A non-local visco-elastic damage model and dynamic fracturing

摘要: We present an extended formulation of a non-linear continuum visco-elastic damage rheology that accounts for non-local accumulation, dynamic fracturing, and transition from solid to granular state in the slip zone. Generalizing standard Hookean strain energy, model has three additional energy terms: non-analytic second-order function first second invariants, term proportional rate, spatial gradient variable. The leads stress–strain relation, with abrupt changes effective elastic moduli upon stress reversal compression tension along damage- stress-induced anisotropy. gives rise Kelvin–Voigt viscous relaxation. resulting combines Maxwell visco-elasticity, accounting both long-term relaxation short-term dissipation stabilizing evolution. third produces finite length scale diffusion eliminates unrealistic singular localization local model. An equation evolution derived basic thermodynamic considerations quantifies kinetics under different conditions, including quasi-static degradation gradual healing. In vicinity macroscopic failure, at critical level associated loss convexity function, includes damaged flow dynamics. provides framework studying multiple aspects brittle deformation, potential feedback mechanisms between evolving related properties zone subsequent rupture behavior. Several features existence width slow rapid are illustrated using numerical simulations. analysis clarifies dependency some parameters on examined domain boundary conditions which simpler descriptions appropriate.