Homogenization of elastic grids containing rigid elements

TL;DR

This paper develops a homogenization method for 2D elastic grids with rigid elements, enabling the design of advanced architected materials with tailored mechanical properties like auxeticity.

Contribution

A novel homogenization tool for elastic grids with rigid elements, accounting for different joint constraints, facilitating the design of complex metamaterials.

Findings

Rigid element constraints significantly affect mechanical behavior.

Homogenization method tested on complex geometries like Chinese lattices.

Results enable tailored mechanical properties in architected materials.

Abstract

The inclusion of rigid elements into elastic composites may lead to superior mechanical properties for the equivalent elastic continuum, such as, for instance, extreme auxeticity. To allow full exploitation of these properties, a tool for the homogenization of two-dimensional elastic grids containing rigid elements is developed and tested on elaborate geometries, such as, for instance, Chinese lattices. The rigid elements are assumed to be either jointed with full continuity of displacement or hinged to the elastic rods. It is shown that the two different constraints induce strongly different mechanical characteristics of the equivalent elastic solid. The presented results open the way to the design of architected materials or metamaterials containing both elastic and rigid parts.