Homogenization assumptions for coupled multiscale analysis of structural elements: beam kinematics

This contribution proposes a multiscale scheme for structural elements considering beam kinematics. The scheme is based on a first-order homogenization approach fulfilling the Hill–Mandel condition. Within this paper, special focus is given to the transverse shear stiffness. Using basic boundary conditions, the transverse shear stiffness drastically depends on the size of the representative volume element (RVE). The reason for this size dependency is identified. As a consequence, additional internal constraints are proposed. With these new constraints, the homogenization scheme leads to cross-sectional values independent of the size of the RVE. As they are based on the beam assumptions, a homogeneous material distribution in the length direction yields optimal results. Furthermore, outcomes of the scheme are verified with simple linear elastic benchmark tests as well as nonlinear computations involving plasticity and cross-sectional deformations.