Toggling stiffness via multistability

TL;DR

The paper addresses the challenge of achieving discrete, toggleable stiffness in lightweight mechanical systems by engineering multistable metamaterials. It introduces bistable unit cells where stiffness switching arises from rotation transfer from slender support beams to a curved beam, and provides design rules linking slenderness and hinge placement to the stiffness contrast, supported by Abaqus/COMSOL analyses and 3D-printed TPU experiments. A two-cell metamaterial validates the concept under shear, while a monolithic soft clutch demonstrates practical, actuator-free stiffness modulation with four distinct levels. The work offers a pathway to adaptive, lightweight soft structures for soft robotics and vibration control, with future directions including integration with soft actuators and scaling down to smaller devices.

Abstract

Mechanical metamaterials enable unconventional and programmable mechanical responses through structural design rather than material composition. In this work, we introduce a multistable mechanical metamaterial that exhibits a toggleable stiffness effect, where the effective shear stiffness switches discretely between stable configurations. The mechanical analysis of surrogate beam models of the unit cell reveal that this behavior originates from the rotation transmitted by the support beams to the curved beam, which governs the balance between bending and axial deformation. The stiffness ratio between the two states of the unit cell can be tuned by varying the slenderness of the support beams or by incorporating localized hinges that modulate rotational transfer. Experiments on 3D-printed prototypes validate the numerical predictions, confirming consistent stiffness toggling across different geometries. Finally, we demonstrate a monolithic soft clutch that leverages this effect to achieve programmable, stepwise stiffness modulation. This work establishes a design strategy for toggleable stiffness using multistable metamaterials, paving the way for adaptive, lightweight, and autonomous systems in soft robotics and smart structures.

Figures (6)

• Figure 1: Conceptual sketch of the toggling stiffness. Geometry of the unit cell in State 0 (a) and State 1 (b) when a tensile force is applied and its nonlinear force-displacement behaviour. c) Difference in stiffness between the two states under a shear load. 3D printed bistable unit cell in State 0 (d) and State 1 (e).
• Figure 2: Results from Model A. (A) Deformations for State 0 and State 1 under isolated horizontal force $F$, isolated bending moment $M$, and the combined load case. (B) Parameter sweep showing the stiffness ratio between states as a function of the applied bending moment $M$.
• Figure 3: Results from Model B. a) Model of the unit cell in the beam analysis. b) Variation of the stiffness ratio with the slenderness of the support beams in the case of no hinge, bottom hinge and top hinge. c) Deformation patterns for State 0 and State 1 at representative slenderness values ($s = 0.1$, $s = 0.3$, $s = 0.8$) for all hinge configurations.
• Figure 4: Mechanical characterization of two-cell metamaterials (support beam slenderness $s=0.7$) with the standard unit cell (a) and with hinges, at the bottom (b) and at the top (c). Stiffness ratios are $\eta=0.5$ for the bottom hinge design, $\eta=0.6$ for no hinge, and $\eta=0.7$ for the top hinge design.
• Figure 5: Comparison of the experimental results (left column) and the numerical simulations (right column) of two-cell metamaterials with different dimensions of the support beams.