TY - JOUR
T1 - Energy release rate approximation for small surface cracks in three-dimensional domains using the topological derivative
AU - Alidoost, Kazem
AU - Feng, Meng
AU - Geubelle, Philippe H.
AU - Tortorelli, Daniel A.
N1 - Publisher Copyright:
Copyright © 2020 by ASME
PY - 2020/4
Y1 - 2020/4
N2 - The topological derivative describes the variation of a response functional with respect to infinitesimal changes in topology, such as the introduction of an infinitesimal crack or hole. In this three-dimensional fracture mechanics work, we propose an approximation of the energy release rate field associated with a small surface crack of any boundary location, direction, and orientation combination using the topological derivative. This work builds on the work of Silva et al. (“Energy Release Rate Approximation for Small Surface-Breaking Cracks Using the Topological Derivative,” J. Mech. Phys. Solids 59(5), pp. 925–939), in which the authors proposed an approximation of the energy release rate field which was limited to two-dimensional domains. The proposed method is computationally advantageous because it only requires a single analysis. By contrast, current boundary element and finite element-based methods require an analysis for each crack length-location-direction-orientation combination. Furthermore, the proposed method is evaluated on the non-cracked domain, obviating the need for refined meshes in the crack tip region.
AB - The topological derivative describes the variation of a response functional with respect to infinitesimal changes in topology, such as the introduction of an infinitesimal crack or hole. In this three-dimensional fracture mechanics work, we propose an approximation of the energy release rate field associated with a small surface crack of any boundary location, direction, and orientation combination using the topological derivative. This work builds on the work of Silva et al. (“Energy Release Rate Approximation for Small Surface-Breaking Cracks Using the Topological Derivative,” J. Mech. Phys. Solids 59(5), pp. 925–939), in which the authors proposed an approximation of the energy release rate field which was limited to two-dimensional domains. The proposed method is computationally advantageous because it only requires a single analysis. By contrast, current boundary element and finite element-based methods require an analysis for each crack length-location-direction-orientation combination. Furthermore, the proposed method is evaluated on the non-cracked domain, obviating the need for refined meshes in the crack tip region.
KW - Asymptotic analysis
KW - Computational mechanics
KW - Energy release rate
KW - Failure criteria
KW - Mixed mode fracture
KW - Surface cracks
KW - Topological derivative
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U2 - 10.1115/1.4045793
DO - 10.1115/1.4045793
M3 - Article
AN - SCOPUS:85087786591
SN - 0021-8936
VL - 87
JO - Journal of Applied Mechanics, Transactions ASME
JF - Journal of Applied Mechanics, Transactions ASME
IS - 4
M1 - 041004
ER -