Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

Abstract

Instabilities in solids and structures are ubiquitous across all length and time scales, and engineering design principles have commonly aimed at preventing instability. However, over the past two decades, engineering mechanics has undergone a paradigm shift, away from avoiding instability and toward taking advantage thereof. At the core of all instabilities-both at the microstructural scale in materials and at the macroscopic, structural level-lies a nonconvex potential energy landscape which is responsible, e.g., for phase transitions and domain switching, localization, pattern formation, or structural buckling and snapping. Deliberately driving a system close to, into, and beyond the unstable regime has been exploited to create new materials systems with superior, interesting, or extreme physical properties. Here, we review the state-of-the-art in utilizing mechanical instabilities in solids and structures at the microstructural level in order to control macroscopic (meta)material performance. After a brief theoretical review, we discuss examples of utilizing material instabilities (from phase transitions and ferroelectric switching to extreme composites) as well as examples of exploiting structural instabilities in acoustic and mechanical metamaterials.

Nonreciprocal wave phenomena in spring-mass chains with effective stiffness modulation induced by geometric nonlinearity

“…While the parameters considered in this work were chosen to keep the effective stiffness everywhere positive, the points of instability can be reached by further increasing the respective parameter variations. These instabilities, while interesting in their own right (see [34] and references therein), would violate the assumptions of a slowly-varying pump wave and are outside the scope of the present study. Nevertheless, buckling structures may be useful in future studies to achieve strong and highly tunable modulations by operating near, but not fully reaching, instability.…”

Programmable higher-order Euler buckling modes in hierarchical beams

“…We conclude this work by noting that the proposed simple hierarchical beams provide a gateway to multimodal instability-induced patterns by use of their intriguing and programmable undulated morphologies. Such hierarchical structures can be used in a number of applications from functional surfaces to structural self-similar hierarchical materials (Wang and Zhao, 2016;Kochmann and Bertoldi, 2017). Furthermore, the response of the proposed hierarchical structures is highly scalable since it is mainly dominated by the inherent geometrical nonlinearities.…”

“…Harnessing geometrical instabilities (such as buckling) to achieve programmable patterns and curvature is a challenge of current soft matter physics and mechanics. Soft materials represent an ideal platform for designing systems that may reversibly change curvature or shape when instabilities and buckling set in (Kochmann and Bertoldi, 2017). Instabilities in soft matters yield a number of geometrical features (Li et al, 2012).…”

Reversible signal transmission in an active mechanical metamaterial

“…Substituting travelling wave variables f (z) =û(x,t) and h(z) =â(x,t), where z =x − ct ∈ R, into equations (6) and (7), and dividing by c 2 − 1, gives the travelling wave model:…”

“…Mechanical metamaterials are artificially constructed and have mechanical properties defined by their structure [1]. Simple metamaterials consist of a one, two, or three-dimensional array of elements connected by links [1][2][3] that may be elastic [4][5][6][7], magnetic [8,9] or electrostatic [4]. Mechanical metamaterials are highly tuneable [10][11][12] and by altering the structure of these elements, and the properties of the links, materials have been developed that selectively transmit signals [13,14], behave as logic gates [5,15] or buckle after the application of external stimulus [2].…”