Two-dimensional nonlinear shear waves in materials having hexagonal lattice structure. (January 2016)

• Record Type: Journal Article
• Authors: Porubov, AV; Berinskii, IE
• Other Names: Eremeyev Victor A guest-editor.; Porubov Alexey V guest-editor.; Placidi Luca guest-editor.
• Is Part Of: Mathematics and mechanics of solids. Volume 21:Number 1(2016:Jan.)
• Page Start: 94
• Page End: 103
• Publication Date: 2016-01
• Subjects: Nonlinear hexagonal lattice -- continuum limit -- nonlinear differential equation -- asymptotic solution; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286515577040
• Languages: English
• ISSNs: 1081-2865

Abstract

An asymptotic procedure is developed to obtain governing two-dimensional nonlinear equations as a result of the continuum limits of the original discrete hexagonal lattice model. Possible continualization is analyzed on the basis of linearized discrete equations. New weakly nonlinear continuum equations for plane and weakly transverse disturbed shear waves in a hexagonal lattice are obtained using different continuum limits. It is shown that nonlinear plane shear waves are described different from the model of isotropic continuum.