A coupled two-scale shell model with applications to layered structures

SUMMARYIn this paper a coupled two‐scale shell model is presented. A variational formulation and associated linearization for the coupled global–local boundary value problem is derived. For small strain problems, various numerical solutions are computed within the so‐called FE 2 method. The discretization of the shell is performed with quadrilaterals, whereas the local boundary value problems at the integration points of the shell are discretized using 8‐noded or 27‐noded brick elements or so‐called solid shell elements. At the bottom and top surface of the representative volume element stress boundary conditions are applied, whereas at the lateral surfaces the in‐plane displacements are prescribed. For the out‐of‐plane displacements link conditions are applied. The coupled nonlinear boundary value problems are simultaneously solved within a Newton iteration scheme. With an important test, the correct material matrix for the stress resultants assuming linear elasticity and a homogeneous continuum is verified.Copyright © 2013 John Wiley & Sons, Ltd.