Level‐set topology optimization for maximizing fracture resistance of brittle materials using phase‐field fracture model

• Published in: International journal for numerical methods in engineering Vol. 121; no. 13; pp. 2929 - 2945
• Main Authors: Wu, Chi, Fang, Jianguang, Zhou, Shiwei, Zhang, Zhongpu, Sun, Guangyong, Steven, Grant P., Li, Qing
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 15.07.2020; Wiley Subscription Services, Inc
• Subjects: Algorithms; Brittle fracture; Brittle materials; Composite structures; Computer simulation; Crack initiation; Crack propagation; Dental bridges; Dental materials; Dentures; Failure modes; Fracture mechanics; fracture resistance; Fracture toughness; Inclusions; level‐set; Mathematical analysis; Matrix materials; Maximization; Optimization; phase‐field; Prostheses; Time dependence; Topology optimization
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6340

Summary Fracture is one of the most common failure modes in brittle materials. It can drastically decrease material integrity and structural strength. To address this issue, we propose a level‐set (LS) based topology optimization procedure to optimize the distribution of reinforced inclusions within matrix materials subject to the volume constraint for maximizing structural resistance to fracture. A phase‐field fracture model is formulated herein to simulate crack initiation and propagation, in which a staggered algorithm is developed to solve such time‐dependent crack propagation problems. In line with diffusive damage of the phase‐field approach for fracture; topological derivatives, which provide gradient information for the topology optimization in a LS framework, are derived for fracture mechanics problems. A reaction‐diffusion equation is adopted to update the LS function within a finite element framework. This avoids the reinitialization by overcoming the limitation to time step with the Courant‐Friedrichs‐Lewy condition. In this article, three numerical examples, namely, a L‐shaped section, a rectangular slab with predefined cracks, and an all‐ceramic onlay dental bridge (namely, fixed partial denture), are presented to demonstrate the effectiveness of the proposed LS based topology optimization for enhancing fracture resistance of multimaterial composite structures in a phase‐field fracture context.