MESHFREE SIMULATION OF FRACTURE MECHANICS PROBLEMS UNDER THERMO-MECHANICAL LOADING

Abstract

The quest for perfection has led us to all the scientific developments and technological advancements. In spite of all the scientific developments, the flaws and imperfection in materials often leads to catastrophic consequences. Fracture is one of the most prevalent damage phenomena that society has faced for as long as there have been man-made structures. Over the past few decades, greater understanding of fracture mechanics has prevented a substantial number of structural failures. Cracks are inevitable in all engineering components. External loadings may result in either the propagation of pre-existing cracks or may initiate new cracks in the structures. This may finally lead to catastrophic failure of the components resulting in loss of property and lives. Due to the scarcity of analytical solutions and also due to the versatility of the numerical methods in handling complex practical problems, research efforts continue to focus on improving the numerical schemes. A new class of numerical methods known as meshfree method has been developed over the past 15 years. The meshfree method is a rather interesting complement to the traditional finite element method. The first advantage of a meshfree method is that it is possible to construct arbitrarily high order approximation for higher order problems. Secondly, the numerical integration can be performed on arbitrary cells covering the computational domain so that the expensive meshing and remeshing process can be avoided. Moreover, the mesh distortion insensitivity makes them a boon for the problems involving large deformation. These characteristics together, proffer the potential of meshfree methods in simplifying adaptive analysis and crack growth modeling in fracture mechanics. Present research work focuses on the implementation and extension of the most popular meshfree method known as the element free Galerkin method (EFGM) to analyze a variety of fracture mechanics problems under thermal/mechanical loads. The versatility and the effectiveness of EFGM have been demonstrated through the solution of various problems. Moreover, few modifications have been proposed and implemented to enhance the proficiency of EFGM. ii Abstract Simulating the problem of fracture mechanics requires some suitable crack modeling criterion. A comparison of various crack modeling techniques in EFGM unveiled the advantages of intrinsic enrichment criterion. Owing to its accuracy, convergence, ease of implementation and modifications, the intrinsic enrichment criterion was further exploited to accomplish the remaining research work. Weak discontinuities in EFGM were modeled and compared using different existing criteria. The Jump function approach proved to be best among the available techniques for the modeling of material discontinuities. A new criterion for modeling bi-material interfacial crack using Jump function has been proposed. The proposed method involves only four enrichment functions in the basis instead of the usual twelve. Thus, computational complexity is significantly reduced. In an attempt to simulate and analyze the effect of multiple cracks interaction in both convex and non-convex domains, a new intrinsic enrichment based criterion has been proposed, and implemented. Apart from accurate simulation, the proposed criterion effectively reduces the computational cost of the EFGM. The EFGM has also been extended to simulate two-dimensional thermo-elastic fracture problems in isotropic material. Both temperature and mechanical fields were enriched intrinsically in order to represent the discontinuous temperature, heat flux, displacement and traction across the crack surface. Some example problems of fracture in functionally graded materials were tackled by EFGM under thermal/mechanical loads. Motivated by the wide applicability of EFGM and to establish it as a robust tool for solving problems of fracture mechanics, the simulation of elasto-plastic fracture problems has been carried out for two dimensional cracked bodies. The enriched basis functions were used in order to capture the HRR (Hutchinson-Rice-Rosengren) singularity. Finally, a new enrichment based EFGM criterion has been developed for modeling the kinked cracks. The proposed criterion was used for the simulation of quasi-static crack growth problems under mixed-mode loading conditions. The ease of modeling quasi-static crack growth highlights the strength of the proposed criterion. Moreover, the crack growth simulation also demonstrates the modeling capability of EFGM without any requirement of re-meshing.