Buckling vs unilateral constraint for a multistable metamaterial element

TL;DR

This paper explores a multistable metamaterial element based on a bifurcating strut, demonstrating its nonlinear quasi-static response and equivalence to unilateral constraints, revealing bistable and tetrastable behaviors.

Contribution

It introduces a novel structural element with bifurcation-based multistability, linking buckling to unilateral constraints and analyzing its nonlinear static response.

Findings

The element exhibits bistability and tetrastability.

Buckling at zero load is equivalent to unilateral constraints.

The structure's nonlinear response shows multistability.

Abstract

A structural element is designed and investigated, forming the basis for the development of an elastic multistable metamaterial. The leitmotif of the structural design is the implementation of a strut characterized by a bifurcation occurring at either vanishing tensile or compressive load. It is shown that buckling at null load leads to a mechanical equivalence with a unilateral constraint formulation, introducing shocks in dynamics. Towards a future analysis of the latter, the nonlinear quasi-static response is investigated, showing the multistable character of the structure, which may appear as bistable or tetrastable.