Stick-slip dynamics in an interleaved system with self-amplified friction

TL;DR

The paper addresses how stick-slip dynamics emerge in a multicontact system where friction is amplified by converting traction into normal compression across interleaved sheets. It combines force measurements with high-resolution imaging and uses a friction-amplification model together with a classical spring-block framework to interpret the data, linking peak forces and event amplitudes to evolving normal loads and an effective number of contributing sheets. Key findings include that $F_{\max}$ follows the amplification model with $T^*=3$ mN and $\mu=0.89$, that stick-slip amplitudes scale with the effective normal load via $\Delta F(d_v)=A\mathcal{N}(d_v)$ with $A\approx0.34$, and that the global stiffness decays with detachment due to uneven horizontal deformation, captured by an effective sheet count $M_{\text{eff}}(d)$. The work underscores the nontrivial coupling between internal stress distribution and mechanical response, with implications for granular materials, textiles, fibrous systems, and metamaterials that exploit friction amplification.

Abstract

Understanding how stick-slip dynamics manifests in diverse physical conditions is a crucial topic in tribology. Although it has been extensively studied in simple frictional configurations, the characterization of stick-slip behavior in complex assemblies is challenging. This work presents the first systematic investigation of stick-slip dynamics in a system with multiple contact surfaces undergoing friction amplification through conversion of traction forces into normal compression. Using interleaved paper blocks as a model system, we combine force measurements and image processing to characterize stick-slip events occurring when the two blocks are pulled apart at different detachment velocities. We find that both the peak force and the amplitude of the stick-slip events decrease along with the system's detachment. By combining a previously designed model for friction amplification and the stick-slip dynamics predicted by a simple frictional spring-block system, we link the observed behavior to the evolving normal compression within the assembly. Through force measurements and imaging, we extract the effective stiffness of the system from stick-slip events at low velocities and relate it to the system's normal compression. We then predict the observed decrease of the global stiffness as function of the detachment by considering the spatial distribution of normal forces within the assembly, which determines an effective number of sheets contributing to the system's mechanical response. Our findings reveal a non-trivial interplay between internal stress distribution and mechanical response mediated by frictional forces, with implications for granular materials, textiles, fibrous systems, and mechanical metamaterials.

Figures (13)

• Figure 1: a) Picture of the experimental setup. Two interleaved Post-it® blocks are mounted on a traction machine able to pull them apart by imposing a vertical displacement. A camera is placed behind the assembly to capture images of the interleaved zone during traction tests. The black marks on the block highlight the top and the bottom interleaving points. b) Schematic representation of the left-hand side of the interleaved assembly. A $x$-$z$ reference system is defined. The sheets go from the clumping point to the interleaved point, forming an angle $\theta(n)$ that increases from the central to the external part of the assembly. According to these angles, the traction force (green arrows) is converted into orthogonal components (red arrows), which then compress the interleaved part of the assembly horizontally. The separation distance between the clumping and the interleaved point is denoted as $d$, while $L$ is the distance between the clamping point and the end of a sheet.
• Figure 2: Measured total traction force as a function of the separation distance for an experiment performed with pulling velocity $V=10$ mm/min. From left to right, the insets show the system's initial elastic response, typical early-stage stick-slip events (high amplitude, asymmetric) and typical late-stage stick-slip events (low amplitude, symmetric). Green circles refer to local maxima $F_{\text{max}}$ within single stick-slip events (also defined as $F_p=F(d_p)$ in Sec. \ref{['sec:ststic:stFeat']}), pink squares refer to local minima defined as $F_v=F(d_v)$ in Sec. \ref{['sec:ststic:stFeat']}. The green dashed line in the main panel shows the result of fitting $F_{\text{max}}(d)$ via Eq. \ref{['eq::model']} with $T^*=3$ mN and $\mu=0.89$.
• Figure 3: Maximum local force within single stick-slip events as a unction of the separation distance for different pulling velocities. The dashed line shows the prediction of Eq. \ref{['eq::model']} obtained with $T^*=3$ mN and $\mu=0.89$. The effects of velocity are negligible for this observable.
• Figure 4: Force-displacement curves within single stick-slip events. Different panels show data obtained at different pulling velocities. Within each panel, we show stick-slip events starting at different separation distances $d_v$, which correspond to local force minima. In panel d, we define the stick-slip amplitude $\Delta F$ as well as the stick $\Lambda_{\text{st}}$ and slip $\Lambda_{\text{sl}}$ lengths. Each panel shows (on the pink curve) the subset of points used to estimate the effective stiffness of the assembly from the slope of the central part of the stick phase. Panel b) explicitly illustrates that this slope is representative of a significant portion of the stick.
• Figure 5: Stick-slip amplitude as a function of the separation distance at the beginning of the stick for different pulling velocities. We note that the curves collapse at low velocities. The dashed line shows that the decay is relatively well approximated by the effective normal force acting on the assembly. This is proportional to the decay predicted by Eq. \ref{['eq::model']} with $T^*=3$ mN and $\mu=0.89$ through a prefactor $A/\mu$, with $A=0.34$.