Homogenization of architected materials incorporating shearable beams

TL;DR

This paper enhances the homogenization of 2D architected materials by incorporating shear deformability via Timoshenko beam theory, enabling more accurate modeling and expanded design capabilities of microstructured grids.

Contribution

It introduces a homogenization method that accounts for shear deformation in elastic beams, broadening the design space of architected materials.

Findings

Shear deformability significantly affects effective material properties.

Design of microstructures can achieve extreme mechanical characteristics.

Expanded control over Poisson's ratio beyond slender beam limits.

Abstract

Two-dimensional architected materials are often realized as periodic grids of elastic beams. Conventional homogenization methods represent these structures as equivalent elastic solids but neglect shear deformation in the constituent beams. This article addresses this limitation by incorporating shear deformability through Timoshenko beam theory, enabling accurate modeling of stubby beams. Moreover, shearable beams with extreme mechanical characteristics can be obtained through the design of appropriate microstructures. Introducing shearable beams into the grid expands the design space, allowing, for instance, the control of the effective Poisson's ratio beyond the limits achievable with slender beams.