An enriched element‐failure method (REFM) for delamination analysis of composite structures

This paper develops an enriched element-failure method for delamination analysis of composite structures. This method combines discontinuous enrichments in the extended finite element method and element-failure concepts in the element-failure method within the finite element framework. An improved discontinuous enrichment function is presented to effectively model the kinked discontinuities; and, based on fracture mechanics, a general near-tip enrichment function is also derived from the asymptotic displacement fields to represent the discontinuity and local stress intensification around the crack-tip. The delamination is treated as a crack problem that is represented by the discontinuous enrichment functions and then the enrichments are transformed to external nodal forces applied to nodes around the crack. The crack and its propagation are modeled by the ‘failed elements’ that are applied to the external nodal forces. Delamination and crack kinking problems can be solved simultaneously without remeshing the model or re-assembling the stiffness matrix with this method. Examples are used to demonstrate the application of the proposed method to delamination analysis. The validity of the proposed method is verified and the simulation results show that both interlaminar delamination and crack kinking (intralaminar crack) occur in the cross-ply laminated plate, which is observed in the experiment. Copyright © 2009 John Wiley & Sons, Ltd.

[1]  Toshio Nagashima,et al.  Stress intensity factor analysis of interface cracks using X‐FEM , 2003 .

[2]  Mark A Fleming,et al.  ENRICHED ELEMENT-FREE GALERKIN METHODS FOR CRACK TIP FIELDS , 1997 .

[3]  René de Borst,et al.  Computational modelling of delamination , 2006 .

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

[5]  E. Ramm,et al.  Interface material failure modeled by the extended finite-element method and level sets , 2006 .

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

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

[8]  D. Borst,et al.  A NON-LINEAR FINITE ELEMENT APPROACH FOR THE ANALYSIS OF MODE-I FREE EDGE DELAMINATION IN COMPOSITES , 1993 .

[9]  Bhushan Lal Karihaloo,et al.  XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi‐materials , 2004 .

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

[11]  Vincent B. C. Tan,et al.  Damage progression by the element-failure method (EFM) and strain invariant failure theory (SIFT) , 2005 .

[12]  A. Giannakopoulos,et al.  A finite element analysis of configurational stability and finite growth of buckling driven delamination , 1995 .

[13]  Tong Earn Tay,et al.  Characterization and analysis of delamination fracture in composites: An overview of developments from 1990 to 2001 , 2003 .

[14]  K. Lam,et al.  Determination of fracture parameters of laminated thermoplastic composite materials: a finite element approach , 2000 .

[15]  Kunigal N. Shivakumar,et al.  An equivalent domain integral method in the two-dimensional analysis of mixed mode crack problems , 1990 .

[16]  E. Dill,et al.  Theory of Elasticity of an Anisotropic Elastic Body , 1964 .

[17]  M. Crisfield,et al.  Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues , 2001 .

[18]  Alireza Asadpoure,et al.  Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method , 2007 .

[19]  G. Sih,et al.  Mathematical theories of brittle fracture. , 1968 .

[20]  V. V. Bolotin.  Delaminations in composite structures: Its origin, buckling, growth and stability , 1996 .

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

[22]  P. C. Paris,et al.  On cracks in rectilinearly anisotropic bodies , 1965 .

[23]  Vincent B. C. Tan,et al.  Element-failure concepts for dynamic fracture and delamination in low-velocity impact of composites , 2003 .

[24]  J. Rice.  A path-independent integral and the approximate analysis of strain , 1968 .

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

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

[27]  John D. Whitcomb,et al.  Finite Element Analysis of Instability Related Delamination Growth , 1981 .

[28]  Zhigang Suo,et al.  Partition of unity enrichment for bimaterial interface cracks , 2004 .

[29]  Ekkehard Ramm,et al.  Modeling of failure in composites by X-FEM and level sets within a multiscale framework , 2008 .

[30]  Ted Belytschko,et al.  Modelling crack growth by level sets in the extended finite element method , 2001 .

[31]  Ted Belytschko,et al.  Arbitrary discontinuities in finite elements , 2001 .

[32]  Vincent B. C. Tan,et al.  Element-Failure: An Alternative to Material Property Degradation Method for Progressive Damage in Composite Structures , 2005 .

[33]  Tong Earn Tay,et al.  Modeling delamination growth in laminated composites , 2001 .

[34]  F. Erdogan,et al.  On the Crack Extension in Plates Under Plane Loading and Transverse Shear , 1963 .

[35]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

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

[37]  Brian Moran,et al.  Energy release rate along a three-dimensional crack front in a thermally stressed body , 1986, International Journal of Fracture.