RADIAL MULTIPLIERS METHOD IN NON-LOCAL ELASTICITY AND FRACTURE MECHANICS

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Lurie, S A; Volkov-Bogorodsky, D B; Mardaleishvili, N V

RADIAL MULTIPLIERS METHOD IN NON-LOCAL ELASTICITY AND FRACTURE MECHANICS Journal Article

Mechanics, Materials Science & Engineering, 19 , 2019, ISSN: 2412-5954.

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Authors: S.A. Lurie, D.B. Volkov-Bogorodsky, N.V. Mardaleishvili

ABSTRACT. A generalized theory of elasticity for nonlocal generalized displacements constructed by way of averaging over finite regions with accuracy up to high order derivatives is considered. The solution of a boundary value problems for the formulated gradient theory of elasticity is constructed through potentials that satisfy the Laplace and Helmholtz equations on the base of the generalized Papkovich-Neuber representation. Theorems about the structure of fundamental solutions in the radial multipliers method and about their connection with fundamental solutions of the Helmholtz and Laplace equations are presented. On the basis of the radial multipliers method the solution of the generalized non-local elasticity is constructed explicitly for a number of important applied problems used in the modeling and prediction of the effective properties of dispersed-reinforced composites (with allowance for scale effects) and in problems of nonsingular fracture mechanics.

Keywords: radial multipliers, non-local elasticity, fracture mechanics

DOI 10.2412/mmse.81.73.713

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