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Sensitivity of Interfacial Cracks to Non‐linear Crack Front Perturbations
Author(s) -
Kovtunenko V.A.
Publication year - 2002
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 - 10.1002/1521-4001(200206)82:6<387::aid-zamm387>3.0.co;2-i
Subject(s) - elasticity (physics) , linear elasticity , perturbation (astronomy) , mathematical analysis , anisotropy , boundary value problem , homogeneous , mathematics , surface energy , mechanics , materials science , physics , finite element method , composite material , thermodynamics , quantum mechanics , combinatorics
The 3D‐elasticity model of an anisotropic, non‐homogeneous, bonded solid is considered. The interface is thought of as being a smooth surface comprising the connected part under the transmission condition and the crack under the stress‐free boundary condition. We investigate the sensitivity of the model to the non‐linear perturbation of the crack front along the interface. Expansions of the energy functionals at least up to the second‐order terms are obtained by global derivatives of the solution with respect to the shape of the crack front. These derivatives are constructed over the whole non‐smooth domain as iterative solutions of the same elasticity problem with specified fictitious forces. We consider only energetic solutions of the H 1 ‐class using the week formulation of the elasticity problem. Properties of the constructed derivatives of the energy functionals are discussed.