An XFEM plate element for high gradient zones resulted from yield lines

SUMMARY A high gradient of displacement field occurs when a yield line is formed in a plate with elasto-plastic material. For such applications, the extended finite element method has shown to be an effective numerical method to capture the behavior of a plate with a locally nonsmooth displacement field, and a displacement field with a high gradient. In this article, a six-node isoparametric plate element with extended finite element method formulation is presented to capture the elasto-plastic behavior of a plate in small-deformation analyses. The Hermite function is adopted at the element level to enrich both the translational and the rotational displacement approximation fields so that nonsmoothness in displacement fields near a yield line can be simulated. Copyright © 2013 John Wiley & Sons, Ltd.

[1]  T. Belytschko,et al.  The extended/generalized finite element method: An overview of the method and its applications , 2010 .

[2]  Dominique Chapelle,et al.  Towards improving the MITC6 triangular shell element , 2007 .

[3]  T. Belytschko,et al.  MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD , 2001 .

[4]  Analytical determination of the optimal strain and stress points for the displacement model of the finite element method , 1991 .

[5]  M. A. Crisfield,et al.  Finite elements in plasticity—theory and practice, D. R. J. Owen and E. Hinton, Pineridge Press, Swansea , 1981 .

[6]  T. Fries.  A corrected XFEM approximation without problems in blending elements , 2008 .

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

[8]  K. Bathe,et al.  Development of MITC isotropic triangular shell finite elements , 2004 .

[9]  Chi King Lee,et al.  A two-dimensional co-rotational Timoshenko beam element with XFEM formulation , 2011, Computational Mechanics.

[10]  H. Nguyen-Xuan,et al.  A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates , 2010 .

[11]  Timon Rabczuk,et al.  Linear buckling analysis of cracked plates by SFEM and XFEM , 2011 .

[12]  Ted Belytschko,et al.  An extended finite element method with higher-order elements for curved cracks , 2003 .

[13]  Jean-François Remacle,et al.  A computational approach to handle complex microstructure geometries , 2003 .

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

[15]  Ted Belytschko,et al.  Immersed particle method for fluid–structure interaction , 2009 .

[16]  T. Belytschko,et al.  Analysis of three‐dimensional crack initiation and propagation using the extended finite element method , 2005 .

[17]  T. Rabczuk,et al.  A meshfree thin shell method for non‐linear dynamic fracture , 2007 .

[18]  E. Ramm,et al.  A unified approach for shear-locking-free triangular and rectangular shell finite elements , 2000 .

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

[20]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[21]  Phill-Seung Lee,et al.  Phantom-node method for shell models with arbitrary cracks , 2012 .

[22]  G. Ventura,et al.  A regularized XFEM model for the transition from continuous to discontinuous displacements , 2008 .

[23]  Ted Belytschko,et al.  On XFEM applications to dislocations and interfaces , 2007 .

[24]  T. Rabczuk,et al.  A Meshfree Thin Shell for Arbitrary Evolving Cracks Based on An Extrinsic Basis , 2006 .

[25]  T. Belytschko,et al.  Non‐linear analysis of shells with arbitrary evolving cracks using XFEM , 2005 .

[26]  T. Belytschko,et al.  Two‐scale shear band evolution by local partition of unity , 2006 .

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

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

[29]  P Kerfriden,et al.  Natural frequencies of cracked functionally graded material plates by the extended finite element method , 2011 .