Thermo-responsive jamming by particle shape change

Abstract

Granular materials transition between unjammed (deformable) and jammed (rigid) states when adjusting their packing density. Here, we report on experiments demonstrating that the same kind of phase transition can be alternatively achieved through temperature-controlled particle shape change. Using a confined system of randomly-packed rod-like particles made of shape memory alloy (SMA), we exploit that shape recovery of these bent rods with rising temperature at a constant packing density leads to a jammed state. The responsible physical processes are elucidated with numerical simulations based on the Discrete Element Method. As an exemplary application of the uncovered mechanism, we engineer a smart clamp that can actively grip or release an object through the thermo-induced jamming or unjamming of the granular material, and robustly so under cyclic temperature changes. In the jammed state, its load-bearing capability surpasses the total SMA weight by a tunable margin, up to over 800-fold. The clamping design paves the way towards a new kind of functional devices based on the thermo-responsive jamming of shape memory granular materials.

Fig. 1. Operating principles of the clamp.

A Schematic of the clamp components. B Clamping procedure. C XCT images of individual SMA rods of AR = 30 within the clamp container of solid volume fraction $\varphi =$ 0.28 at T = 25 °C and 85 °C. D Probability density function (PDF) of normalized tip distance $L_{\mathrm{tip}}/L_0$ (where $L_0$ is the length of the SMA rod in its straight shape) for the SMA rods in the clamp container at T = 25 °C and 85 °C. E Illustration of unjamming-to-jamming phase transition based on the temperature T and solid volume fraction $\varphi$.

Fig. 2. Effects of temperature T and solid volume fraction ϕ on clamp performance.

A Pull-out force as a function of stick displacement for various temperatures at $\varphi$ = 0.28. B Pull-out force as a function of stick displacement for various solid volume fractions at $T=$ 80 °C. C Phase diagram illustrating the peak pull-out force $F_{\max }$ based on T and $\varphi$. D Probability density function (PDF) of normalized tip distance $L_{\mathrm{tip}}/L_0$ for the SMA rods at $T=$ 80 °C and various solid volume fractions. E An illustration of inclination angle of a rod $\alpha$. F Mean inclination angles of the SMA rods $\overline{\alpha }$ for various solid volume fractions at $T=$ 25 °C and $T=$ 80 °C. The results (A–F) are obtained from the experiments and XCT measurements. G, H, I Depict the results obtained from DEM simulations, showing the average normalized rod tip distance $L_{\mathrm{tip}}/L_0$, coordination number, and mean contact force $F_{\mathrm{con}}/\left(E^{\mathrm{M}}A\right)$, respectively, as a function of temperature T for various $\varphi$ values. The coordination numbers obtained from the XCT experiment are included in (H) for a comparison with the simulation results. The widths of shaded bands in the above figures represent the standard deviations from the mean values out of multiple measurements.

Fig. 3. Clamping robustness subject to cyclic temperature changes.

A Pull-out force as a function of stick displacement (colors are used to differentiate the results in different temperature cycles). B Peak pull-out forces $F_{\max }$ at $T=$ 80 °C and $\varphi$ = 0.24 across multiple temperature cycles. C Mean peak pull-out force ${\overline{F}}_{\max }$ as a function of solid volume fraction $\varphi$. The widths of shaded bands in (B) and (C) represent the standard deviations from the mean values of the results at multiple temperature cycles. D Probability density function (PDF) of the SMA rod displacement relative to its initial position at the beginning of the temperature changes $\delta$ normalized by the rod diameter $d_{\mathrm{rod}}$ at $\varphi =$ 0.18 over different cycles. E Mean rod displacement $\overline{\delta }/d_{\mathrm{rod}}$ relative to its initial position as a function of temperature cycle count at $\varphi =$ 0.18. F Mean rod displacement $\overline{\delta }\prime /d_{\mathrm{rod}}$ relative to its position in the previous cycle as a function of temperature cycle count at $\varphi$ = 0.18 and $T=$ 80 °C.

Fig. 4. Effects of rod aspect ratio (AR) on clamp performance.

A Experimental results of peak pull-out force $F_{\max }$ as a function of AR for various solid volume fractions $\varphi$. DEM simulation results of (B) average normalized rod tip distance $L_{\mathrm{tip}}/L_0$ varying with temperature T, (C) coordination number and (D) SMA rod-stick contact number as a function of $L_{\mathrm{tip}}/L_0$, (E) mean rod internal bending moment $M/\left(E^{\mathrm{M}}I\right)$ and (F) mean contact force $F_{\mathrm{con}}/\left(E^{\mathrm{M}}A\right)$ varying with T.

Fig. 5. Effects of system size on clamp performance.

A Pull-out force versus stick displacement for different normalized inner diameters of the clamp container $D_{\mathrm{in}}/L_0$ at T=80 °C. B Variation of mean inclination angle $\overline{\alpha }$ with $D_{\mathrm{in}}/L_0$ at T=25 °C. C Probability density function (PDF) of the normalized tip distance $L_{\mathrm{tip}}/L_0$ for various $D_{\mathrm{in}}/L_0$ at T=25 °C. D Peak pull-out force as a function of $D_{\mathrm{in}}/L_0$ for various solid volume fractions $\varphi$ at T=80 °C. The results are obtained from the experiments and XCT measurements of the rod systems with AR = 40. The band widths of shaded regions in A and lengths of error bars in D represent the standard deviations from the mean values out of multiple measurements.

Fig. 6. Clamping enhancement through addition of small balls to the packing of SMA rods.

A An illustration with the addition of small balls. Experimental results of (B) pull-out force as a function of stick displacement for various overall solid volume fractions ${\varphi }_{\mathrm{ball}+\mathrm{SMA}}$ and the variation of peak force with ${\varphi }_{\mathrm{ball}+\mathrm{SMA}}$ for a specified volume fraction of SMA rods ${\varphi }_{\mathrm{SMA}}$ = 0.18, (C) pull-out force as a function of stick displacement for various ${\varphi }_{\mathrm{SMA}}$ at a specified ${\varphi }_{\mathrm{ball}+\mathrm{SMA}}$ = 0.28, and (D) peak pull-out force $F_{\max }$ as a function of ${\varphi }_{\mathrm{ball}+\mathrm{SMA}}$ with the addition of steel and glass balls. E Numerical simulation results of the normalized peak pull-out force $F_{\max }/F_{\max }^0$ for various friction coefficients between SMA rods and steel balls, in which $F_{\max }^0$ is the peak pull-out force at ${\varphi }_{\mathrm{SMA}}$ = 0.18 and ${\varphi }_{\mathrm{ball}}$ = 0. The widths of shaded bands in (B–D) represent the standard deviations from the mean values out of multiple measurements.