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


Correspondence to: F. Gruttmann, Fachgebiet Festkörpermechanik, Technische Universität Darmstadt, Petersenstr. 13, 64287 Darmstadt, Germany.



In 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.