ABSTRACT
This paper deals with the first-order and second-order computational homogenization 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 discretized microstructure is considered, without focusing on detailed specific discretization 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 level is based on Hill's averaging theorem. We focus on deformation-driven microstructures where overall macroscopic deformation is controlled.