The problem with crack under nonlinear boundary conditions is considered as a minimization of the total potential energy functional. The functional is nonconvex by assuming the surface energy at a crack presented in a general form. The correctness properties of the nonconvex minimization problem with constraints are investigated. Applying the shape sensitivity analysis, the problem of shape perturbation is formulated, and the derivative of the total potential energy functional with respect to the perturbation parameter is calculated. Examples on the rectilinear and the planar cracks are presented.
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Victor A. Kovtunenko (2005) studied this question.
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