TY - JOUR
T1 - Energy release rate approximation for edge cracks using higher-order topological derivatives
AU - Alidoost, Kazem
AU - Geubelle, Philippe H.
AU - Tortorelli, Daniel A.
N1 - Funding Information:
Acknowledgements The authors gratefully acknowledge the support of the National Science Foundation (Award CMI-1200086). The authors also appreciate the rewarding comments from the reviewers, the invaluable conversations with Tom Curtin of BEASY USA - Computational Mechanics Inc, and the excellent work of Mariana Silva Sohn at the University of Illinois at Urbana-Champaign. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Funding Information:
The authors gratefully acknowledge the support of the National Science Foundation (Award CMI-1200086). The authors also appreciate the rewarding comments from the reviewers, the invaluable conversations with Tom Curtin of BEASY USA - Computational Mechanics Inc, and the excellent work of Mariana Silva Sohn at the University of Illinois at Urbana-Champaign. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Publisher Copyright:
© 2018, Springer Science+Business Media B.V., part of Springer Nature.
PY - 2018/3/1
Y1 - 2018/3/1
N2 - Topological derivatives provide the variation of a functional when an infinitesimal hole is introduced into the domain. In Silva et al. (J Mech Phys Solids 59(5):925–939, 2011), the authors developed a first-order approximation of the energy release rate associated with a small crack at any boundary location and at any orientation using a first-order topological derivative. This approach offers significant computational advantages over other methods because (i) it requires only a single analysis while other methods require an analysis for each crack size-location-direction combination, and (ii) it is performed on the non-cracked domain, removing the need to create very fine meshes in the vicinity of the crack. In the present study, higher-precision approximations of the energy release rate are developed using higher-order topological derivatives which allow the analyst to accurately treat longer cracks and determine the crack lengths for which the first-order approximation is accurate.
AB - Topological derivatives provide the variation of a functional when an infinitesimal hole is introduced into the domain. In Silva et al. (J Mech Phys Solids 59(5):925–939, 2011), the authors developed a first-order approximation of the energy release rate associated with a small crack at any boundary location and at any orientation using a first-order topological derivative. This approach offers significant computational advantages over other methods because (i) it requires only a single analysis while other methods require an analysis for each crack size-location-direction combination, and (ii) it is performed on the non-cracked domain, removing the need to create very fine meshes in the vicinity of the crack. In the present study, higher-precision approximations of the energy release rate are developed using higher-order topological derivatives which allow the analyst to accurately treat longer cracks and determine the crack lengths for which the first-order approximation is accurate.
KW - Asymptotic analysis
KW - Edge cracks
KW - Energy release rate
KW - Topological derivative
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U2 - 10.1007/s10704-018-0271-1
DO - 10.1007/s10704-018-0271-1
M3 - Article
AN - SCOPUS:85042217265
SN - 0376-9429
VL - 210
SP - 187
EP - 205
JO - International Journal of Fracture
JF - International Journal of Fracture
IS - 1-2
ER -