Arbitrary discontinuities in finite elements

A technique for modelling arbitrary discontinuities in finite elements is presented. Both discontinuities in the function and its derivatives are considered. Methods for intersecting and branching discontinuities are given. In all cases, the discontinuous approximation is constructed in terms of a signed distance functions, so level sets can be used to update the position of the discontinuities. A standard displacement Galerkin method is used for developing the discrete equations. Examples of the following applications are given: crack growth, a journal bearing, a non-bonded circular inclusion and a jointed rock mass. Copyright © 2001 John Wiley & Sons, Ltd.

[1]  T. Belytschko,et al.  Arbitrary branched and intersecting cracks with the eXtended Finite Element Method , 2000 .

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

[3]  J. Oliyer.  Continuum modelling of strong discontinuities in solid mechanics using damage models , 1995 .

[4]  Thomas J. R. Hughes,et al.  On modelling thermal oxidation of Silicon II: numerical aspects , 2000 .

[5]  T. Strouboulis,et al.  The generalized finite element method: an example of its implementation and illustration of its performance , 2000 .

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

[7]  Ted Belytschko,et al.  A computer method for stability analysis of caverns in jointed rock , 1984 .

[8]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[9]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[10]  L. Keer,et al.  Separation of a smooth circular inclusion from a matrix , 1973 .

[11]  J. Oliver.  MODELLING STRONG DISCONTINUITIES IN SOLID MECHANICS VIA STRAIN SOFTENING CONSTITUTIVE EQUATIONS. PART 2: NUMERICAL SIMULATION , 1996 .

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

[13]  Ted Belytschko,et al.  EFG approximation with discontinuous derivatives , 1998 .

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