Mechanical non-reciprocity programmed by shear jamming in soft composite solids

TL;DR

This work introduces a shear-jamming based principle to program static and dynamic non-reciprocity in soft continuum solids, achieved by embedding shear-jammed inclusion networks within a compliant matrix and, for dynamics, by modulating magnetic domains. A continuum fiber-reinforced anisotropic model couples semi-rigid force chains with nonlinear matrix elasticity, capturing how proximity to the shear-jamming boundary and matrix stiffness control direction-dependent responses in both shear and normal stresses. The study demonstrates scalable, multi-segment programmability and demonstrates non-reciprocal active solids with magnetically driven bending and locomotion in confinement, supported by FEM validation and energy-density analyses. By bridging granular physics with soft-material design, the work outlines a versatile path toward mechano-intelligent materials with tunable direction-dependent transport and actuation capabilities, with potential extensions to electrical and thermal transport via conductive jammed particles.

Abstract

Mechanical non-reciprocity-manifested as asymmetric responses to opposing mechanical stimuli-has traditionally been achieved through intricate structural nonlinearities in metamaterials. However, continuum solids with inherent non-reciprocal mechanics remain underexplored, despite their promising potential for applications such as wave guiding, robotics, and adaptive materials. Here, we introduce a design principle by employing the shear jamming transition from granular physics to engineer non-reciprocal mechanics in soft composite solids. Through the control of the interplay between inclusion contact networks and matrix elasticity, we achieve tunable, direction-dependent asymmetry in both shear and normal mechanical responses. In addition to static regimes, we demonstrate programmable non-reciprocal dynamics by combining responsive magnetic profiles with the anisotropic characteristics of shear-jammed systems. This strategy enables asymmetric spatiotemporal control over motion transmission, a previously challenging feat in soft materials. Our work establishes a novel paradigm for designing non-reciprocal matter, bridging granular physics with soft material engineering to realize functionalities essential for mechano-intelligent systems.

Figures (9)

• Figure 1: Soft composites with non-reciprocal mechanics. (a) Schematic illustration of materials exhibiting mechanical reciprocity and non-reciprocity. (b) Process of encoding shear-jammed inclusions into soft composites. Steps I to III depict the formation of shear-jammed contact networks during the pre-cured PS–PDMS suspension stages, with the red spheres representing the force-bearing particles. In step IV, the suspension is cured into a composite. (c) Preparation of a jammed network in the pre-cured PS–PDMS suspension. After jamming under a shear strain $\gamma^*$, the shear stress decreases from $\sigma_t^*$ to $\sigma_{t0}$ while maintaining a constant $\gamma^*$. (d) & (e) Asymmetric mechanical responses in shear stress ($\sigma_t$) and normal stress ($\sigma_n$) as the composites are sheared from undeformed states, respectively. Gray dashed loops indicate the corresponding stress-strain hysteresis. Insets in (e) show both unprocessed (gray) and processed (colored) images of the composite-air interfaces under shear. Scale bar: 200 $\mu$m. (f) Asymmetric shape reversibility. At $\gamma = 5$ %, the composite-air interface retains the induced surface deformation, whereas at $\gamma = -5$ %, the interface fully recovers from surface deformation. Scale bar: 250 $\mu$m.
• Figure 1: Enhanced non-reciprocal responses of NaCl–PDMS composites. (a) Plot of asymmetric mechanical responses in shear stress ($\sigma_t$) against shear strain ($\gamma$) for NaCl–PDMS composites ($\phi = 59\%$, $G_m = 0.11$ kPa, and $\sigma_t^* = 80$ Pa). The dashed line indicates the averaged stress-strain curve. The differential moduli $G_t^+$ and $G_t^-$ are obtained by measuring the slopes of the averaged stress-strain curve at $\gamma$=0.05 and $\gamma$=-0.05. At $\gamma = \pm 0.05$, the degree of non-reciprocity in shear stress and differential modulus reaches $\vert \sigma_t^+/\sigma_t^-\vert \approx 10$ and $G_t^+/G_t^- \approx 50$, respectively. Inset: Image of NaCl hexahedral particles in uncured PDMS base solution. Scale bar: 300 $\mu$m. (b) Plot of asymmetric normal stress ($\sigma_n$) against shear strain ($\gamma$).
• Figure 2: Mechanical non-reciprocity controlled by shear jamming transition. (a) Plots of shear stress ($\sigma_t$) against shear strain ($\gamma$) for PS–PDMS composites with a constant $\phi = 0.63$ prepared under varying critical shear stresses ($\sigma^*_t$) ranging from 1 Pa to $25$ Pa. The connected dots represent the mean values of $\sigma_t(\gamma)$ obtained by averaging hysteresis loops at each strain. Inset: plots of associated non-reciprocal normal stress ($\sigma_n$) against $\gamma$ for these composites. (b) Plots of hysteresis loop areas $E_D^+$ and $E_D^-$ against $\sigma^*_t$. (c) Relationship between the shear jamming transition of inclusion and the degree of shear non-reciprocity of the resulting composites. Open circles represent the boundary of shear-jamming transition for PS–PDMS suspensions, fitted to Eq. \ref{['eqn: SJ']} (dashed line). Squares mark the material parameters $(\phi, \gamma^*)$ used to prepare different composite samples, with the filled colors representing the degree of shear non-reciprocity $\vert \sigma_t^+/\sigma_t^-\vert$. The error bars in panels (b) and (c) indicate the standard deviations obtained from the measurements of three to five independently fabricated samples.
• Figure 2: Selective flow control with non-reciprocal active solids. (a) Schematic of the experimental setup where a sheet-shaped composite is placed in a “Y” chamber (inner diameter: 3.3 mm). A movable rotational magnet, attached beneath the chamber, controls the movement and shape change of composite samples. The magnitude of the magnetic field was held constant at $B=15$ mT. The Rhodamine-dyed water is then injected into the left inlet of the Y-chamber. (b) Schematic illustrations of the asymmetric bending for non-reciprocal composites within a flow channel. The left and right panels highlight the bending differences resulting from anisotropic shear-jammed networks. (c) A reciprocal composite fails to block the channel flow in either anchoring directions. The snapshots at four time points ($t_0$, $t_1$, $t_2$, and $t_3$) are presented to demonstrate this response. $t_0$: Initial state. $t_1$: The sample migrates to the lower branch due to the movement of an external rotating magnet field. $t_2, t_3$: Water leaks occur in both anchoring configurations. (d) The non-reciprocal composite achieves switchable blocking and releasing of the channel flow. At $t_2$, the water flow is blocked. By reversing the bending configuration at $t_3$, the water leak occurs again. Scale bar: $1$ cm. The blue arrow represents the direction of the external $\mathbf{B}$ field direction.
• Figure 3: Scalable and programmable mechanical non-reciprocity. (a) Plots of non-reciprocal shear stress ($\sigma_t$) and normal stress ($\sigma_n$) for the composites with the diameters of $D=25$ mm (color) and $D = 43$ mm (grey), respectively. Scale bar: 5 mm. (b) Plots of $\sigma_t$ and $\sigma_n$ against $\gamma$ for half-disk samples cut from the $D=25$ composite shown in (a). To minimize the sample-to-sample variations induced by cutting. Panel (b) shows the results by averaging four individual measurements. (c) Plots of $\sigma_t$ and $\sigma_n$ against $\gamma$ for a two-segment sample created by stacking two composites with force chains aligned in parallel. (d) Plots of $\sigma_t$ and $\sigma_n$ against $\gamma$ for a two-segment sample formed by stacking two composites with force chains aligned perpendicularly.