Robust analysis of delaminating composites using adaptive isogeometric shell elements

Fibre reinforced composites are considered to be one of the material categories that offer the best possibilities to create efficient lightweight designs. Many companies in the transport sector therefore work towards increasing the amount of fibre composites in their products, in an attempt to lower the fuel consumption of their vehicles. However, from the perspective of simulation-driven design, an increased use of composite materials is accompanied with new modelling challenges. In this thesis, two such challenges have been considered.The first challenge concerns the often computationally demanding models needed to simulate delamination in fibre composites. The heterogeneous through-thickness nature of fibre composites necessitates a very fine through-thickness discretisation in order to capture the delamination process, which leads to very long (or even infeasible) simulation times. The second challenge addressed in this thesis is related to the difficulties arising when simulating the post-failure response of fibre composites. Specifically, in quasi-static simulations, the brittle material interfaces of layered fibre composites can lead to sudden failure, which standard incremental Newton-Raphson solvers are not able to trace.To address these problems, two new computational tools have been developed that can aid the design process of fibre reinforced composites. Firstly, in Paper A, an adaptive isogeometric shell element has been developed, that can refine its through-thickness kinematics as delamination propagates. Consequently, only the lowest level of detail needed to capture delamination is included in the model, which improves efficiency. To address the second issue, a dissipation based path-following solver has been developed in Paper B, which is able to robustly trace the equilibrium path of the post-peak response in quasi-static simulations.Both Paper A and Paper B shows that the developed adaptive isogeometric shell element and the dissipation based path-following solver can be combined to robustly and efficiently simulate composite structures with brittle delamination behaviour. Consequently, it is shown that the computational tools developed in this thesis can be used to aid the design process of fibre reinforced structures