In recent years, discretization methods have been proposed which are more flexible and which have the potential of capturing (moving) discontinuities in a robust and efficient manner. This monograph assembles contributions of leading experts with the most recent developments in this rapidly evolving field. It provides the most comprehensive coverage of state-of-the art numerical methods for treating discontinuities in mechanics.

Preface; Meshless Finite Element Methods: Meshless discretisation of nonlocal damage theories, by H. Askes, T. Bennett and S. Kulasegaram; Three-dimensional non-linear fracture mechanics by enriched meshfree methods without asymptotic enrichment, by S. Bordas, C. Zi and T. Rabczuk; Accounting for weak discontinuities and moving boundaries in the context of the Natural Element Method and model reduction techniques, by F. Chinesta, F. Cueto, P. Joyot and P. Villon; Discontinuous Galerkin Methods: Modeling evolving discontinuities with spacetime discontinuous Galerkin methods, by R. Abedi, S.-H. Chung, M.A. Hawker, J. Palaniappan and R.B. Haber; Analysis of a finite element formulation for modelling phase separation G.N. Wells and K. Garikipati; Finite Element Methods with Embedded Discontinuities: Recent developments in the formulation of finite elements with embedded strong discontinuities, by F. Armero and C. Linder; Evolving material discontinuities: Numerical modeling by the Continuum Strong Discontinuity Approach (CSDA), by J. Oliver, A.E. Huespe, S. Blanco and D.L. Linero; A 3D cohesive investigation on branching for brittle materials, by R.C. Yu, A. Pandolfi and M. Ortiz; Partition-of-Unity Based Finite Element Methods: On applications of XFEM to dynamic fracture and dislocations, by T. Belytschko, J.-H. Song, H. Wang and R. Gracie; Some improvements of XFEM for cracked domains, by E. Chahine, P. Laborde, J. Pommier, Y. Renard and M. Salaün; 2D X-FEM simulation of dynamic brittle crack propagation, by A. Combescure, A. Gravouil, H. Maigre, J. Réthoré and D. Gregoire; A numerical framework to model 3-D fracture in bone tissue with application to failure of the proximal femur, by T.C. Gasser and G.A. Holzapfel; Application of X-FEM to 3D real cracks and elastic-plastic fatigue crack growth, by A. Gravouil, A. Combescure, T. Elguedj, E. Ferrié, J.-Y. Buffière and W. Ludwig; Accurate simulation offrictionless and frictional cohesive crack growth in quasi-brittle materials using XFEM B.L. Karihaloo and Q.Z. Xiao; On the application of Hansbo's method for interface problems, by B. Kuhi, Ph. Jãger, J. Mergheim and P. Steinmann; An optimal explicit time stepping scheme for cracks modeled with X-FEM, by T. Menouillard, N. Moës and A. Combescure; Variational Extended Finite Element Model for cohesive cracks: Influence of integration and interface law, by G. Meschke, P. Dumstorff and W. Fleming; An evaluation of the accuracy of discontinuous finite elements in explicit dynamic calculations, by J.J. C. Remmers, R. de Borst, A. Needleman; A discrete model for the propagation of discontinuities in a fluid-saturated medium, by J. Réthoré, R. de Borst and M.-A. Abellan; Single domain quadrature techniques for discontinuous and non-linear enrichments in local Partition of Unity FEM, by G. Ventura; Other Discretization Methods: Numerical determination of crack stress and deformation fields in gradient elastic solids, by G.F. Karlis, S.V. Tsinopoulos, D. Polyzos and Th.E. Beskos; The variational formulation of brittle fracture: Numerical implementation and extensions, by B. Bourdin; Measurement and identification techniques for evolving discontinuities, by F. Hild, J. Réthoré and S. Roux; Conservation under incompatibility for fluid-solid-interaction problems: The NPCL method, by E.H. van Brummelen and R. de Borst; Author Index; Subject Index.