Cite the paper
Mechanics, Materials Science & Engineering, 19 , 2019, ISSN: 2412-5954.
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
 Carpinteri A, Paggi M., 2009, Eng. Fracture Mech., 76, 1771–84.
 Lazar M., 2013, Int. J. Solids Struct. 50, 352–62.
 Altan B. S. and Aifantis E. C., 1997, J. Mech. Behav. Mater., 8, 231–82.
 Lurie S., Belov P., Volkov-Bogorodsky D. and Tuchkova N., 2006, J. Mater. Sci. 41, 6693–707
 Lurie S.A., Volkov-Bogorodsky D.B., Zubov V.I. and Tuchkova N.P., 2009, Int. J. Comp. Mater. Sci., 45, 709–14.
 Lurie S., Volkov-Bogorodskii D. and Tuchkova N. 2016, Acta Mech., 227, 127–38 .
 Lurie S.A., Volkov-Bogorodskii D.B. and Aifantis E.C., 2011, Int. J. Eng. Sci., 49, 1517–25.
 Vasil’ev V.V. and Lurie S.A., 2015, Mech. Solids, 50, 379–88.
 Papkovich P.F., 1939 Elasticity theory (Moscow, Leningrad: GITTL).
 Vladimirov V.S., 1971 Equations of mathematical physics (New York: Marcel Dekker Inc).
Mechanics, Materials Science & Engineering Journal by Magnolithe GmbH is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at www.mmse.xyz.