Efficient Computational Strategies for Higher‐Order Homogenisation of Large‐Scale Unit Cell Models

ABSTRACT Multiscale modelling methods are important for accurately predicting the behaviour of complex, heterogeneous materials. First‐order homogenisation (1OH) has been widely used in this context but shows limitations in cases where the microstructural length scale becomes comparable to the macrostructural length scale, such as in the case of woven composites. To address these limitations, second‐order homogenisation (2OH) methods have been developed which incorporate higher‐order deformation gradients into the formulation of the RVE boundary value problem. However, the computational cost and memory requirements of 2OH, particularly in large‐scale simulations, pose significant challenges due to dense constraint matrices and non‐scalable operations. This paper presents computational solutions aimed at overcoming these bottlenecks, enabling the efficient application of 2OH to large‐scale RVE models. We introduce a predictor–corrector scheme that replaces the conventional direct displacement method in the downscaling process, significantly reducing runtime and memory usage. For upscaling, we identify memory bottlenecks during the evaluation of constitutive tangents, where we highlight limitations of conventional approaches and evaluate alternatives to provide recommendations for large‐scale RVE models. The methods are implemented on a 3D woven composite RVE, and the results demonstrate a significant reduction in computational time and memory requirements.