Machine‐learning‐based asymptotic homogenisation and localisation considering boundary layer effects

Abstract

AbstractAsymptotic homogenisation offers a way to efficiently analyse the mechanical behaviour of multiscale configurations. But near a multiscale boundary, the homogenisation strategy should be modified, as the underlying periodicity assumption breaks down there. In this article, we introduce a machine‐learning‐based asymptotic homogenisation and localisation scheme to formulate such boundary layer effects. To this end, we define a set of boundary layer cells, where external loading conditions are imposed on one side of the cell, and matching conditions with the interior periodic cells are imposed on the opposite side. The formulation is also extended to cover situations where the multi‐scale structure is not fully periodic, but spatially varying. Implied from the asymptotic results, neural networks can be trained to memorise the interrelationship between key local quantities, such as the magnitude of the local maximum von Mises stress, and the local mechanical and geometric features. Equipped with the trained neural networks, the online calculation for key (boundary‐localised) quantities of interest under arbitrary loading conditions is expected to be accelerated substantially. Numerical examples are further presented to show the reliability of the proposed work for boundary stress prediction.