A local-effective relation in planar linear elasticity

TL;DR

This paper presents a specific relation between local and effective elastic properties in planar linear elastic structures, exemplified by a perforated plate with periodic isotropic material properties.

Contribution

It introduces a new relation linking local and effective elastic properties in 2D periodic structures, considering geometric constants.

Findings

Established a relation between local and effective properties in planar elasticity.

Applied the relation to perforated plates with isotropic, homogeneous elasticity.

Provided insights into the influence of geometry on elastic behavior.

Abstract

We give an example of a relation between local and effective properties for elastic structures, up to geometric constants. The model considered is a periodic structure with isotropic and homogeneous local elasticity tensor in planar linear elasticity. The corresponding physical model is a flat two dimensional body with holes as, for example, a perforated plate.