The rs‐method for material failure simulations

A new method for propagating arbitrary failure modes is presented. Arbitrary failure modes are resolved on a refined local patch of elements and then embedded into the coarse grid using partition of unity method. Strong discontinuities are propagated by means of element erosion in the superimposed patch of elements only. The method, coined as the rs-version of the finite element method (or reduced order s-method), has been integrated in ABAQUS and verified on several test problems. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  Ted Belytschko,et al.  Embedded hinge lines for plate elements , 1989 .

[2]  Jacob Fish,et al.  On adaptive multilevel superposition of finite element meshes for linear elastostatics , 1994 .

[3]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[4]  Robert H. Dodds,et al.  Numerical procedures to model ductile crack extension , 1993 .

[5]  I. Babuska,et al.  The design and analysis of the Generalized Finite Element Method , 2000 .

[6]  Mark S. Shephard,et al.  3D anisotropic mesh adaptation by mesh modification , 2005 .

[7]  Paul A. Wawrzynek,et al.  Automated 3‐D crack growth simulation , 2000 .

[8]  Wing Kam Liu,et al.  Reproducing kernel particle methods for structural dynamics , 1995 .

[9]  Jacob Fish,et al.  Adaptive s-method for linear elastostatics , 1993 .

[10]  Mark S. Shephard,et al.  Automatic crack propagation tracking , 1985 .

[11]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[12]  M. Ortiz,et al.  FINITE-DEFORMATION IRREVERSIBLE COHESIVE ELEMENTS FOR THREE-DIMENSIONAL CRACK-PROPAGATION ANALYSIS , 1999 .

[13]  T. Belytschko,et al.  Physical stabilization of the 4-node shell element with one point quadrature , 1994 .

[14]  Ted Belytschko,et al.  Elements with embedded localization zones for large deformation problems , 1988 .

[15]  T. Liszka,et al.  A generalized finite element method for the simulation of three-dimensional dynamic crack propagation , 2001 .

[16]  J. Fish.  The s-version of the finite element method , 1992 .

[17]  Ted Belytschko,et al.  Combined extended and superimposed finite element method for cracks , 2004 .

[18]  S. Nemat-Nasser,et al.  Thermomechanical response of DH-36 structural steel over a wide range of strain rates and temperatures , 2003 .

[19]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[20]  T. Belytschko,et al.  A finite element with embedded localization zones , 1988 .

[21]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[22]  Ivo Babuška,et al.  The p-Version of the Finite Element Method for Parabolic Equations. Part 1 , 1981 .

[23]  A. Hillerborg,et al.  Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements , 1976 .

[24]  J. Fish,et al.  Hierarchical modelling of discontinuous fields , 1992 .

[25]  J. C. Simo,et al.  An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids , 1993 .

[26]  L. Freund,et al.  Computational methods based on an energy integral in dynamic fracture , 1985 .

[27]  D. Parks.  The virtual crack extension method for nonlinear material behavior , 1977 .

[28]  M. Ortiz,et al.  Computational modelling of impact damage in brittle materials , 1996 .

[29]  Integral equations for the plane potential problem on domains with a corner or a slit , 1993 .

[30]  F. Armero,et al.  An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids , 1996 .

[31]  G. R. Johnson,et al.  An element-failure algorithm for dynamic crack propagation in general directions , 1998 .

[32]  T. Belytschko,et al.  Extended finite element method for three-dimensional crack modelling , 2000 .

[33]  M. Ortiz,et al.  A finite element method for localized failure analysis , 1987 .

[34]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[35]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[36]  Ted Belytschko,et al.  A multiscale projection method for macro/microcrack simulations , 2007 .