Frictional slip plane growth by localization detection and the extended finite element method (XFEM)

This paper is concerned with developing a numerical tool for detecting instabilities in elasto-plastic solids (with an emphasis on soils) and inserting a discontinuity at these instabilities allowing the boundary value problem to proceed beyond these instabilities. This consists of implementing an algorithm for detection of strong discontinuities within a finite element (FE) framework. These discontinuities are then inserted into the FE problem through the use of a displacement field enrichment technique called the extended finite element method (XFEM). The newly formed discontinuities are governed by a Mohr–Coulomb frictional law that is enforced by a penalty method. This implementation within an FE framework is then tested on a compressive soil block and a soil slope where the discontinuity is inserted and grown according to the localization detection. Copyright © 2010 John Wiley & Sons, Ltd.

[1]  J. Oliver,et al.  Strong discontinuities and continuum plasticity models: the strong discontinuity approach , 1999 .

[2]  Jean H. Prevost,et al.  Dynamic strain localization in elasto-(visco-)plastic solids, Part 2. Plane strain examples , 1990 .

[3]  R. Borst,et al.  Localisation in a Cosserat continuum under static and dynamic loading conditions , 1991 .

[4]  T. Belytschko,et al.  New crack‐tip elements for XFEM and applications to cohesive cracks , 2003 .

[5]  L. J. Sluys,et al.  Viscoplasticity for instabilities due to strain softening and strain‐rate softening , 1997 .

[6]  Timon Rabczuk,et al.  A new approach for modelling slip lines in geological materials with cohesive models , 2006 .

[7]  Félix Darve,et al.  Bifurcation modeling in geomaterials: From the second-order work criterion to spectral analyses , 2009 .

[8]  Richard A. Regueiro,et al.  Embedded strong discontinuity finite elements for fractured geomaterials with variable friction , 2007 .

[9]  T. Belytschko,et al.  Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment , 2003 .

[10]  J. Prévost,et al.  Adaptive meshing for dynamic strain localization , 1996 .

[11]  Michael Ortiz,et al.  Finite element analysis of strain localization in frictional materials , 1989 .

[12]  Tae-Yeon Kim,et al.  A mortared finite element method for frictional contact on arbitrary interfaces , 2006 .

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

[14]  J. Prévost,et al.  Finite element simulation of dynamic strain-localization: A multi-scale problem , 1995 .

[15]  J. Rice.  Localization of plastic deformation , 1976 .

[16]  Kenneth Runesson,et al.  Discontinuous bifurcations of elastic-plastic solutions at plane stress and plane strain , 1991 .

[17]  Ted Belytschko,et al.  An extended finite element method for modeling crack growth with frictional contact , 2001 .

[18]  B. Lawn.  Fracture of Brittle Solids by Brian Lawn , 1993 .

[19]  R. Borja.  Assumed enhanced strain and the extended finite element methods: A unification of concepts , 2008 .

[20]  J. Rice,et al.  CONDITIONS FOR THE LOCALIZATION OF DEFORMATION IN PRESSURE-SENSITIVE DILATANT MATERIALS , 1975 .

[21]  J. Hadamard,et al.  Leçons sur la propagation des ondes et les equations de l'hydrodynamique , 2015 .

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

[23]  T. Triantafyllidis,et al.  Experimental investigation of shear band patterns in granular material , 2003 .

[24]  Amir R. Khoei,et al.  An enriched finite element algorithm for numerical computation of contact friction problems , 2007 .

[25]  T. Belytschko,et al.  Continuum–discontinuum modelling of shear bands , 2005 .

[26]  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 .

[27]  L. J. Sluys,et al.  Analysis of slip planes in three-dimensional solids , 2001 .

[28]  Zenon Mróz,et al.  Finite element analysis of deformation of strain‐softening materials , 1981 .

[29]  T. Belytschko,et al.  A simplified mesh‐free method for shear bands with cohesive surfaces , 2007 .

[30]  J. Prévost,et al.  Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation , 2003 .

[31]  T. Rabczuk,et al.  Discontinuous modelling of shear bands using adaptive meshfree methods , 2008 .

[32]  R. Hill.  Acceleration waves in solids , 1962 .

[33]  N. S. Ottosen,et al.  Properties of discontinuous bifurcation solutions in elasto-plasticity , 1991 .

[34]  Ronaldo I. Borja,et al.  A contact algorithm for frictional crack propagation with the extended finite element method , 2008 .

[35]  Richard Bellman,et al.  Plastic Flow and Fracture in Solids , 1962 .

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

[37]  Richard A. Regueiro,et al.  FE Modeling of Strain Localization in Soft Rock , 2000 .

[38]  J. Prévost,et al.  Dynamic strain localization in elasto-(visco-)plastic solids, Part 1. General formulation and one-dimensional examples , 1990 .

[39]  Jean H. Prevost,et al.  A simple plasticity theory for frictional cohesionless soils , 1985 .