Second-Order Computational Homogenization Scheme Preserving Microlevel <i>C</i><sup>1</sup> Continuity

Abstract

The paper deals with a new second-order computational homogenization procedure for modeling of heterogeneous materials at small strains, where C1 continuity is preserved at the microlevel. The multiscale model is based on the Aifantis theory of gradient elasticity. The C1 two dimensional triangular finite element used for the discretization of macro-and microlevel is described. Contrary to the C1 - C0 transition, here besides the displacements, the displacement gradients are included into the boundary conditions on the representative volume element (RVE). According to the second order continuum at microlevel, the relevant homogenization relations are derived. Finally, the performance of the algorithms derived is investigated. Dependency of homogenized stresses on mesh density and microstructural parameter l are examined in simple loading cases.