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

A generalised path-following solver for robust analysis of material failure

When analysing complex structures with advanced damage or material models, it is important to use a robust solution method in order to trace the full equilibrium path. In light of this, we propose a new path-following solver based on the integral of the rate of dissipation in each material point, for solving problems exhibiting large energy dissipating mechanisms. The method is a generalisation and unification of previously proposed dissipation based path-following solvers, and makes it possible to describe a wider range of dissipation mechanisms, such as large strain plasticity. Furthermore, the proposed method makes it possible to, in a straightforward way, combine the effects from multiple dissipation mechanisms in a simulation. The capabilities of the solver are demonstrated on four numerical examples, from which it can be concluded that the proposed method is both versatile and robust, and can be used in different research domains within computational structural mechanics and material science

An adaptive isogeometric shell element for the prediction of initiation and growth of multiple delaminations in curved composite structures

In order to model prominent failure modes experienced by multi-layered composites, a fine through-thickness discretisation is needed. If the structure also has large in-plane dimensions, the computational cost of the model becomes large. In light of this, we propose an adaptive isogeometric continuum shell element for the analysis of multi-layered structures. The key is a flexible and efficient method for controlling the continuity of the out-of-plane approximation, such that fine detail is only applied in areas of the structure where it is required. We demonstrate how so-called knot insertion can be utilised to automatise an adaptive refinement of the shell model at arbitrary interfaces, thereby making it possible to model multiple initiation and growth of delaminations. Furthermore, we also demonstrate that the higher-order continuity of the spline-based approximations allows for an accurate recovery of transverse stresses on the element level, even for doubly-curved laminates under general load. With this stress recovery method, critical areas of the simulated structures can be identified, and new refinements (cracks) can be introduced accordingly. In a concluding numerical example of a cantilever beam with two initial cracks, we demonstrate that the results obtained with the adaptive isogeometric shell element show good correlation with experimental data

Variationally consistent homogenisation of plates

Advanced fibre composite materials are often used for weight-efficient thin-walled designs, making a plate-based modelling approach suitable for their structural assessment. However, as the sub-structural geometrical features of these materials govern much of their behaviour, a multi-scale approach is necessary. A related challenge, however, is that the in-plane variation of these sub-structural features may be much larger than the total thickness of the material, whereby tailored homogenisation techniques for shell elements are needed. Existing frameworks for plate- and shell-based homogenisation are typically developed using second-order homogenisation in combination with the Hill–Mandel (macro-homogeneity) condition. However, it has been reported in the literature that this approach can lead to kinematic inconsistencies in the macro- to micro-scale transition. One inconsistency that is commonly reported, is the inability to correctly account for the macro-scale transverse shear behaviour on the sub-scale level. In this contribution, we show how the method of Variationally Consistent Homogenisation (VCH) can be used to develop a homogenisation framework for Reissner-Mindlin plate elements, which guarantees kinematically consistent prolongation and homogenisation operations. The homogenisation approach is demonstrated in four numerical examples, where it is shown that the method accurately homogenise the effective sectional plate stiffnesses of homogeneous and heterogeneous sub-structures