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

作者：Lyakhovsky Vladimir^*; Hamiel Yariv; Ben Zion Yehuda

来源：Journal of the Mechanics and Physics of Solids, 2011, 59(9): 1752-1776.

DOI：10.1016/j.jmps.2011.05.016

• Fracture
• Phase transformation
• Dynamics
• Constitutive Behavior
• Damage rheology

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

• 出版日期2011-9