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Crack nucleation sensitivity analysis
Author(s) -
Van Goethem N.,
Novotny A. A.
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1313
Subject(s) - nucleation , sensitivity (control systems) , mathematics , axiom , simple (philosophy) , derivative (finance) , fracture mechanics , mathematical analysis , fracture (geology) , topology (electrical circuits) , geometry , physics , materials science , thermodynamics , composite material , engineering , combinatorics , electronic engineering , philosophy , epistemology , financial economics , economics
A simple analytical expression for crack nucleation sensitivity analysis is proposed relying on the concept of topological derivative and applied within a two‐dimensional linear elastic fracture mechanics theory (LEFM). In particular, the topological asymptotic expansion of the total potential energy together with a Griffith‐type energy of an elastic cracked body is calculated. As a main result, we derive a crack nucleation criterion based on the topological derivative and a criterion for determining the direction of crack growth based on the topological gradient. The proposed methodology leads to an axiomatic approach of crack nucleation sensitivity analysis. Copyright © 2010 John Wiley & Sons, Ltd.