Invariant energy integrals for the non-linear crack problem with possible contact of the crack surfaces |
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| Institution: | 1. Department of Mechanical Engineering, Tufts University, Robinson Hall, Room 161, 200 College Avenue, Medford, MA 02155 USA;2. Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg 195251, Russian Federation;3. Mechanical Engineering Research Institute of the Russian Academy of Sciences, 85, Belinskogo str., Nizhny Novgorod 603950, Russian Federation |
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| Abstract: | Generally two-dimensional and three-dimensional formulations of the non-linear crack problem when the crack surfaces do not overlap for a non-uniform anisotropic linearly elastic body are considered. The first derivative of the potential energy function with respect to the perturbation parameter and its representation in the form of an invariant integral over an arbitrary closed contour are obtained for a general form of the differentiable perturbation of a region with a cut, using the method of material derivatives. The sufficient conditions for the existence of an invariant energy integral are derived in general form, and examples of invariant integrals are constructed for different types of perturbations and a different geometry of the cut. |
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