based on thermodynamic principles, leads to a system of kinetic equations for the evolution of damage. An effective viscosity inversely proportional to the rate of damage increase is introduced to account for gradual accumulation of irreversible deformation due to dissipative processes. A power-law relation between the damage variable and elastic moduli leads to a non-linear coupling between the rate of damage evolution and the damage variable itself. This allows the model to reproduce a transition from stable to unstable fracturing of brittle rocks and the Kaiser effect. 3-D numerical simulations based on the model formulation for homogeneous and heterogeneous materials account for the main features of rock behaviour under large strain. The model coefficients are constrained, using triaxial laboratory experiments with low-porosity Westerly granite and high-porosity Berea sandstone samples.