Modelling woven composites with shell elements: An application of second-order computational homogenisation

3D woven composites are gaining traction in the aerospace industry due to their enhanced mechanical properties. However, their complex internal architectures pose challenges in understanding their behaviour across different length scales. Computational homogenisation techniques emerge as a practical alternative to high-fidelity modelling, facilitating analysis on the structural scale. While the classical first-order homogenisation framework is well-established, it has limitations that are addressed by higher-order approaches such as second-order homogenisation. These advanced approaches incorporate strain gradients and higher-order deformation modes into fine-scale models, proving effective in bending-dominated problems. The current study implements a thick shell-based second-order homogenisation framework to multi-layer 2D and 3D woven composites. It underscores the framework's proficiency in providing accurate constitutive relations for bending components. Through simulation of ASTM standardised tests, comparative studies are conducted for first and second-order homogenisation against high-fidelity models, which not only demonstrates their effectiveness but also identifies their limitations.