Adaptable nonlinear bimode metamaterials with rigid bars, pivots, and actuators

TL;DR

This paper introduces a new class of periodic planar nonlinear bimode metamaterials constructed from rigid bars and pivots, capable of controlled macroscopic deformation through embedded actuators, with potential for adaptive structural design.

Contribution

It presents the design and analysis of nonlinear bimode metamaterials with controllable deformation, and discusses the concept of adaptable nonlinear affine and non-affine materials.

Findings

Bimode metamaterials have deformation paths on a 2D surface in invariants space.

Adding actuators enables control of macroscopic deformation.

Examples of non-affine unimode and bimode materials are provided.

Abstract

A large family of periodic planar non-linear bimode metamaterials are constructed from rigid bars and pivots. They are affine materials in the sense that their macroscopic deformations are only affine deformations: at large distances any deformation must be close to an affine deformation. Bimode means that the paths of all possible deformations of Bravais lattices that preserve the periodicity of the lattice lie on a two dimensional surface in the three dimensional space of invariants describing the deformation (excluding translations and rotations). By adding two actuators inside a single microscopic cell one can control the macroscopic deformation, which may be useful for the design of adaptive structures. The design of adaptable nonlinear affine trimode metamaterials (for which the macroscopic deformations lie within a three-dimensional region in the space of invariants) is discussed, although their realization remains an open problem. Examples are given of non-affine unimode and non-affine bimode materials. In these materials the deformation can vary from cell to cell in such a way that the macroscopic deformation is non-affine.