On the statics and dynamics of granular-microstructured rods with higher order effects

Abstract

Granular-microstructured rods show strong dependence of grain-scale interactions in their mechanical behavior, and therefore, their proper description requires theories beyond the classical theory of continuum mechanics. Recently, the authors have derived a micromorphic continuum theory of degree n based upon the granular micromechanics approach (GMA). Here, the GMA is further specialized for a one-dimensional material with granular microstructure that can be described as a micromorphic medium of degree 1. To this end, the constitutive relationships, governing equations of motion and variationally consistent boundary conditions are derived. Furthermore, the static and dynamic length scales are linked to the second-gradient stiffness and micro-scale mass density distribution, respectively. The behavior of a one-dimensional granular structure for different boundary conditions is studied in both static and dynamic problems. The effects of material constants and the size effects on the response of the material are also investigated through parametric studies. In the static problem, the size-dependency of the system is observed in the width of the emergent boundary layers for certain imposed boundary conditions. In the dynamic problem, microstructural effects are always present and are manifested as deviations in the natural frequencies of the system from their classical counterparts.

Parametric Experimentation to Evaluate Chiral Bars Representative of Granular Motif

“…The findings of this work suggest future enhancements in both the theoretical model and the experimental campaign. From a theoretical viewpoint, there is need to introduce additional kinematic features [39], which may allow for the prediction of boundary layers as well the evaluation of deformation under multiple boundary conditions. These theoretical predictions would need corresponding experimental investigations in which the boundary conditions and the geometric features were controlled with greater precision, which may better reveal the effect of microfeatures at the macroscale.…”

“…This form accounts for micro-macro transfer of energy (coupling) and length scale effects in the axial deformation of rods. If it is further assumed that 11 0   , the result is a second gradient model of a rod incorporating length scale effects[39]. Within the scope of the present paper, the case considered is the one in which the kinematic measure 111  vanishes (such that the polynomial expansion of…”

Shear vibration modes of granular structures: Continuous and discrete approaches

“…Cosserat continuum model (Cosserat & Cosserat [12,13]) which is tantamount as micropolar continuum or non-classical continuum theories (Nowacki [14], Eringen [15,16]), introduce intrinsic length scales through the consideration of additional DOF (Eringen [17,18,19]). Studying one-dimensional problems which are assumed as a first step to investigate the enriched continuum mechanics efficiently and precisely, is taken into consideration by many authors either by using bar-chain (Duan et al [20], Zhang et al [21], Wang et al [22]) or granular chain (Challamel et al [23], Nejadsadeghi and Misra [24]).…”