title: Universal relations for solitary waves in granular crystals under shocks with finite rise and decay times.
abstract: We focus on solitary waves generated in arrays of lightly contacting spherical elastic granules by shock forces of steep rise and slow decay durations and establish a priori: (i) whether the peak value of the resulting solitary wave would be greater than, equal to, or less than the peak value of the input shock force; (ii) the magnitude of the peak value of the solitary waves; (iii) the magnitude of the linear momentum in each solitary wave; (iv) the magnitude of the linear momentum added to the remaining granules if the first granule is ejected; and (v) a quantitative estimate of the effect of the granules' radius, density, and stiffness on force amplification or mitigation. We have supported the analytical results by direct numerical simulations.
authors.affiliation: Department of Mechanical and Aerospace Engineering, Center of Excellence for Advanced Materials, Jacobs School of Engineering, University of California, San Diego, California 92093-0416, USA.
authors.forename: M
authors.initials: M
authors.lastname: Arif Hasan
authors.affiliation: Department of Mechanical and Aerospace Engineering, Center of Excellence for Advanced Materials, Jacobs School of Engineering, University of California, San Diego, California 92093-0416, USA.
authors.forename: Sia
authors.initials: S
authors.lastname: Nemat-Nasser