Multi-scale modelling of sandwich structures using hierarchical kinematics

The aim of this paper is to present a multi-scale method for the mechanical modelling of sandwich structures. Low- and high-order sandwich elements are formulated on the basis of Carrera's Unified Formulation (CUF) and bridged within the Arlequin framework. According to CUF, an N-order polynomials approximation is assumed on the beam cross-section for the unknown displacements, being N a free parameter of the formulation. Low-order, computationally cheap elements are used to describe the global mechanical response. High-order, computationally demanding elements are used to capture the local effects in the boundary layers. CUF framework is here enhanced by the assumption of the Constrained Variational Principle (CVP) in order to derive a new class of layered beam finite elements with an independent kinematic field for each lamina. Results are assessed towards two- and three-dimensional finite element solutions. The numerical results show that, in the context of CUF, the Arlequin method effectively couples sub-domains modelled via variable order finite elements. The proposed coupled models yield accurate results, being able to predict both the global solution and the local effects, with a reduced computational cost.