Extended Finite Element Method

Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics * Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. The finite element method (FEM) technique has been developed to simulate and analyze complex engineering problems. However, there are a number of drawbacks with finite element simulation of discontinuous problems, such as fracture mechanics problems, including the computational cost of a very fine finite element mesh and the complex remeshing strategy in capturing discontinuity. The extended finite element method (XFEM) has therefore been developed to improve the performance of the conventional finite element method in discontinuity problems.Extended Finite Element Method: Theory and Applications introduces the theory and applications of XFEM in the linear and nonlinear problems of continua, structures, and geomechanics. It begins by introducing the concept of a partition of unity, various enrichment functions, and fundamentals of XFEM formulation. It then covers the theory and application of XFEM in large deformations, plasticity, and contact problems. The implementation of XFEM in fracture mechanics, including linear, cohesive, and ductile crack propagation, is also covered. Finally, the theory and applications of XFEM in multiphase fluid flow, including hydraulic fracturing in soil saturated media and crack propagation in thermo-hydro-mechanical porous media, are discussed in detail. Key features:• Comprehensively introduces XFEM analysis • Explains the theory and applications of XFEM in various continuum and geo-mechanical problems• Includes worked examples• Accompanied by a website hosting source code and examples Extended Finite Element Method: Theory and Applications is a comprehensive introduction to XFEM analysis for researchers and practitioners in industry, and is also an ideal textbook for graduate students in mechanical and civil engineering.ccompanied by a website hosting source code and examples Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems Accompanied by a website hosting source code and examples

In the extended finite element method (XFEM), a standard displacement based finite element approximation is enriched by additional (special) functions using the framework of partition of unity. In the XFEM, the finite element mesh need not conform to the internal boundaries (cracks, material interfaces, voids, etc.), and hence a single mesh suffices for modeling as well as capturing the evolution of material interfaces and cracks. This book mainly focuses on the application of XFEM in modeling dynamic fracture in thin plates and shells. New crack tip enrichment functions are extracted from analytical solutions and several enrichment schemes are introduced for various elements. As an application, the problem of cracked thin tubes under gaseous detonation loading is simulated by the introduced Dynamic-XFEM formulation and the obtained response of the tube to moving detonation loading is compared with ANSYS-LS DYNA results.