Thin layer shear and second order homogenization method

Abstract

This paper deals with the second-order computational homogenisation of a heterogeneous material undergoing small displacements. Typically, in this approach a representative volume element (RVE) of nonlinear heterogeneous material is defined. An a priori given discretised microstructure is considered, without focusing on detailed specific discretisation techniques. The key contribution of this paper is the formulation of equations coupling micro- and macro-variables and the definition of generalized boundary conditions for the microstructure. The coupling between macroscopic and microscopic levels is based on Hill's averaging theorem. We focus on deformation-driven microstructures where overall macroscopic deformation is controlled. In the end a numerical example of a thin layer shear is presented.