The rs-method for material failure simulations

The rs-method for material failure simulations R. Fan and J. Fish Rensselaer Polytechnic Institute Troy, NY 12180 Abstract 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.

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

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

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

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

[5]  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 .

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

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

[8]  G. R. Johnson,et al.  Numerical Algorithms in a Lagrangian Hydrocode. , 1997 .

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

[10]  M. Zivkovic,et al.  Extended Finite Element Method for Two-dimensional Crack Modeling , 2008 .

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

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

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

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

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

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

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

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

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

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

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

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

[23]  Mark S. Shephard,et al.  anisotropic mesh adaptation by mesh modification , 2005 .

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

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