On optimization of heterogeneous materials for enhanced resistance to bulk fracture

TL;DR

This paper introduces a Bayesian optimization approach to design heterogeneous materials with tailored microstructures, significantly improving their fracture toughness under mode-I loading by optimizing inclusion shapes and positions.

Contribution

The paper presents a novel Bayesian optimization framework combined with phase-field fracture modeling to optimize microstructural features for enhanced fracture resistance.

Findings

Optimized microstructures show increased fracture toughness.

Method effectively accounts for initial crack location sensitivity.

Numerical results outperform homogeneous materials.

Abstract

We propose a novel approach to optimize the design of heterogeneous materials, with the goal of enhancing their effective fracture toughness under mode-I loading. The method employs a Gaussian processes-based Bayesian optimization framework to determine the optimal shapes and locations of stiff elliptical inclusions within a periodic microstructure in two dimensions. To model crack propagation, the phase-field fracture method with an efficient interior-point monolithic solver and adaptive mesh refinement, is used. To account for the high sensitivity of fracture properties to initial crack location with respect to heterogeneities, we consider multiple cases of initial crack and optimize the material for the worst-case scenario. We also impose a minimum clearance constraint between the inclusions to ensure design feasibility. Numerical experiments demonstrate that the method significantly improves the fracture toughness of the material compared to the homogeneous case.