Longitudinal and transverse elastic waves in 1D granular materials modeled as micromorphic continua

Abstract

In this paper, the granular micromechanics approach proposed by Misra and Poorsolhjouy (2016) is used to study the dispersive behavior of granular materials in response to elastic deformation waves. This study is motivated by the typical lack of connection between the mathematical models, the parameters involved, and the physics of granular materials. Therefore, extensive parametric studies are carried out in order to understand how each intergranular stiffness coefficient contributes to the dispersive behavior of the material. Two cases of one dimensional wave propagation problems have been investigated. Case 1 focuses upon longitudinal wave propagation in a one dimensional continuum, while case 2 considers transverse wave propagation in a one dimensional continuum that has a two-dimensional micro-structure. Results predict the emergence of frequency band gaps and negative group velocities for certain values of the parameters involved. Such phenomena can be produced by starting from the micro-structure and producing materials for which the inter-granular stiffness parameters are the ones the granular micromechanics approach predict. This, however, is not a one to one mapping, and therefore, sets of solutions to achieve a particular behavior might exist. Therefore, granular micromechanics provides a systematic material design process, eliminating ad-hoc processes and potentially leading to large data libraries.