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Wave fronts in second-order elasticity determined by perturbation method applied to the eikonal equation

Continuum Mechanics and Thermodynamics volume 25, pages 229–242 (2013)Cite this article

Abstract

In Marasco and Romano (Math Comput Model 49(7–8)1504–1518, 2009), Marasco (Math Comput Model 49(7–8):1644–1652, 2009; Int J Eng Sci 47(4):499–511, 2009), we have proposed a perturbation method to determine the speed and the amplitude of the acceleration waves in a second-order elastic body. In this paper, using the above results, we apply a perturbation procedure to analyze the evolution of the wave front of an acceleration wave in the same class of elastic materials. In particular, a second-order approximate solution of the eikonal equation is determined introducing a suitable system of coordinates. The general results are applied to an infinitesimal deformation, and the analytical solution of the eikonal equation is compared with the exact numerical one.

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Authors and Affiliations

  1. Department of Mathematics and Applications “R. Caccioppoli”, University of Naples Federico II, Via Cintia, 80126, Naples, Italy

    A. Marasco & A. Romano

Authors
  1. A. Marasco
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  2. A. Romano
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Correspondence to A. Marasco.

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Communicated by Francesco dell'Isola and Samuel Forest.

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Marasco, A., Romano, A. Wave fronts in second-order elasticity determined by perturbation method applied to the eikonal equation. Continuum Mech. Thermodyn. 25, 229–242 (2013). https://doi.org/10.1007/s00161-012-0243-z

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  • DOI: https://doi.org/10.1007/s00161-012-0243-z

Keywords

  • Wave fronts
  • Eikonal equation
  • Nonlinear elasticity
  • Perturbation method
  • Second-order effects