Non-uniform pneumatic actuation switches macroscopic properties of elastomeric honeycombs

TL;DR

This work addresses activating pattern-forming behavior in hexagonal honeycomb metamaterials via non-uniform pneumatic actuation, enabling on-demand switching between three buckling patterns described by $\vec{\pi}_1$, $\vec{\pi}_2$, and $\vec{\pi}_3$ and their associated macroscopic properties. The authors combine plane-strain finite-element simulations with a 3M fictitious medium to model pneumatic loading, first-order numerical homogenization to extract effective stiffness, and Bloch dispersion analysis to map acoustic bandgaps, demonstrating stiffness reduction and anisotropy control tied to the selected pattern. They identify four pressurization schemes ($s_0$–$s_3$) that robustly trigger the patterns and show that pre-bifurcation bandgaps and post-bifurcation gaps depend on scheme and pattern, enabling active tuning of wave propagation. Experimental validation on small (19 voids) and large (61 voids) silicone rubber samples confirms the numerically predicted patterns and reveals boundary/friction effects that shift critical loads, yet preserves the core concept of reversible, scheme-driven patterning. Overall, the work provides a proof-of-concept for actively reconfigurable mechanical metamaterials with tunable stiffness anisotropy and acoustic properties, with potential applications in soft robotics and morphing structures.

Abstract

Honeycomb microstructures with circular voids are well known to undergo pattern transformations under macroscopic strain loading. Depending on the biaxiality of the applied strain, they deform into three different patterns. Here we demonstrate that the same three patterns can be triggered also by pneumatic actuation of the voids, with resulting patterns depending on an applied pressurization scheme, i.e., the ratio of suction pressures introduced in different voids within the microstructure. Our numerically obtained findings are experimentally validated on two finite size samples made of silicone rubber cast in a 3D printed mold. In numerical studies, we first showcase the evolution of homogenized stiffness and its anisotropy during the genesis of pneumatically-induced patterns. Our loading schemes result in macroscopic stiffness varying by a factor of two with loading direction, chosen by a reversible actuation independent of the load itself. Second, we study the effect of the pneumatic actuation on acoustic properties of the microstructure, finding the proposed method viable to trigger different acoustic bandgaps.

Figures (19)

• Figure 1: Instability patterns resulting from internal buckling of a microstructure comprising (a) square stacking of circular voids, and (b-d) hexagonal stacking of circular voids, under compressive macroscopic strain. Undeformed configurations and applied external loads are shown in the top row, and corresponding deformed configurations are plotted in the bottom row.
• Figure 2: The different modes $\vec{\varphi}_i$, $i \in \{1,2,3\}$, of the pattern $\vec{\pi}_1$ on a hexagonal lattice of circular voids. These shear modes differ only in their orientation with regards to the symmetry axes od the reference geometry.
• Figure 3: Pressurization scheme $s_0$ (constant) and the resulting evolution of the patterning process. (a) Pressure setting. (b) Evolution of selected macroscopic effective stiffness tensor components $\bar{D}_{ijkl}$ and macroscopic effective deformation gradient components $\bar{F}_{ij}$ with increasing pneumatic load $\Delta p < 0$. All stress and stiffness values are normalized by the bulk material Young's modulus $E$. Deformed states at various stages of loading are shown as insets in (b), depicting the shift in the microstructure between different internal patterns.
• Figure 4: Pressurization scheme $s_1$ (constant with a pattern $\vec{\pi}_3$ modification) and the resulting evolution of the patterning process. (a) Pressure setting. (b) Evolution of selected macroscopic effective stiffness tensor components $\bar{D}_{ijkl}$ and macroscopic effective deformation gradient components $\bar{F}_{ij}$ with increasing pneumatic load $\Delta \tilde{p}$ . All stress and stiffness values are normalized by the bulk material Young's modulus $E$. Deformed states at and post-bifurcation are shown as insets in (b), depicting the patterning process.
• Figure 5: Pressurization scheme $s_2$ (row-wise) and the resulting evolution of the patterning process, leading to butterfly pattern $\vec{\pi}_2$. (a) Pressure setting. (b) Evolution of selected macroscopic effective stiffness tensor components $\bar{D}_{ijkl}$ and macroscopic effective deformation gradient components $\bar{F}_{ij}$ with increasing pneumatic load $\Delta \tilde{p}$. All stress and stiffness values are normalized by the bulk material Young's modulus $E$. Deformed states at and post-bifurcation are shown as insets in (b), depicting the patterning process.