Adaptive topology optimization for enhancing resistance to brittle fracture using the phase field model - Zhang, Qi (2024)
Computational cost is one of the challenges in the field of fracture resistance topology optimization. An efficient topology optimization approach is proposed for enhancing resistance to structural fracture based on the adaptive isogeometric–meshfree method. The mesh can be adaptively refined in the computational and design domains simultaneously to capture the fracture and structural boundary delicately, which significantly reduces the degree of freedom and improves the efficiency of the topology optimization problems related to crack propagation. The proposed approach naturally inherits the advantages of both the computer-aided design and continuity of the higher-order basis functions, where the geometry and the analysis models in the process of topology optimization are integrated. The problem is formulated to maximize the absorbed energy throughout the crack process using the solid isotropic material with penalization method under volume constraints. The phase field method is used for modeling crack propagation, thereby eliminating the need of an explicit representation of the crack surface and complex tracking procedures, while a delicate mesh is still required. With this approach, the external work required during the fracture process is maximized, and the crack growth is delayed remarkably. Several representative examples are demonstrated to verify the effectiveness of the present approach in fracture-resistance-enhanced topology optimization, and the computational cost shows remarkable improvement.