Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Extended Finite Element Method: Theory and Applications introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics. The XFEM approach is based on an extension of standard finite element method based on the partition of unity method. Extended Finite Element Method: Theory and Applications begins by introducing the concept of 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 the linear, cohesive, and ductile crack propagation is also covered. The theory and applications of the XFEM in multiphase fluid flow, including the hydraulic fracturing in soil saturated media and crack propagation in thermo-hydro-mechanical porous media, is also discussed in detail. 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
Extended Finite Element Method provides an introduction to the extended finite element method (XFEM), a novel computational method which has been proposed to solve complex crack propagation problems. The book helps readers understand the method and make effective use of the XFEM code and software plugins now available to model and simulate these complex problems. The book explores the governing equation behind XFEM, including level set method and enrichment shape function. The authors outline a new XFEM algorithm based on the continuum-based shell and consider numerous practical problems, including planar discontinuities, arbitrary crack propagation in shells and dynamic response in 3D composite materials. Authored by an expert team from one of China's leading academic and research institutions Offers complete coverage of XFEM, from fundamentals to applications, with numerous examples Provides the understanding needed to effectively use the latest XFEM code and software tools to model and simulate dynamic crack problems
|Author||: Sylvie Pommier,Anthony Gravouil,Nicolas Moes,Alain Combescure|
|Publisher||: John Wiley & Sons|
|Release Date||: 2013-03-04|
|ISBN 10||: 1118622693|
|Pages||: 254 pages|
Novel techniques for modeling 3D cracks and their evolution in solids are presented. Cracks are modeled in terms of signed distance functions (level sets). Stress, strain and displacement field are determined using the extended finite elements method (X-FEM). Non-linear constitutive behavior for the crack tip region are developed within this framework to account for non-linear effect in crack propagation. Applications for static or dynamics case are provided.
Extended Finite Element and Meshfree Methods provides an overview of, and investigates, recent developments in extended finite elements with a focus on applications to material failure in statics and dynamics. This class of methods is ideally suited for applications, such as crack propagation, two-phase flow, fluid-structure-interaction, optimization and inverse analysis because they do not require any remeshing. These methods include the original extended finite element method, smoothed extended finite element method (XFEM), phantom node method, extended meshfree methods, numerical manifold method and extended isogeometric analysis. This book also addresses their implementation and provides small MATLAB codes on each sub-topic. Also discussed are the challenges and efficient algorithms for tracking the crack path which plays an important role for complex engineering applications. Explains all the important theory behind XFEM and meshfree methods Provides advice on how to implement XFEM for a range of practical purposes, along with helpful MATLAB codes Draws on the latest research to explore new topics, such as the applications of XFEM to shell formulations, and extended meshfree and extended isogeometric methods Introduces alternative modeling methods to help readers decide what is most appropriate for their work
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.
|Author||: Michael James Swindeman|
|Release Date||: 2011|
|Pages||: 90 pages|
As the use of composite materials in aerospace structures continues to increase, the need to properly characterize these materials, especially in terms of damage tolerance, takes on additional importance. The world wide failure exercises (WWFE) are an example of the international interest in this issue. But though there has been a great deal of progress in understanding the initiation of damage and modeling damage propagation along known interfaces, methods that can capture the effects of interactions among various failure modes accurately remain elusive. A method of modeling coupled matrix cracks and delamination in laminated composite materials based on the finite element method has been developed and experimentally validated. Damage initiation is determined using the LARC03 failure criterion. Delamination along ply interfaces is modeled using cohesive zones. Matrix cracks are incorporated into the discretization of the problem domain through a robust Mesh-Independent Cracking (MIC) technique. The matrix cracking technique, termed the Regularized Extended Finite Element Method (Rx-FEM), uses regularized forms of the Heaviside and Dirac Delta generalized functions to transform the crack surface into a volumetric crack zone. The Regularized Extended Finite Element method is compared to benchmark cases. The sensitivity of the solution to mesh size and parameters within the cohesive zone model is studied. Finally, the full method with delamination is employed to study a set of experimental tests performed on open-hole quasi-isotropic laminates. The trends of hole-size and ply thickness are well predicted for the laminates. Rx-FEM is also able to simulate the pattern of damage, as demonstrated by comparisons to x-ray images. From the results of this series of analyses it can be concluded that failures occur when delamination originating at the hole links up with delamination originating at the edge along the path of matrix cracks.
|Author||: Alaskar Alizada|
|Release Date||: 2012-12-14|
|ISBN 10||: 9783844015034|
|Pages||: 171 pages|
|Author||: John Everett Dolbow|
|Release Date||: 1999|
|Pages||: 396 pages|
The modeling of a discontinuous field with a standard finite element approximation presents unique challenges. The construction of an approximating space which is discontinuous across a given line or surface places strict restrictions on the finite element mesh. The simulation of an evolution of the discontinuity is in turn burdened by the requirement to remesh at each stage of the calculation. This work approaches the problem by locally enriching the standard element-based approximation with discontinuous functions. The enriched basis is formed from a union of the set of nodal shape functions with a set of products of nodal shape functions and enrichment functions. The construction of the approximating space in this fashion places the formulation in the class of partition of unity methods. By aligning the discontinuities in the enrichment functions with a specified geometry, a discontinuous field is represented independently of the finite element mesh. This capability is shown to significantly extend the standard method for a number of applications in applied mechanics.
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.
|Author||: Stéphane P. A. Bordas,Erik Burman,Mats G. Larson,Maxim A. Olshanskii|
|Release Date||: 2018-03-13|
|ISBN 10||: 3319714317|
|Pages||: 361 pages|
This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering.
|Release Date||: 2011|
|Pages||: 28 pages|