Nucleation and propagation of solitary Schallamach waves

A skin-inspired durable de-icing surface with boosting interfacial cracks

Fracture-based interfacial breakage has shown promise in efficiently removing ice accretion. Here, intrigued by the response of human skin to stress-induced deformation, we present a strategy to design tough-skin de-icing surfaces (TSDSs) that actively manipulate crack-induced ice-substrate interfacial breakage during ice removal. This design leverages the surface instability of thin films to generate extensive wrinkling at the ice-substrate interface, which serves as crack initiation sites. We demonstrate efficient ice shedding by creating wrinkles at two length scales: macro-wrinkles for actively initiating the cracks at the rim of the ice and micro-wrinkles for further promoting the stress concentration at the ice-substrate interface. The TSDS (τ < 10 kPa) displays excellent durability and weather resistance, achieving a large-area ice-self-shedding effect solely through gravity. The universality of the proposed mechanism is verified on multiple materials and potential applications. This design concept offers valuable insights into the creation of durable de-icing materials with enhanced ice-shedding properties.

Creasing in microscale, soft static friction

Utilizing colloidal probe, lateral force microscopy and simultaneous confocal microscopy, combined with finite element analysis, we investigate how a microparticle starts moving laterally on a soft, adhesive surface. We find that the surface can form a self-contacting crease at the leading front, which results from a buildup of compressive stress. Experimentally, creases are observed on substrates that exhibit either high or low adhesion when measured in the normal direction, motivating the use of simulations to consider the role of adhesion energy and interfacial strength. Our simulations illustrate that the interfacial strength plays a dominating role in the nucleation of a crease. After the crease forms, it progresses through the contact zone in a Schallamach wave-like fashion. Interestingly, our results suggest that this Schallamach wave-like motion is facilitated by free slip at the adhesive, self-contacting interface within the crease.

Fifty years of Schallamach waves: from rubber friction to nanoscale fracture

The question of how soft polymers slide against hard surfaces is of significant scientific interest, given its practical implications. Specifically, such systems commonly show interesting stick-slip dynamics, wherein the interface moves intermittently despite uniform remote loading. The year 2021 marked the 50th anniversary of the publication of a seminal paper by Adolf Schallamach (Wear, 1971), which first revealed an intimate link between stick-slip and moving detachment waves, now called Schallamach waves. We place Schallamach's results in a broader context and review subsequent investigations of stick-slip, before discussing recent observations of solitary Schallamach waves. This variant is not observable in standard contacts so that a special cylindrical contact must be used to quantify its properties. The latter configuration also reveals the occurrence of a dual wave-the so-called separation pulse-that propagates in a direction opposite to Schallamach waves. We show how the dual wave and other, more general, Schallamach-type waves can be described using continuum theory and provide pointers for future research. In the process, fundamental analogues of Schallamach-type waves emerge in nanoscale mechanics and interface fracture. The result is an ongoing application of lessons learnt from Schallamach-type waves to better understand these latter phenomena. This article is part of the theme issue 'Nanocracks in nature and industry'.

Dependence of adhesive friction on surface roughness and elastic modulus

Friction is one of the leading causes of energy loss in moving parts, and understanding how roughness affects friction is of utmost importance. From creating surfaces with high friction to prevent slip and movement, to creating surfaces with low friction to minimize energy loss, roughness plays a key role. By measuring shear stresses of crosslinked elastomers on three rough surfaces of similar surface chemistry across nearly six decades of sliding velocity, we demonstrate the dominant role of adhesive frictional dissipation. Furthermore, while it was previously known that roughness-induced oscillations affected the viscoelastic dissipation, we show that these oscillations also control the molecular detachment process and the resulting adhesive dissipation. This contrasts with typical models of friction, where only the amount of contact area and the strength of interfacial bonding govern the adhesive dissipation. Finally, we show that all the data can be collapsed onto a universal curve when the shear stress is scaled by the square root of elastic modulus and the velocity is scaled by a critical velocity at which the system exhibits macroscopic buckling instabilities. Taken together, these results suggest a design principle broadly applicable to frictional systems ranging from tires to soft robotics.

