Numerical simulations of dynamic fracture and fragmentation problems by a novel diffusive damage model

Abstract

In this paper, we report numerical simulations for dynamic fracture and fragmentation problems in brittle materials using a recently developed split strain energy diffusive mass-field damage model in terms of standard finite element method (FEM). The enhanced constitutive laws for mass source and mass flux by means of strain energy decomposition are adopted to overcome certain drawbacks of the original non-split model. We present theoretical formulations in a more general way that is suitable and valid for both small and finite deformation regimes. The coupled system of equations is derived in which the momentum is governed to describe the time-dependent deformation of brittle solids whereas the mass-diffusion balance equations are for the evolution of mass density. We also develop simple techniques for determining crack velocity and estimating amount of mass loss. Numerical examples are considered for both small and finite deformations. The accuracy and performance of the developed theory for dynamic brittle fracture are illustrated through comparison and verification, which are to compare the computed results with respect to experimental data and other numerical methods in terms of crack path trajectories, dynamic response, energy dissipation, and other relevant numerical aspects.