Multiscale modelling of sandwich structured composites using direct FE2

Abstract

In finite element analyses, composite laminates are often homogenised and modelled using beam and plate elements for computational efficiency. Aside from difficulties in deriving homogenised properties for nonlinear materials and the loss in fine-scale deformation details, such structural elements are notoriously inaccurate for laminates comprising plies of distinctly different in-plane stiffnesses, notably, sandwich structured composites. A multiscale layerwise beam model is proposed to address these shortcomings. The model is based on the Timoshenko-Ehrenfest beam theory with layerwise kinematics incorporated to capture the key deformation modes of bending and transverse shear, and implemented using Direct FE2 – a versatile computational homogenisation scheme. Beyond homogenisation for the structural elements, Direct FE2 also captures deformation mechanisms at the mesoscale. More importantly, it is readily implemented using available functions in commercial FE codes, allowing for ease of adoption. A foam core sandwich structure is modelled to demonstrate that the proposed approach leads to macroscale responses and resolution to the mesoscale deformations that are almost identical to that of finely meshed solid element models, while taking only 23% of the computation time.