Harnessing mechanical instabilities for functional structures using nonlinear building blocks

Instabilities in mechanical structures have traditionally been viewed as failure modes to be avoided. Recently, however, they have emerged as opportunities to embed advanced functionalities such as sensing, actuation, and programmability. This thesis explores how to harness and understand the complex behaviors arising from such instabilities, with a focus on nonlinear interactions between mechanical building blocks.

We first introduce and experimentally demonstrate countersnapping instabilities, in which structures exhibit counterintuitive responses, such as contracting under tension or generating sudden force increases upon snapping. These behaviors arise from self-intersecting force–displacement curves and are achieved through carefully designed assemblies of geometrically nonlinear elements. We show that these systems enable unique functionalities, including programmable stiffness, unidirectional actuation, and passive vibration control, and that their coupling leads to richer, hierarchical behaviors.

To support the analysis and design of such systems, we develop a computational framework based on flexels, reduced-order elements that encode complex force–displacement relationships into energy potentials. This approach allows efficient modeling of a wide range of nonlinear systems and is implemented as an open-access Python library.

Finally, we combine these concepts to study the interaction between a warped plate and nonlinear pillars, demonstrating enhanced geometric rectification enabled by countersnapping behavior. More broadly, we extract transition graphs from force-displacement curves and use them as a tool to analyze complex nonlinear responses.

Together, this work establishes a framework for designing and understanding mechanical systems comprising building blocks that exploit instabilities to achieve advanced and unconventional functionalities.