Tuning the Size and Stiffness of Inflatable Particles

TL;DR

This work addresses how inflatable particles can simultaneously vary in size and compressive stiffness to tune robotic granular materials. By fabricating two geometries (Type I cylindrical shells and Type II toroidal shells) from EcoFlex 50 and systematically inflating them, the authors show that the slope of the stiffness–inflation curve, $k(p)$, can be steered from increasing to decreasing with inflation through the dimensionless ratio $r/t$, with strain localization near corners driving softening as $r/t \to 0$. Complementary ABAQUS neo-Hookean and spring-network FEM models, along with experiments, reveal that the observed behavior is governed by localized deformation and can be reproduced by tuning the local stiffness via the spring network parameter $a$. The results provide design rules for creating inflatable particles with tailored size and stiffness, enabling programmable, adaptable soft robotic granular materials and new avenues for stiffness modulation in inflatable systems.

Abstract

We describe size-varying cylindrical particles made from silicone elastomers that can serve as building blocks for robotic granular materials. The particle size variation, which is achieved by inflation, gives rise to changes in stiffness under compression. We design and fabricate inflatable particles that can become stiffer or softer during inflation, depending on key parameters of the particle geometry, such as the ratio of the fillet radius to the wall thickness, r/t. We also conduct numerical simulations of the inflatable particles and show that they only soften during inflation when localization of large strains occurs in the regime r/t -> 0. This work introduces novel particle systems with tunable size and stiffness that can be implemented in numerous soft robotic applications.

Figures (8)

• Figure 1: Schematic of the two types of particles (left) with images in the uninflated (middle) and inflated (right) states. Side views of (A) type I and (B) type II particles. (C) Top view of a type II particle. The type I and II particles have been inflated to $\sim 3.4 \unit{\kilo \pascal}$ and $\sim 8.6 \unit{\kilo \pascal}$, respectively. All scale bars correspond to 10 mm.
• Figure 2: Summary of the particle fabrication process. Each type of particle requires two sets of molds: one for molding the two halves (mold A) and one for assembling the two halves together (mold B). The components of the molds are 3D-printed out of Polyvinyl Lactic Acid (PLA). The blue (green) molds are used for type I (type II) particles. The fabrication process for both particle types is nearly identical, except for the use of slightly different mold designs. The seven-step fabrication process for type II particles is shown. The particles (pink) are molded from EcoFlex™ 50.
• Figure 3: (A) Sketch of the spring network model for (left panel) a type I particle (cyan) with $r/t=4$ compressed between two parallel rough, rigid plates (black) in a direction perpendicular to the cylindrical axis. (center panel) Cross-sectional view of the particle in the left panel, which shows the connections between nodes of the spring network (blue lines) and rough surface of the walls modeled by spheres on a square lattice. (right panel) The inflation pressure is applied through forces ${\vec{F}}_{p,f}$ split evenly on each node of each triangle $f$ that tessellate the interior surface of the cylindrical shell of the particle. (B) Spring network meshes (blue lines) for type I particles with different ratios of the fillet radius to the wall thickness $r/t$ (from left to right and from top to bottom): $r/t = 0$, $0.5$, $1$, and $2$. The Cartesian coordinate systems in both panels illustrate the particle orientations.
• Figure 4: (A) Compressive stiffness $k$ of type I particles with different ratios of the fillet radius to the wall thickness $r/t$ (indicated by color) normalized by $k_0$ at zero inflation pressure plotted versus the inflation pressure $p$ (in kPa). Both the experimental (solid symbols with dashed lines) and ABAQUS simulation results using a neo-Hookean model (open symbols with solid lines) are indicated. Each data point in experiments is an average over three samples measured three times each, with the error bars indicating the standard deviation. (B) $k/k_0$ versus $p$ for type I particles simulated in ABAQUS with the same $r/t = 2$, $R/t = 5$, and $H/t = 5$, but different $t$: $t = 1\unit{\milli\meter}$ (upward triangles), $1.5\unit{\milli\meter}$ (squares), $2\unit{\milli\meter}$ (circles), $2.5\unit{\milli\meter}$ (diamonds), $3\unit{\milli\meter}$ (leftward triangles), and $4\unit{\milli\meter}$ (pentagons). (C) Spatial distribution of the maximum principal strain, $\lambda_1-1$, at $p=6.89$ kPa inflation pressure from the ABAQUS simulations. The particles from left to right and top to bottom have $r/t = 0$, $0.5$, $1$, and $2$. The cross section is through the particle center and perpendicular to both compression plates and the particle's long axis. The Cartesian coordinate system illustrates the orientation of the particles. The color bar indicates values of $\lambda_1 - 1$ for all panels. (D) Mean value of the highest $1\%$ of $\left\langle \lambda_1 \right\rangle - 1$ values in the particle as a function of the inflation pressure for type I particles with different $r/t$ from ABAQUS simulations.
• Figure 5: The mean of the highest $1\%$ of strains $\left\langle \lambda_i \right\rangle - 1$ plotted as a function of the inflation pressure $p$ for type I particles with various $r/t$ modeled using spring networks with (A) $a = 1$ and (B) $0$. (C) Mean of the highest $1\%$ of strains $\left\langle \lambda_i \right\rangle - 1$ plotted versus $a$ at $p=6.89$ kPa for type I particles with various $r/t$ modeled using spring networks. The vertical dashed lines in (A) and (B) indicate the pressure used for the data in (C).