The meshfree methods in computational mechanics have been actively proposed and increasingly developed in order to overcome some drawbacks in the conventional numerical methods. Over past three decades meshfree methods have found their way into many different application areas ranging from classical astronomical problems to solid mechanics analysis, fluid flow problems, vibration analysis, heat transfer and optimization to the numerical solution of all kind of (partial) differential equation problems. The present work is an effort to provide a comprehensive review of various Meshfree methods, their classification, underlying methodology, application area along with their advantages and limitations. Key contributions of mesh free techniques to the area of fracture mechanics have been discussed with applications of element free Galerkin method (EFGM) to fracture analysis as primary concern.

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In the present work, element-free Galerkin method (EFGM) has been extended and implemented to simulate thermal fracture in functionally graded materials. The thermo-elastic fracture problem is decoupled into two separate parts. Initially, the temperature distribution over the domain is obtained by solving the heat transfer problem. The temperature field so obtained is then employed as input for the mechanical problem to determine the displacement and stress fields. The crack surfaces are modelled as non-insulated boundaries; hence the temperature field remains undisturbed by the presence of crack. A modified conservative M-integral technique has been used in order to extract the stress intensity factors for the simulated problems. The present analysis shows that the results obtained by EFGM are in good agreement with those available in the literature.

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