ABSTRACT
This chapter presents a brief description of various meshfree methods, along with their developments over the course of time. A brief description of one of the most prevalent and robust meshfree methods, known as the element-free Galerkin method, is explored. Theoretical aspects of the element-free Galerkin method are introduced, including the terminology and basic concepts. There is a special focus on the application of the element-free Galerkin technique to modeling and simulation of fracture mechanics problems. A number of numerical problems are discussed in the chapter to illustrate the adaptability and robustness of the element-free Galerkin Method.
