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arXiv · 2605.10952

Homogenization of one-dimensional periodic rod networks as special Cosserat rods

Vinayak·Ajeet Kumar
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Abstract

One-dimensional periodic rod networks are the structures that are obtained by periodically assembling its microstructural unit, a network of rods itself, in just one direction. In this work, we present a scheme for obtaining the nonlinear constitutive response of such structures when homogenized macroscopically as a continuum rod. To accurately capture arbitrary and large deformations, the geometrically exact special Cosserat rod theory is used for modeling the rod at both micro- and macroscales. By assuming the periodic structure to be strained uniformly, at macroscale, along its arc length, the full structure problem is reduced to just that of its microstructural unit but subjected to helically periodic boundary condition. The microscale problem, consisting of a network of rods and formulated in a variational setting, is solved in the presence of rod-joint constraints and helically periodic boundary conditions. The expressions for the macroscale rod's stress resultants, i.e. internal contact force and moment, and stiffnesses are then obtained. Finally, several numerical examples having different microstructural units are presented to demonstrate our method. First, the results corresponding to simpler square and cross microstructural units are presented and validated with the existing literature. Square microstructural units having helical constituent rods are then taken up which have application as artificial muscle fiber material. Eventually, homogenization of auxetic tubular metamaterials is performed. It is shown how various design parameters of these microstructural units can be tuned to obtain the desired macroscopic response.

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BibTeXRIS

Vinayak, Ajeet Kumar. 2026-04-30. Homogenization of one-dimensional periodic rod networks as special Cosserat rods. https://arxiv.org/abs/2605.10952

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