Use of effective multiscale cohesive models in the simulation of spall in metal plates

Ductile fracture of metals is the net result of void nucleation, growth and coalescence mechanisms that operate at the microscale. Optimal scaling analysis provides the analytical form of the effective material law that models the ductile fracture phenomena at the macroscale. The upscaled model of ductile behavior assumes the form of a cohesive relation—surface traction versus displacement—of the power-law type with well-defined exponents. In the present work, we demonstrate how the effective cohesive law derived from optimal scaling can be conveniently inserted into macroscale calculations by recourse to cohesive elements. The plastic deformation outside the cohesive elements is of moderate size and can be modeled by means of conventional plasticity models. In particular, the mesh size is dictated by accuracy considerations at the macroscale structural level and is not in any way constrained by microscale features and mechanisms, which happen at the subgrid level and are accounted for by the effective cohesive law. We illustrate the multiscale paradigm by means of spall calculations.