Error estimation of stress intensity factors for mixed‐mode cracks

This paper presents an a posteriori error estimator for mixed-mode stress intensity factors in plane linear elasticity. A surface integral over an arbitrary crown is used for the separate calculation of the combined mode's stress intensity factors. The error in the quantity of interest is based on goal-oriented error measures and estimated through an error in the constitutive relation. Copyright © 2006 John Wiley & Sons, Ltd.

[1]  J. Tinsley Oden,et al.  Practical methods for a posteriori error estimation in engineering applications , 2003 .

[2]  Y. Murakami Stress Intensity Factors Handbook , 2006 .

[3]  Étude de la qualité locale de différentes versions de l’estimateur d’erreur en relation de comportement , 2003 .

[4]  J. Peraire,et al.  Computing upper and lower bounds for the J-integral in two-dimensional linear elasticity , 2006 .

[5]  S. Ohnimus,et al.  Local error estimates of FEM for displacements and stresses in linear elasticity by solving local Neumann problems , 2001 .

[6]  Per Heintz,et al.  On adaptive strategies and error control in fracture mechanics , 2004 .

[7]  John R. Rice,et al.  The Bending of Plates of Dissimilar Materials With Cracks , 1964 .

[8]  A Posteriori Error Control and Mesh Adaptation for FE models in Elasticity and Elasto-Plasticity , 1998 .

[9]  I. Babuska,et al.  A‐posteriori error estimates for the finite element method , 1978 .

[10]  Pierre Ladevèze,et al.  ERROR ESTIMATION AND MESH OPTIMIZATION FOR CLASSICAL FINITE ELEMENTS , 1991 .

[11]  Anthony T. Patera,et al.  Bounds for Linear–Functional Outputs of Coercive Partial Differential Equations : Local Indicators and Adaptive Refinement , 1998 .

[12]  Erwin Stein,et al.  Goal-oriented a posteriori error estimates in linear elastic fracture mechanics , 2006 .

[13]  O. C. Zienkiewicz,et al.  A simple error estimator and adaptive procedure for practical engineerng analysis , 1987 .

[14]  R. S. Dunham,et al.  A contour integral computation of mixed-mode stress intensity factors , 1976, International Journal of Fracture.

[15]  D. W. Kelly,et al.  Procedures for residual equilibration and local error estimation in the finite element method , 1989 .

[16]  R. Rannacher,et al.  A feed-back approach to error control in finite element methods: application to linear elasticity , 1997 .

[17]  T. Strouboulis,et al.  A posteriori estimation and adaptive control of the error in the quantity of interest. Part I: A posteriori estimation of the error in the von Mises stress and the stress intensity factor , 2000 .

[18]  Eric Florentin,et al.  Evaluation of the local quality of stresses in 3D finite element analysis , 2002 .

[19]  Ivo Babuška,et al.  The post‐processing approach in the finite element method—Part 2: The calculation of stress intensity factors , 1984 .

[20]  Pierre Ladevèze,et al.  New advances on a posteriori error on constitutive relation in f.e. analysis , 1997 .

[21]  Pierre Ladevèze,et al.  Local error estimators for finite element linear analysis , 1999 .

[22]  Serge Prudhomme,et al.  On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors , 1999 .