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This book describes the basics and developments of the new XFEM approach to fracture analysis of structures and materials. It provides state of the art techniques and algorithms for fracture analysis of structures including numeric examples at the end of each chapter as well as an accompanying website which will include MATLAB resources, executables, data files, and simulation procedures of XFEM. The first reference text for the extended finite element method (XFEM) for fracture analysis of structures and materials. Includes theory and applications, with worked numerical problems and solutions, and MATLAB examples on an accompanying website with further XFEM resources. Provides a comprehensive overview of this new area of research, including a review of Fracture Mechanics, basic through to advanced XFEM theory, as well as current problems and applications. Includes a chapter on the future developments in the field, new research areas and possible future applications of the method.