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

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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

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  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

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