On a Theory of Nonlocal Elasticity of Bi-Helmholtz Type and Some Applications
Document Type
Article
Publication Date
3-2006
Department
Department of Mechanical Engineering-Engineering Mechanics
Abstract
A theory of nonlocal elasticity of bi-Helmholtz type is studied. We employ Eringen's model of nonlocal elasticity, with bi-Helmholtz type kernels, to study dispersion relations, screw and edge dislocations. The nonlocal kernels are derived analytically as Green functions of partial differential equations of fourth order. This continuum model of nonlocal elasticity involves two material length scales which may be derived from atomistics. The new nonlocal kernels are nonsingular in one-, two- and three-dimensions. Furthermore, the nonlocal elasticity of bi-Helmholtz type improves the one of Helmholtz type by predicting a dispersion relationship with zero group velocity at the end of the first Brillouin zone. New solutions for the stresses and strain energy of screw and edge dislocations are found.
Publication Title
International Journal of Solids and Structures
Recommended Citation
Lazar, M.,
Maugin, G.,
&
Aifantis, E. C.
(2006).
On a Theory of Nonlocal Elasticity of Bi-Helmholtz Type and Some Applications.
International Journal of Solids and Structures,
43(6), 1404-1421.
http://doi.org/10.1016/j.ijsolstr.2005.04.027
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/6576
Publisher's Statement
© 2005 Elsevier Ltd. All rights reserved.