Mesh objective simulations of large strain ductile fracture: A new nonlocal Johnson-Cook damage formulation for the Total Lagrangian Material Point Method

Abstract

We present mesh objective simulations of large strain fracture of metals using a Total Lagrangian Material Point Method. The mesh objectivity is obtained by developing two nonlocal formulations of the well known Johnson-Cook damage criterion: an integral and a gradient enhanced formulation. Unlike previous nonlocal models in which the nonlocal variable is the plastic strain, we adopt the ratio of the plastic strain and the failure strain as the nonlocal variable. Using one simulation we demonstrate that the integral type nonlocal formulation results in incorrect damage initiation (i.e., not at the sample edge but within the sample). We then focus on the gradient enhanced formulation and use it to simulate three common benchmarks for quasi-static large strain ductile fracture of metals and one impact fracture of a metal plate hit by a blunt bullet. All the results exhibit mesh independence and are in good agreement with previous findings and experiments.