This important textbook provides an introduction to the concepts of the newly developed extended finite element method (XFEM) for fracture analysis of structures, as well as for other related engineering applications.

One of the main advantages of the method is that it avoids any need for remeshing or geometric crack modelling in numerical simulation, while generating discontinuous fields along a crack and around its tip. The second major advantage of the method is that by a small increase in number of degrees of freedom, far more accurate solutions can be obtained. The method has recently been extended to nonlinear materials and other disciplines such as modelling contact and interface, simulation of inclusions and holes, moving and changing phase problems, and even to multiscale analyses.

The book is self contained, with summaries of both classical and modern computational techniques. The main chapters include a comprehensive range of numerical examples describing various features of XFEM.

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This book introduces the development of the extended finite element method for fracture mechanics and crack analysis. XFEM is an extension to the classical finite element method using the concepts of partition of unity and meshless approaches.One of the main advantages of the method is that by increasing a small number of degrees of freedom, far more accurate solutions can be obtained. Also, it eliminates the need for remeshing or geometric crack modelling in numerical simulation, while generating discontinuous fields along a crack and around its tip. Analysis may start with an initial mesh, generated independently from any crack. Then the method uses an enrichment field to represent any discontinuous field along the crack length and around its tip, based on the existing finite element nodes (non-aligned to crack). These enrichment functions are defined from available analytical solutions of isotropic and anisotropic media in the framework of partition of unity, and can be estimated at a node according to a node based (meshless) approximation at its supporting nodes. Similar procedures apply to crack propogation and cohesive crack problems.The method has recently been extended to nonlinear materials and other disciplines such as modelling contact and interface, simulation of inclusions and holes, moving and changing phase problems, and even to the topology optimization.

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Extended Finite Element Method: for Fracture Analysis of Structures

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