J. D. Goddard, “Nonlinear Elasticity and Pressure-Dependent Wave Speeds in Granular Media,” Proceedings of the Royal Society of London A, Vol. 430, No. 1878, 1990, pp. 105-131.

has been cited by the following article:

• TITLE: Towards a Mathematical Model for Elastic Wave Propagation in Granular Materials

  AUTHORS: Leonardo Trujillo, Vanessa Torres, Franklin Peniche, Leonardo Di G. Sigalotti

  KEYWORDS: Granular Media; Elastic Waves; Nonlinear Elasticity; Hydrostatic Compression; Granular Elasticity

  JOURNAL NAME: Engineering, Vol.4 No.12A, December 31, 2012

  ABSTRACT: A theoretical model for the propagation of acoustic waves in dry granular media is presented within the framework of the nonlinear granular elasticity. An essential ingredient is the dependence of the elastic moduli on compression. For the purpose of illustration, we analyze the case of a time-harmonic plane wave propagation under isotropic compression. We derive explicit relations for the wave speed dependence with the confining pressure. The present approach provides an accurate description of acoustic wave propagation in granular packings and represents a powerful tool to interpret the results of current experiments.