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Error estimation for the finite element evaluation of GI and GII in mixed-mode linear elastic fracture mechanics

Error estimation for the finite element evaluation of GI and GII in mixed-mode linear elastic fracture mechanics
Error estimation for the finite element evaluation of GI and GII in mixed-mode linear elastic fracture mechanics
A discretization error estimator for the finite element evaluation of the strain energy release rates (SERRs) I, GII is presented for mixed-mode bidimensional problems of the linear elastic fracture mechanics (LEFM). The estimator is related to one of the most efficient energetic methods: the equivalent domain integral method (EDI). A continuum approach of the shape design sensitivity analysis (SDSA) is applied to the fracture mechanics problem in combination with the field decomposition technique to obtain separate estimates of the discretization error for each mode. The error estimator enables an a posteriori improvement of I, GII for a given finite element mesh. The improvement is achieved by adding the estimated errors to the previously calculated values of GI, GII by means of the discrete analytical stiffness derivative method (DASD). This is verified through numerical examples based on the Westergaard's problem and a finite domain problem.
0168-874X
1079-1104
Giner, E.
25794254-7133-4500-8d6e-7b9f96e748ef
Fuenmayor, F.J.
452423ef-ca4b-4004-8ece-9e3dd0ca886e
Baeza, L.
09dc5565-ad4b-49af-a104-d4b6ad28e1b0
Tarancón, J.E.
4f994549-2f0f-4408-8a64-f2e0e0d8ad4f
Giner, E.
25794254-7133-4500-8d6e-7b9f96e748ef
Fuenmayor, F.J.
452423ef-ca4b-4004-8ece-9e3dd0ca886e
Baeza, L.
09dc5565-ad4b-49af-a104-d4b6ad28e1b0
Tarancón, J.E.
4f994549-2f0f-4408-8a64-f2e0e0d8ad4f

Giner, E., Fuenmayor, F.J., Baeza, L. and Tarancón, J.E. (2005) Error estimation for the finite element evaluation of GI and GII in mixed-mode linear elastic fracture mechanics. Finite Elements in Analysis and Design, 41 (11-12), 1079-1104. (doi:10.1016/j.finel.2004.11.004).

Record type: Article

Abstract

A discretization error estimator for the finite element evaluation of the strain energy release rates (SERRs) I, GII is presented for mixed-mode bidimensional problems of the linear elastic fracture mechanics (LEFM). The estimator is related to one of the most efficient energetic methods: the equivalent domain integral method (EDI). A continuum approach of the shape design sensitivity analysis (SDSA) is applied to the fracture mechanics problem in combination with the field decomposition technique to obtain separate estimates of the discretization error for each mode. The error estimator enables an a posteriori improvement of I, GII for a given finite element mesh. The improvement is achieved by adding the estimated errors to the previously calculated values of GI, GII by means of the discrete analytical stiffness derivative method (DASD). This is verified through numerical examples based on the Westergaard's problem and a finite domain problem.

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Published date: June 2005
Additional Information: cited By 11
Organisations: Dynamics Group

Identifiers

Local EPrints ID: 411357
URI: https://eprints.soton.ac.uk/id/eprint/411357
ISSN: 0168-874X
PURE UUID: 86b7364c-91a1-49ad-bc78-6461bd8d0e89
ORCID for L. Baeza: ORCID iD orcid.org/0000-0002-3815-8706

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Date deposited: 19 Jun 2017 16:31
Last modified: 20 Jul 2019 00:28

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