Multi-layer perceptron-based data-driven multiscale modelling of granular materials with a novel Frobenius norm-based internal variable

Abstract

One objective of developing machine learning (ML)-based material models is to integrate them with well-established numerical methods to solve boundary value problems (BVPs). In the family of ML models, recurrent neural networks (RNNs) have been extensively applied to capture history-dependent constitutive responses of granular materials, but these multiple-step-based neural networks are neither sufficiently efficient nor aligned with the standard finite element method (FEM). Single-step-based neural networks like the multi-layer perceptron (MLP) are an alternative to bypass the above issues but have to introduce some internal variables to encode complex loading histories. In this work, one novel Frobenius norm-based internal variable, together with the Fourier layer and residual architecture-enhanced MLP model, is crafted to replicate the history-dependent constitutive features of representative volume element (RVE) for granular materials. The obtained ML models are then seamlessly embedded into the FEM to solve the BVP of a biaxial compression case and a rigid strip footing case. The obtained solutions are comparable to results from the FEM-DEM multiscale modelling but achieve significantly improved efficiency. The results demonstrate the applicability of the proposed internal variable in enabling MLP to capture highly nonlinear constitutive responses of granular materials.

Keywords

• Granular materials
• History-dependence
• Multi-layer perceptron (MLP)
• Discrete element method
• FEM-DEM
• Machine learning