II CONTRIBUTED ARTICLE Can Multiscale-Multiphysics Methods Predict Softening Damage and Structural Failure?

The multi scale approach was pioneered by Tadmor, Ortiz and Phillips [1] for atomistic-based quasi-continuum analysis of dislocations and hardening plasticity of polycrystalline metals. In that case, the structural failure is due to necking, which is caused by nonlinear geometric effects of finite strain, or to sharp fracture, which is modelled separately (see also [2]). There can be no dispute that the multi scale approach is realistic, delivering to the continuum macroscale an essential information on the physical behavior on the subscale. However, applying the multi scale approach to failure due to interacting crack systems, or to softening damage such as distributed cracking, is an entirely different matter. To clarify it, let us discuss a few typical multi-scale approaches representative of a flood of recent publications. Types of Subscale Interactions in Damage or Fracture The multiscale models are intended to capture two types of interactions on the microscale: 1. Interactions among orientations of micro-damage processes, e.g., orientations of tensile or splitting micro-cracks, and frictional micro-slips. 2. Interactions at distance, e.g., among different grains or fibers, or among differen