International Conference «Mathematical and Informational Technologies, MIT-2011»
(IX Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, August, 27–31, 2011

Budva, Montenegro, August, 31 – September, 5, 2011

Rudoy E.M.  

Shape sensitivity analysis for a body with a crack and a rigid inclusion

     We consider a solid with a rigid inclusion and a crack between the inclusion and an elastic part of the body. Nonpenetration conditions are imposed between opposite crack faces which result in a constrained minimization problem describing equilibrium of the solid with the crack and the rigid inclusion. The problem of shape perturbation of the crack and the inclusion is considered.
     Utilizing the variational properties the solution of the equilibrium problem we obtain the general formula for a shape derivative of the potential energy. In particular if we consider the perturbation corresponding quasi-static rectilinear crack growth we get a formula for the derivative of the energy functional with respect to the crack length. Moreover we show that we can rewrite it in the form of a path-independent integral. Such derivative and path-independent integral are widely used in fracture mechanics.

Abstracts file: Tet.doc
Full text file: rudoy.pdf

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