Multi-scale computational homogenisation of the fibre-reinforced polymer composites including matrix damage and fibre-matrix decohesion

This paper summarises the on-going work at the University of Glasgow on the computational modelling of the hygro-mechanical behaviour of textile based fibre reinforced composite materials, including the strong coupling of the solid and moisture phases. A multiscale description is adopted and the associated implementation of the computational homogenisation (CH) scheme is described in detail. The ultimate goal is a multiscale modelling framework for durability assessment. CH delivers the macroscopic constitutive behaviour of the structures based on its microscopically heterogeneous representative volume element (RVE). A single layered plain weave textile composite RVE is considered, which consists of mainly two parts, i.e. yarns and matrix. Elliptical cross sections and cubic splines are used respectively to model the cross sections and paths of the yarns. The RVE geometry along with other input parameters, e.g. material properties and boundary conditions are modelled in CUBIT using a parameterised Python script. The multiscale CH scheme, with a unified imposition of RVE boundary conditions (displacement, traction and periodic) [1], is implemented in our group’s FE software MoFEM (Mesh Oriented Finite Element Method). MoFEM utilises hierarchic basis functions [2], which permits the use of arbitrary order of approximation leading to accurate results for relatively coarse meshes. The matrix and yarns within the RVE are modelled by considering isotropic and transversely isotropic materials models respectively. The principal direction of the yarns required for the transversely isotropic materials model are calculated using a computationally inexpensive potential flow analysis along these yarns. The implementation and performance of the computational tool is demonstrated with numerical examples.