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Multiscale Modelling of Heterogeneous Structures Using Second-Order Computational Homogenization

A second-order two-scale computational homogenization procedure for modelling deformation responses of heterogeneous structures assuming small strains is presented. The macro-to-micro scale transition and generalized periodic boundary conditions on the representative volume element (RVE) are investigated. The macroscale is discretized by means of C1 two-dimensional triangular finite elements, while standard quadrilateral finite elements are used for the RVE discretization. The new proposed multiscale scheme has been implemented into the finite element software ABAQUS using user subroutine. The efficiency of the proposed multiscale homogenization approach is demonstrated by modelling of a pure bending problem.

multiscale analysis, heterogeneous materials, second-order homogenization, C1 finite element, periodic boundary conditions, Abaqus

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