Since the development of linear elastic fracture mechanics (LEFM) decades ago, its limitations have been discussed extensively. Methods of manipulation on how to overcome the problems have been proposed by many enthusiasts. This book also highlights the limitation and at the same time proposes solutions. The effect of fracture on the structure of nano-catalyst and diamond-like carbon coating de-lamination are some of the microscopical research covered in this book. The format of this book is such that the reader can use each chapter independently. It starts with the first chapter outlining the classical review that traces back to early fracture mechanics. It is then continued to broader ranges from experimental and commercial software implementation, to the formulation and implementation of XFEM and piezoelectricity problems.