Computing upper and lower bounds for the J-integral in two-dimensional linear elasticity

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 4-6, 2006, Pages 430-443

  Xuan, Z C ^a,d   Pares N ^b   Peraire, J ^c  

^a TIANJIN UNIVERSITY OF TECHNOLOGY AND EDUCATION   (China)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^c Massachusetts Institute of Technology Cambridge   (United States)

^d NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

J integral; Two dimensional linear elasticity

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; FRACTURE MECHANICS; FUNCTION EVALUATION; INTEGRAL EQUATIONS; LINEAR EQUATIONS; TWO DIMENSIONAL;

J-INTEGRAL; TWO DIMENSIONAL LINEAR ELASTICITY;

ELASTICITY;

ELASTICITY; FINITE ELEMENT METHOD;

EID: 27744563713     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2004.12.031     Document Type: Article

References (17)

1. P. Díez N. Parés A. Huerta Recovering lower bounds of the error postprocessing implicit residual a posteriori error estimates Int. J. Num. Meth. Engrg. 56 10 2003 1465-1488
2. J.D. Eshelby The energy momentum tensor in continuum mechanics Inelastic Behaviour of Solids vol. 77-114 1970 McGraw-Hill New York
3. P. Heintz, K. Samuelsson, On adaptive strategies and error control in fracture mechanics. Tech. Rept. Preprint 2002-14. Chalmers Finite Element Center, Chalmers University of Technology, 2002.
4. P. Heintz, F. Larsson, P. Hansbo, K. Runesson, Adaptive strategies and error control for computing material forces in fracture mechanics. Tech. Rept. Preprint 2002-18. Chalmers Finite Element Center, Chalmers University of Technology, 2002.
5. F.Z. Li C.F. Shih A. Needleman A comparison of methods for calculating energy release rates Engrg. Fract. Mec. 21 2 1985 405-421
6. S.H. Lo C.K. Lee Solving crack problems by an adaptive refinement procedure Engrg. Fract. Mec. 43 2 1992 147-163
7. K.S.R.K. Murthy M. Mukhopadhyay Adaptive finite element analysis of mixed-mode fracture problems containing multiple crack-tips with an automatic mesh generator Int. J. Fract. 108 3 2001 251-274
8. M. Paraschivoiu J. Peraire A.T. Patera A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations Comput. Method. Appl. Mech. Engrg. 150 1-4 1997 289-312
9. N. Pares, J. Bonet, A. Huerta, J. Peraire, The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations, accepted for publication, doi:10.1016/ j.cma.2004.10.013.
10. A.T. Patera, J. Peraire, A general Lagrangian formulation for the computation of a posteriori finite element bounds, Chapter in: Error Estimation and Adaptive Discretization Methods in CFD. Lecture Notes in Computational Science and Engineering, vol. 25, 2002.
11. J. Peraire A.T. Patera Bounds for linear-functional outputs of coercive partial differential equations: Local indicators and adaptive refinement in: P. Ladeveze J.T. Oden (Eds.) Proceedings of the Workshop On New Advances in Adaptive Computational Methods in Mechanics 1998 Elsevier New York
12. J.R. Rice A path independent integral and approximate analysis of strain concentration by notches and cracks J. Appl. Mec. 35 2 1968 379-386
13. M. Rüter, E. Stein, Goal-oriented a posteriori error estimates in elastic fracture mechanics, Fifth World Congress on Computational mechanics, Vienna, Austria, July, 2002.
14. A.M. Sauer-Budge J. Bonet A. Huerta J. Peraire Computing bounds for linear functionals of exact weak solutions to Poisson's equation SIAM J. Numer. Anal. 42 4 2004 1610-1630
15. A.M. Sauer-Budge J. Peraire Computing bounds for linear functionals of exact weak solutions to the advection-diffusion-reaction equation SIAM J. Sci. Comput. 26 2 2003 636-652
16. B.A. Szabo Accuracy Estimates and Adaptive Refinements in Finite Element Computations 1986 John Wiley Chapter 3: Estimation and control of error based on p convergence
17. Z.C. Xuan, K.H. Lee, A.T. Patera, J. Peraire, Computing upper and lower bounds for the J-integral in two-dimensional linear elasticity, Presented at the SMA Symposium, National University of Singapore, Singapore, 2004.