ENHANCING COMPUTATIONAL EFFICIENCY IN MULTI-PHYSICS FRACTURE ANALYSIS AND TOPOLOGY OPTIMIZATION USING ADAPTIVE PHASE-FIELD METHOD

Abstract

In civil engineering, aging structures often develop cracks over time, posing significant risks of failure. Accurately predicting these failures and understanding the underlying fracture processes are crucial for maintaining structural safety. The phase-field fracture (PFF) method is effective in predicting complex crack patterns such as crack initiation, branching, and merging. However, its high computational cost limits its practical application. This thesis addresses the challenge of computational expense in fracture analysis by uti lizing the phase-field method with efficient algorithms like auto sub-stepping and multi level adaptive mesh refinement (ML-AMR). The study focuses on three different PFF mod els—AT1, AT2, and PF-CZM—to explore the behavior of various materials and geometries under mechanical, thermo-mechanical, and dynamic loading conditions. The integration of ML-AMR into the phase-field method results in a significant reduction in computation time, ranging from 50% to 99%, while preserving accuracy in capturing crack paths, peak loads, and total strain energy in multi-physics scenarios. Additionally, the algorithm is extended to in corporate sparse polynomial chaos expansion (PCE) to predict fractures using the phase-field method. Beyond fracture analysis, this research also focuses on topology optimization, driven by advancements in 3D printing technology. Both density-based and phase-field methods are uti lized to address 3D topology optimization problems. State-of-the-art algorithms, developed in-house, are applied to solve various industrial challenges, including plate and shell topology optimization as well as large-scale optimization problems. These algorithms are further ex tended to design auxetic metamaterials using functionally graded materials, demonstrating their efficiency in enhancing fracture resistance. In the context of industrial applications, the developed tools are used to address large scale engineering problems. This research provides valuable strategies for engineers, offering practical insights to prevent crack-induced failures and improve the durability of engineering structures.