A Multi-Scale Scheme for Modelling Fracture under Dynamic Loading Conditions

Abstract

Fracture in heterogeneous materials under dynamic loading is modelled using a multi-scale method. Computational homogenization is considered, in which the overall properties at the global-scale are obtained by solving a boundary value problem for a representative volume element (RVE) assigned to each material point of the global-scale model. In order to overcome the problems with upscaling of localized deformations, a non-standard failure zone averaging scheme is used. Discontinuous cohesive macro-cracking is modelled using the XFEM and a gradient-enhanced damage model is used to model diffuse damage at the local-scale. A continuous-discontinuous computational homogenization method is employed to obtain the traction-separation law for macro-cracks using averaged properties calculated over the damaged zone in the RVE. In the multi-scale model, a dynamic analysis is performed for the global-scale model and the local-scale model is solved as a quasi-static problem. Dispersion effects are then captured by accounting for the inertia forces at the local-scale model via a so-called dispersion tensor which depends on the heterogeneity of the RVE. Numerical examples are presented and the multi-scale model results are compared to direct numerical simulation results. Objectivity of the multi-scale scheme with respect to the RVE size is examined.