On the Radial Multipliers Method in the Gradient Elastic Fracture Mechanics
- Authors: Lurie S.A.1, Volkov-Bogorodskiy D.B.1
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Affiliations:
- Institute of Applied Mechanics
- Issue: Vol 40, No 7 (2019)
- Pages: 984-991
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205074
- DOI: https://doi.org/10.1134/S199508021907014X
- ID: 205074
Cite item
Abstract
A non-singular solution of the gradient elastic fracture mechanics for the cracks of Modes I and II is constructed in this paper. Previously, a similar problem was solved only for cracks of Mode III. A generalized theory of elasticity is used, in which the governing equation in displacements is represented as a product of the Lamé operator and the Helmholtz operator, and the classical boundary value problem for the total stress is completely distinguished in the problems of crack mechanics. As a result, the determination of local stress fields reduces to solving the Helmholtz equations with the known right-hand side of the equations. The Papkovich-Neuber representation in a complex form is used to construct a solution of the mechanics of cracks. We used also the method of radial multipliers, which allows us to construct fundamental solutions of the Helmholtz equations corresponding to analytical functions with a fractional exponent and, as a result, to find solutions that compensate for the singularities.
About the authors
S. A. Lurie
Institute of Applied Mechanics
Author for correspondence.
Email: salurie@mail.ru
Russian Federation, Moscow, 125040
D. B. Volkov-Bogorodskiy
Institute of Applied Mechanics
Author for correspondence.
Email: volkov-bogorodskij@iam.ras.ru
Russian Federation, Moscow, 125040