For understanding the topological effects on the effective in-plane elastic parameters, closed form equations for regular hexagonal, square, and equilateral triangular unit cells listed in Table 2 are compared with the current computational investigations on hexagonal-chiral RVEs.
The results plotted for effective moduli , , and in Figure 6 show that stiffness is favored as the topology changes from hexagonal to triangular RVE.
As stated in [ 3 , 11 ], the main reason is the increasing dominancy of stretching over bending with this type of topological change. According to Figure 6 , the hexagonal-chiral configuration yields the highest shear moduli among all of the investigated topologies.
It is a promising result especially for the materials subject to shear loads—for example, packaging products and cargo containers. However, this response is lower for the triangular RVE and almost negligible for square one. The proposed hexagonal-chiral configuration has and values that are much lower than the regular hexagonal RVE, which are comparable with those for the triangular and square RVEs.
In the present study, topological and morphological effects on the effective stiffness of cellular materials in the transverse plane are investigated by means of a first-order strain-driven computational homogenization method. For this purpose, representative volume elements RVEs of regular hexagonal, square, triangular, and hexagonal-chiral configurations are studied to understand how cell topology i. Closed form solutions for regular hexagonal, square, and triangular RVEs provided in the literature are then taken as the basis for model validation and comparison.
The results show that there is a positive effect of cell wall slenderness on the effective elastic parameters due to increase in the cell wall material volume.
In addition to this, it is also deduced that there are drastic differences between regular hexagonal and hexagonal-chiral configurations, which can be explained in terms of deformation mechanism transformations between bending and stretching due to topological changes.
Hence, the introduced chirality can be used as a tailored solution for materials and structures subject to high shear loads. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the sponsors.
The second author acknowledges support by the National Science Foundation under Grant no. Glaucio Paulino and Dr. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors. Read the winning articles. Journal overview. Special Issues. Academic Editor: Ying Li. Received 10 Apr Accepted 02 Jun Published 19 Jul Abstract The present study investigates the influence of topology and morphology on the effective stiffness of chiral cellular materials in the transverse plane by means of a homogenization method.
Introduction In recent years, with growing interest in energy efficient, robust, and lightweight material systems, cellular materials have found their way into numerous engineering applications. Figure 1. Hexagonal and hexagonal-chiral structures and corresponding representative volume elements.
Figure 2. Strain-driven homogenization scheme with imposed macroscopic strain and computed stress for. Here, and represent the volume and boundary of aggregate, and and represent the volume and boundary of RVE. Figure 3. Schematics of the investigated geometrical properties and matching nodes for periodic boundary conditions: a nodal mapping for periodic boundary conditions and b cell geometric parameters, cell wall thickness , height , and hub diameter.
Case Imposed strains 1 0. Table 1. Figure 4. Schematic representation of loading conditions based on the listed cases in Table 1 presented deformations are scaled larger than the actual ones for readability : a undeformed hexagonal RVE, b deformation under , c deformation under , d deformation under , e undeformed hexagonal-chiral RVE, f deformation under , g deformation under , and h deformation under.
Table 2. Tools that enable essential services and functions, including identity verification, service continuity and site security. This option cannot be declined. Tools that collect anonymous data about website usage and functionality. We use this information to improve our products, services and user experience. Profilometer analysis of the dimples on a steel sheet. When quantitative figures on general roughness are required, analytical techniques with surface scanning features are usually employed.
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