Damage-breakage rheology model and solid-granular transition near brittle instability

We develop a continuum-based theoretical framework that describes brittle instability and localization of deformation into a narrow slip zone as a phase transition between damaged solid and granular material. The formulation is based on irreversible thermodynamics of damage and breakage processes, each associated with a single key state variable, and corresponding energy functions for the damaged solid and granular material. Dynamic instability is associated with a critical level of damage in the solid, leading to loss of convexity of the solid energy function and transition to a granular phase associated with lower energy level. Depending on the confining stress and other conditions, the failure process in the generated granular phase may be associated with mode I and fragmentation or mode II and granular flow. The developed model provides a new approach for analyzing in a unified way various aspects of brittle failure and localization of deformation, with evolving elastic moduli, evolving slip rates and evolving material phases. Numerical simulations indicate that the key parameters governing the evolution from a slow failure process to dynamic slip, and the related transition from damaged solid to granular material, can be constrained by laboratory and seismological observations.