On a theory of nonlocal elasticity of bi-Helmholtz type and some applications

By Markus Lazar, G. Maugin, Elias C. Aifantis. 2006

195 citations recorded by the source corpus.

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.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f098dadb68edaf855a6b3e7b8dfb7910bb3d8ebd

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

On nonconservativeness of Eringen’s nonlocal elasticity in beam mechanics: correction from a discrete-based approach (2014, background): “Hence, such nonlocal models have found numerous applications in the field of wave propagation in heterogeneous materials (see [9] or [10]).”
Second strain gradient elasticity of nano-objects (2016, background): “For instance, the effective first displacement gradient theory was identified from the atomic potentials for nano-porous silicon by Magoariec and Danescu (2009).”