Origami-based impact mitigation via rarefaction solitary wave creation

Abstract

The principles underlying the art of origami paper folding can be applied to design sophisticated metamaterials with unique mechanical properties. By exploiting the flat crease patterns that determine the dynamic folding and unfolding motion of origami, we are able to design an origami-based metamaterial that can form rarefaction solitary waves. Our analytical, numerical, and experimental results demonstrate that this rarefaction solitary wave overtakes initial compressive strain waves, thereby causing the latter part of the origami structure to feel tension first instead of compression under impact. This counterintuitive dynamic mechanism can be used to create a highly efficient—yet reusable—impact mitigating system without relying on material damping, plasticity, or fracture.

Propagation of elastic solitons in chains of pre-deformed beams

“…By contrast, when the impact moves the first beam rightwards (see figure 2(f)), the excited compression pulse disperses as it travels through the structure (see figure 2(g)). As such, in full agreement with previous studies on mechanical chains exhibiting strain-softening [16,33], our experimental results suggest that large amplitude rarefaction waves are stable, whereas compression pulses disperse. Finally, we want to point out that, while the experimental results reported in figures 2(d)-(g) are for a chain with a pre-strain ε st =−0.1, qualitatively similar behaviors are observed in our tests for ε st =−0.2 (see figures 2(h), (i)).…”

“…Following the seminal numerical experiment of Fermi-Pasta-Ulam-Tsingou [1], which was related by Zabusky and Kruskal to the propagation of solitons [2], a variety of model equations, solution methods and experimental platforms have been developed to investigate the dynamics of discrete and nonlinear one-dimensional mechanical systems across many scales [3][4][5][6][7][8]. At the macroscopic scale, propagation of solitary waves has been observed in a variety of nonlinear mechanical systems, including chains of elastic beads [9][10][11][12][13][14], tensegrity structures [15], origami chains [16], wrinkled and creased helicoids [17] and flexible architected solids [18][19][20][21]. Moreover, it has been found that even at the molecular scale solitons affect the properties of a variety of onedimensional structures, including macromolecular crystals [22], polymer chains [23][24][25][26], DNA and protein molecules [27][28][29][30].…”

Self-induced topological transition in phononic crystals by nonlinearity management

“…Previous studies have shown the excellent potential of nonlinear phononic crystals manipulating vibrations in general (see [5,6] and references therein). Especially appealing are elastic systems in which a tremendous degree of nonlinearity management could be achieved through material and geometric parameters, for example, using * rajeshcuw@gmail.com † georgiostheocharis@gmail.com contacts [7], LEGO blocks [8], origami folding [9], tensegrity structures [10], or architected soft media [11]. All these structures and other proposed flexible mechanical metamaterials [12] can thus be excellent model candidates for the fundamental understanding of the interplay of nonlinearity and topology in mechanics.…”

Focusing and Mode Separation of Elastic Vector Solitons in a 2D Soft Mechanical Metamaterial

“…While initial efforts in the field have focused on systems with unusual linear properties, such as negative Poisson's ratio [6][7][8], negative stiffness [9,10], and negative thermal expansion [11,12], large deformation and nonlinearities have been recently embraced as a means toward new functionalities, including programmability [13], energy absorption [14], and shape transformation [15]. Moreover, it has been shown that highly deformable mechanical metamaterials can be designed to support the propagation of a variety of nonlinear waves with large displacement amplitudes [16][17][18][19], providing a convenient platform to study nonlinear wave physics. However, to date the investigation of the nonlinear dynamic response of flexible metamaterials has been limited to one-dimensional (1D) systems.…”