Compliant Mechanisms for Invertible Poisson's Ratio and Tunable Stiffness in Cell Culture Substrates

TL;DR

This work introduces compliant mechanisms that enable an invertible Poisson’s ratio and tunable stiffness for cell culture substrates using bistable Engaging-Disengaging Compliant Mechanisms (EDCM) and an offset linkage. An analytic Castigliano-based model links geometry to stretch ratio and stiffness, treating the system as coupled Λ- and M-shaped frames and validating predictions with FEA and tabletop experiments across multiple examples. By integrating an offset mechanism, the design can balance stiffness between the inverted and non-inverted Poisson states, facilitating controlled studies of cellular response to substrate mechanics. The approach is demonstrated from macro-scale prototypes to a blueprint for microscale fabrication, with a clear path toward cell culture experiments that explore how Poisson’s ratio and stiffness influence cell behavior and tissue engineering outcomes.

Abstract

The mechanical environment of a substrate plays a key role in influencing the behavior of adherent biological cells. Traditional tunable substrates have limitations as their mechanical properties cannot be dynamically altered in-situ during cell culture. We present an alternate approach by using compliant mechanisms that enable realization of tunable substrate properties, specifically, invertible Poisson's ratio and tunable stiffness. These mechanisms transition between positive and negative Poisson's effects with tunable magnitude through a bistable Engaging-Disengaging Compliant Mechanism (EDCM). EDCM allows stiffness between two points of the substrate to switch between zero and theoretically infinite. In the stiffened state, lateral deformation reverses under a constant axial load, while in the zero-stiffness state, the deformation direction remains outward as that of re-entrant structure. EDCM in conjunction with an offset mechanism also allows tuning of the effective stiffness of the entire mechanism. We present analytical models correlating geometric parameters to displacement ratios in both bistable states and through illustrative design cases, demonstrate their potential for designing dynamic and reconfigurable cell culture substrates.

Figures (19)

• Figure 1: Compliant mechanism with invertible Poisson’s ratio. (A-C) Internal EDCMs toggle the connection between re-entrant points to switch Poisson’s behavior. (P-R) Offset mechanism with EDCMs enables stiffness tuning by engaging or disengaging offset links.
• Figure 2: (A-C) Beam models of the re-entrant mechanism: links with engaged EDCMs are modeled as rigid (high stiffness), while disengaged EDCMs are represented as absent (zero stiffness). (P-R) Beam models of the offset mechanism with EDCMs in engaged and disengaged states.
• Figure 3: Compliant mechanism with beams connecting the re-entrant points.
• Figure 4: Geometrical parameters of the mechanism: $a, b, \theta_1, \theta_2$, $h_{\Lambda}, t_{\Lambda}$, $h_{\text{M}}, t_{\text{M}}$. In the enlarged cross-sectional view, $h_{\Lambda}$ and $h_{\text{M}}$ denote the out-of-plane dimensions, while $t_{\Lambda}$ and $t_{\text{M}}$ represent the in-plane dimensions.
• Figure 5: Frame divided as the parallel combination of $\Lambda$ and M part