Isogeometric analysis-based approaches for fracture and contact problems of structures and materials

• Main Author: Huang, Jiazhao
• Other Authors: Zhou Kun
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2020
• Subjects: Engineering::Mechanical engineering
• Online Access: https://hdl.handle.net/10356/137400
• Institution: Nanyang Technological University

The field of fracture mechanics focuses on investigating the crack initiation and propagation in materials. Since the presence of cracks within materials cannot be precluded during the manufacturing processes, the mechanical and physical properties of engineering structures would be significantly affected by cracks, resulting in the fractures of these structures. Contact mechanics is another important subject of engineering as many mechanical components are operating under contact loading conditions. Analysis of stress and deformation induced by contact loading is complicated due to its multi-scale and multi-physical nature. For both fracture and contact problems, isogeometric analysis (IGA) has been developed as a promising computational tool that exhibits significant advantages in terms of geometry exactness, high-order approximation and tailorable inter-element connectivity. This Ph.D. study aims at developing IGA-based solutions for fracture and contact problems of structures and materials. Firstly, a novel extended IGA approach has been developed for the buckling analysis of cracked Mindlin-Reissner plate under prescribed edge pressure. IGA is extended to fracture analysis by applying enrichment functions around the pre-existing crack. Discrete shear gap method is further applied to address shear locking, which allows extended IGA to be applicable for both thick and thin plates. This approach is able to obtain a high convergence of results and preserve the exact geometry of contact surfaces. Secondly, a novel isogeometric-meshfree (IMF) coupling approach has been developed to study the contact of two homogeneous materials. The overall contact domain is divided into two subdomains which are formulated by IGA and meshfree method, respectively. IGA is applied in a thin region along the contact surfaces while meshfree method is adopted within the subsurface. The IMF coupling approach can solve contact problems involving large deformation and sliding through the smooth representation of contact surface. Finally, an adaptive local refinement strategy is introduced into the IMF coupling basis functions to form adaptive IMF (AIMF) coupling approach for the limit analysis problems of cracked structures. The entire parametric domain is represented by a unified IGA and meshfree basis function which allows the adaptive local refinement for IGA to be performed in a straightforward meshfree manner. Guided by an indicator of plastic dissipation, the AIMF coupling approach achieves higher convergence rates than reference methods with global refinement. The work reported in this thesis demonstrated that the development of IGA-based approaches improves our understanding of the fracture and contact behaviours of structures and materials. The research outcomes are envisaged to contribute to function and safety designs of various engineering applications.