Microstructure-Informed Constitutive Modeling based on Neural Network

Abstract

Understanding how microstructural architecture governs macroscopic mechanical behavior is central to multiscale materials design, yet existing microstructure-informed workflows either rely on extensive experimental studies or costly microstructure-homogenization simulations. This thesis develops a unified, data-driven constitutive modeling framework that directly maps continuous two-phase microstructure to linear and nonlinear effective responses using statistical descriptors, bypassing reconstruction and generalizing across diverse morphologies. We first construct Micro3D, a statistically diverse synthetic dataset of binary microstructures using Gaussian random fields and multiple morphology generators, from which two-point statistics are extracted and compressed to serve as compact, physics-meaningful inputs. For the linear regime, a two-branch multilayer perceptron (MLP) is constructed with embedded symmetry and positive-definiteness constraints, using a Cholesky-based representation to predict the effective tensor. For the nonlinear regime, a hybrid framework combining a three-branch architecture, a hypernetwork, and an input-convex neural network (ICNN) is developed to capture complex material behaviors. Both models demonstrate strong generalization to unseen microstructures, with the nonlinear model accurately reproducing responses under previously unseen loading paths. Together, these components provide a practical route to microstructure-informed surrogate models that are interpretable, extensible, and suitable for downstream simulation.