Learning from Data and Physics for Multiscale Modeling of Woven Composites

Abstract

Developing new composite materials with enhanced properties relied on a long trial-and-error process, requiring extensive mechanical testing and deep knowledge about fundamental phenomena and constituent interactions. While analytical micromechanical models have successfully predicted the effective properties of heterogeneous materials with idealized microstructures, computational methods and increased computing power have made it possible to overcome simplifying assumptions. This allows for considering realistic microstructures with complex behaviors and interactive effects of multiple scales on the effective composite behavior.

Despite these advances, simulations of complex multiscale heterogeneous materials, like woven composites, and the transitions from microscale to macroscale still demand significant computational resources, making their integration into fast, practical user codes a persistent challenge. Data-driven surrogate models based on neural networks address the computationally demanding challenge but often suffer from high data requirements, limited interpretability, and poor extrapolation capabilities.

This dissertation explores the intersection of multiscale material analysis and neural networks, aiming to develop a generalized model that can infer woven composites' meso- and macroscale behavior from general load conditions and micromechanical constitutive properties. Several neural network-based surrogate models are designed to serve as efficient alternatives to conventional homogenization techniques, enabling fast and scalable predictions across scales for both elastic and elasto-plastic conditions.

A key focus of this work is to lower the barriers to applying deep learning in multiscale material modeling. To achieve this, strategies are investigated to reduce the required training data while maintaining high-fidelity representations of time-dependent material behavior. Additionally, efforts are made to embed fundamental material constitutive laws directly into neural network architectures. This approach not only follows computational homogenization for woven composites but also enables extrapolation beyond training data while enhancing the explainability of path-dependent network predictions.

Given the interdisciplinary nature of these contributions, the thesis includes introductions that provide the necessary theoretical background for a deeper understanding of the appended papers.