A third gradient elastic material resulting from the homogenization of a von Kármán ribbon‐reinforced composite

Abstract

We study the homogenization of an elastic material reinforced with thin periodic parallel elastic ribbons. We assume perfect adhesion along the common interface between the matrix and the ribbons. We assume that the ribbons are isotropic von Kármán plates of highly contrasting rigidity with respect to that of the matrix. The main result is the derivation of an effective stored energy involving new degrees of freedom implying second and third gradient of displacements.

Wave Behavior Characteristics of Elastically Supported Fluid-Conveying Carbon Nanotubes under the Influence of Magnetic Fields

“…Carbon nanotubes (CNTs) have drawn the extensive interest researchers since their discovery because of their superior electrical, thermal, mechanical , and physical attribute [1][2][3][4][5]. Due to these excellent properties, CNTs are widely used in the development of nano-electro-mechanical systems (NEMS) [6][7][8][9]; The structural properties of CNTs can be used for nanofluid fluid conveying and hydrogen storage 10. Additionally, CNTs can be used to make composites with metals, cements, and glass fibers to compensate for the inadequacies of each material and create high strength, high performance composites [11,12].…”