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Optimal control of cracks in elastic bodies with thin rigid inclusions
Author(s) -
Khludnev A.M.,
Leugering G.
Publication year - 2011
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201000058
Subject(s) - uniqueness , limiting , elasticity (physics) , mathematics , variational inequality , statement (logic) , optimal control , infinity , homogeneous , problem statement , mathematical analysis , mathematical optimization , materials science , economics , combinatorics , engineering , composite material , mechanical engineering , management science , political science , law
In this paper we consider the control of cracks in elastic bodies with rigid inclusion. We first describe the problem statement, provide an equivalent formulation as a variational inequality and prove existence and uniqueness of solutions. Furthermore, we consider this problem as a limiting problem when the elasticity parameters of the inclusion tend to infinity. Then we formulate the optimal control problems and derive an explicit formula for the crack sensitivity and for the energy release rate. We show existence of optimal solutions.