Structural Optimization for Fracture Resistance of Heterogeneous Materials

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Doctoral Thesis
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Singh, Sukhminder

In the realm of structural optimization, a key objective is the maximization of the service life of structures, while avoiding premature failure due to unexpected, brittle fracture. Cracks, which can arise from manufacturing defects or stress concentrations, may propagate through the structure due to fatigue or corrosion. The incorporation of tailored heterogeneous materials can enhance macroscopic fracture toughness by virtue of the interaction between cracks and the heterogeneities. While optimization methods for structural compliance, which consider predefined stationary cracks with volume and/or stress constraints, are well-established, methods that account for propagating cracks are still in an early stage of development. In this work, we propose three optimization frameworks incorporating crack propagation in heterogeneous materials under mode-I loading in a two-dimensional setting, where the shape/material parameters of the embedded elliptical heterogeneities are optimized. The first is an adjoint sensitivity-based optimization framework that enhances interfacial fracture resistance quantified by external mechanical work with respect to orientations of the orthotropic material, considering a small number of potential crack paths. This method is designed to optimize for the worst-case scenario among the defined crack paths. In the second, we propose a novel derivative-free approach for use in a stochastic optimization setting to produce robust designs with respect to shape parameters under noise. Here, an approximate gradient based on Monte Carlo estimation and nearest-neighbor interpolation of the available data is used to take the next optimization step. The third framework employs a Bayesian optimization strategy with Gaussian processes to optimize resistance to bulk fracture, modeled using the phase-field method. An interior-point monolithic solver is used, along with adaptive mesh refinement near the crack tip and subsequent coarsening along the tail of the crack to reduce the computational burden of the fracture simulation. The goal is to maximize the peak J-integral value under surfing boundary conditions, while also considering the high sensitivity of the initial crack's location relative to the periodic microstructure. The presented optimization experiments demonstrate significant improvements in the fracture resistance with justifiable computational cost.

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