An iterative multiscale modelling approach for nonlinear analysis of 3D composites

The advent of new more complex classes of strongly heterogeneous materials, such as 3D woven composites, introduces new challenges for well-established finite element multiscale modelling approaches. These materials'internal architecture dominates the local stress concentrations, damage initiation and damage progression. Additionally, the material loses periodicity during manufacture and conventional homogenization approaches become inapplicable. In this paper, a multiscale modelling approach based on domain decomposition and homogenization is proposed to model the mechanical behaviour of these materials. The proposed model formulates a set of displacement and force compatibility conditions between the various subdomains. The compatibility conditions are formulated by limiting the set of kinematically admissible solutions on the smaller scales in order to satisfy the larger scale basis functions at the interfaces. The different subdomains are solved alongside the compatibility conditions in an iterative process. The proposed multiscale framework reduces the stress artefacts on the subdomains' boundaries. This feature allows the 3D woven material internal architecture represented at the smaller scales to control the structural response at the global scale. Additionally, this framework allows for selective application of nonlinear material models to the subdomains of interest through its ability to redistribute stresses across the subdomains boundaries.