Wavefront in Second-Order Elasticity Determined by PerturbationMethod Applied to the Eikonal Equation

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.