Linearly polarized waves of finite amplitude in pre-strained elastic materials. (19th June 2019)

• Record Type: Journal Article
• Authors: Pucci, Edvige; Saccomandi, Giuseppe; Vergori, Luigi
• Is Part Of: Proceedings. Volume 475:Number 2226(2019)
• Publication Date: 2019-06-19
• Subjects: wave propagation in incompressible isotropic hyperelastic materials -- viscosity admissibility criterion for shock waves -- asymptotic analysis; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2018.0891
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : We study the propagation of linearly polarized transverse waves in a pre-strained incompressible isotropic elastic solid. Both finite and small-but-finite amplitude waves are examined. Irrespective of the magnitude of the wave amplitude, these waves may propagate only if the (unit) normal to the plane spanned by the directions of propagation and polarization is a principal direction of the left Cauchy–Green deformation tensor associated with the pre-strained state. A rigorous asymptotic analysis of the equations governing the propagation of waves of small but finite amplitude reveals that the time scale over which the nonlinear effects become significant depends on the direction along which the wave travels. Moreover, we design theoretically an experimental procedure to determine the Landau constants of the fourth-order weakly nonlinear theory of elasticity.