Lazar, Markus; Maugin, Gérard A.; Aifantis, Elias C. On a theory of nonlocal elasticity of bi-Helmholtz type and some applications. (English) Zbl 1120.74342 Int. J. Solids Struct. 43, No. 6, 1404-1421 (2006). Summary: 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. Cited in 1 ReviewCited in 55 Documents MSC: 74B99 Elastic materials Keywords:Nonlocal elasticity; dislocations PDFBibTeX XMLCite \textit{M. Lazar} et al., Int. J. Solids Struct. 43, No. 6, 1404--1421 (2006; Zbl 1120.74342) Full Text: DOI