Numerical methods for multiscale modelling of fibre composites

Doctoral thesis, 2024

Fibre composite materials are inherently heterogeneous, often characterised by a complex internal substructure that includes various material phases and interfaces. The intricate substructure, at both the microscale and mesoscale, gives rise to a wide range of damage mechanisms that grow and propagate before they eventually manifest at the macroscale. To accurately capture and predict fibre composite behaviour at the macroscale, a comprehensive multiscale approach which includes information from the subscale is essential. This thesis addresses key challenges for multiscale modelling of fibre composites, focusing on the development of numerical methods at the macroscale, mesoscale, and the coupling between them.

In order to incorporate information from the mesoscale into the model at the macroscale, we develop a two-scale computational homogenisation framework. As fibre composites are often used in thin-ply applications, the homogenisation framework is developed for plate elements, specifically plates with Reissner–Mindlin kinematics. Moreover, a vital part for any effective homogenisation framework is to establish accurate prolongation and homogenisation constraints. To this end, we demonstrate how Variationally Consistent Homogenisation (VCH) can be employed to derive constraints which link the mesoscale and macroscale in a kinematically consistent manner.

At the macroscale, we address the challenges related to efficient and robust modelling of delamination in multilayered composites. Current state-of-the-art modelling techniques typically resolve each individual layer using multiple solid elements in conjunction with cohesive zone elements at the laminae interfaces, which results in computationally demanding models. In response to this, we develop an isogeometric shell element which can adaptively refine its through-thickness discretisation in areas where delamination is active. Thereby, the computational effort is kept low. To address the convergence issues typically encountered when simulating brittle delamination, we develop an arc-length solver that is augmented with the dissipation rate of the system. In this manner, we are able to trace the initiation and propagation of multiple delamination in a robust manner.

For accurate mesoscale modelling, it is crucial to include a detailed representation of the geometry and material constituents (fibre and matrix phases). However, incorporating high levels of geometric detail of the mesoscale structure presents significant challenges for meshing software, as it complicates the generation of good quality meshes. To address these challenges, we investigate the use of Immersed Boundary Methods, whose primary advantage is the automation of the discretisation process. We propose a modelling framework that streamlines the discretisation process for mesoscale models, demonstrating its ability to homogenise stiffness properties and accurately predict the subscale stress field.