On derivative of energy functional for elastic bodies with cracks and unilateral conditions

Authors:
A. M. Khludnev, K. Ohtsuka and J. Sokołowski

Journal:
Quart. Appl. Math. **60** (2002), 99-109

MSC:
Primary 74G65; Secondary 74P10, 74R99

DOI:
https://doi.org/10.1090/qam/1878261

MathSciNet review:
MR1878261

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Abstract: In this paper we consider elasticity equations in a domain having a cut (a crack) with unilateral boundary conditions considered at the crack faces. The boundary conditions provide a mutual nonpenetration between the crack faces, and the problem as a whole is nonlinear. Assuming that a general perturbation of the cut is given, we find the derivative of the energy functional with respect to the perturbation parameter. It is known that a calculation of the material derivative for similar problems has the difficulty of finding boundary conditions at the crack faces. We use a variational property of the solution, thus avoiding a direct calculation of the material derivative.

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DOI:
https://doi.org/10.1090/qam/1878261

Article copyright:
© Copyright 2002
American Mathematical Society