Concurrent and upscaling methods in multi scale modelling – case studies

Selected examples of applications of multi scale modeling in various areas of mechanics and materials science are presented in the paper. Advantages and disadvantages of these approaches are shown. Based on the literature review a classification of multi scale methods into two groups was pointed out. The first is upscaling group based on representative volume element. The second is concurrent group, where the method used to describe the fine scale is usually applied to a part of the whole domain of the solution. Detailed discussion of these two groups is based on the multi scale models developed by the Authors. The concurrent model is based on the combination of the molecular dynamic with the boundary element method and is applied to simulation of material failure. The upscaling model is called CAFE and is based on the combination of the cellular automata with the finite element method. Applications of this model to prediction strain localization in materials subjected to plastic deformation are also demonstrated in the paper.