A new fully coupled two-scales modelling for mechanical problems involving microstructure: The 95/5 technique

In this work, we propose a new fully coupled two-scales modelling for mechanical problems involving microstructure which makes use of a meshless constrained natural element approximation for accounting the large and very localized variations in the nodal density. This approach is an appealing choice for treating problems involving a microstructure (requiring fine local descriptions) whose evolution can be accurately described in the macroscopic scale using coarse approximations. This approach leads to a model where more than 95% of the nodes are in less than 5% of the considered domain volume.The technique proposed in this paper allows considering simultaneously both scales, the one related to the microstructure description and the one related to its evolution (the macroscopic one). Moreover, in contrast to the vast majority of homogenization techniques, the presented approach allows an accurate description of the boundary conditions, because the microscopic domains can be located on the domain boundary.