Damage Mechanics Based Deep Learning Model Surrogates for Fracture Prediction and Inverse Design

Abstract

Characterizing the mechanical behavior of heterogeneous composites presents significant challenges due to variations in material properties and scale-dependent phenomena. Accurate modeling of microscale damage requires advanced computational methods. The phase field damage model, coupled with the finite element method (FEM), effectively predicts fracture strength and damage patterns in quasi-brittle materials but is computationally demanding for heterogeneous composites. This computational complexity has motivated the exploration of more efficient surrogate models, including those based on micromechanics and deep learning (DL). Recent advances in DL, particularly Convolutional Neural Networks (CNNs) and grid-based neural networks, offer promising opportunities. DL's ability to extract complex patterns from diverse data forms makes it well-suited for mechanics problems that require understanding full-field values and their evolution. The customizable target function and differentiability of the DL model facilitate the incorporation of physics-based information and simplify its application to solving inverse problems. However, DL applications in computational damage mechanics for heterogeneous composites remain relatively unexplored. This dissertation seeks to develop efficient DL frameworks, including data-driven surrogates and a physics-informed cell-based network, to enhance phase-field damage model predictions of microscopic damage patterns, mechanical performance characterization, and inverse design in heterogeneous materials. The key contributions of this dissertation are: (i) the development of a two-stage CNN-based surrogate model for predicting peak load, which first transforms a given fiber-encoded microstructure image into a continuous damage field and then predicts the peak load based on that damage field; (ii) the establishment of an inverse design framework for optimizing microstructures, integrating a CNN surrogate for the phase-field damage model with a differentiable simulator; and (iii) the implementation of a physics-informed cell representation for the variational formulation of phase-field damage and multiscale elliptic partial differential equations, which enables the use of a decoupled training scheme to apply Dirichlet boundary conditions and a parameter-sharing scheme to enforce periodic boundary conditions.