Propagating Schallamach-type waves resemble interface cracks

Intermittent motion, called stick-slip, is a friction instability that commonly occurs during relative sliding of two elastic solids. In adhesive polymer contacts, where elasticity and interface adhesion are strongly coupled, stick-slip arises due to the propagation of slow detachment waves at the interface. Here we analyze two distinct detachment waves moving parallel (Schallamach wave) and antiparallel (separation wave) to applied remote sliding. Both waves cause slip in the same direction, travel at speeds much lesser than any elastic wave speed, and are therefore describable using the same perturbative elastodynamic framework with identical boundary conditions. A numerical scheme is used to obtain interface stresses and velocities for arbitrary Poisson ratio, along with closed-form solutions for incompressible solids. Our calculations reveal a close correspondence between moving detachment waves and bimaterial interface cracks, including the nature of the singularity and the functional forms of the stresses. Based on this correspondence, and coupled with a fracture analogy for dynamic friction, we develop a phase diagram showing domains of possible occurrence of stick-slip via detachment waves vis-á-vis steady interface sliding. Our results have interesting implications for sliding and stick-slip phenomena at soft interfaces.

Slow wave propagation in soft adhesive interfaces

Stick-slip in sliding of soft adhesive surfaces has long been associated with the propagation of Schallamach waves, a type of slow surface wave. Recently it was demonstrated using in situ experiments that two other kinds of slow waves-separation pulses and slip pulses-also mediate stick-slip (Viswanathan et al., Soft Matter, 2016, 12, 5265-5275). While separation pulses, like Schallamach waves, involve local interface detachment, slip pulses are moving stress fronts with no detachment. Here, we present a theoretical analysis of the propagation of these three waves in a linear elastodynamics framework. Different boundary conditions apply depending on whether or not local interface detachment occurs. It is shown that the interface dynamics accompanying slow waves is governed by a system of integral equations. Closed-form analytical expressions are obtained for the interfacial pressure, shear stress, displacements and velocities. Separation pulses and Schallamach waves emerge naturally as wave solutions of the integral equations, with oppositely oriented directions of propagation. Wave propagation is found to be stable in the stress regime where linearized elasticity is a physically valid approximation. Interestingly, the analysis reveals that slow traveling wave solutions are not possible in a Coulomb friction framework for slip pulses. The theory provides a unified picture of stick-slip dynamics and slow wave propagation in adhesive contacts, consistent with experimental observations.

Stick-slip at soft adhesive interfaces mediated by slow frictional waves

Stick-slip is a friction instability that governs diverse phenomena from squealing automobile brakes to earthquakes. At soft adhesive interfaces, this instability has long been attributed to Schallamach waves, which are a type of slow frictional wave. We use a contact configuration capable of isolating single wave events, coupled with high speed in situ imaging, to demonstrate the existence of two new stick-slip modes. It is shown that these modes also correspond to the passage of slow waves-separation pulse and slip pulse-with distinct nucleation and propagation characteristics. The slip pulse, characterized by a sharp stress front, propagates in the same direction as the Schallamach wave. In contrast, the separation pulse, involving local interface detachment and resembling a tensile neck, travels in exactly the opposite direction. A change in the stick-slip mode from the separation to the slip pulse is effected simply by increasing the normal force. Taken together, the three waves constitute all possible stick-slip modes in low-velocity sliding. The detailed observations enable us to present a phase diagram delineating the domains of occurrence of these waves. We suggest a direct analogy between the observed slow frictional waves and well known muscular locomotory waves in soft bodied organisms. Our work answers basic questions about adhesive mechanisms of frictional instabilities in natural and engineered systems, with broader implications for slow surface wave phenomena.

Adhesion-induced instabilities and pattern formation in thin films of elastomers and gels

A hydrostatically stressed soft elastic film circumvents the imposed constraint by undergoing a morphological instability, the wavelength of which is dictated by the minimization of the surface and the elastic strain energies of the film. While for a single film, the wavelength is entirely dependent on its thickness, a co-operative energy minimization dictates that the wavelength depends on both the elastic moduli and thicknesses of two contacting films. The wavelength can also depend on the material properties of a film if its surface tension has a pronounced effect in comparison to its elasticity. When such a confined film is subjected to a continually increasing normal displacement, the morphological patterns evolve into cracks, which, in turn, govern the adhesive fracture behavior of the interface. While, in general, the thickness provides the relevant length scale underlying the well-known Griffith-Kendall criterion of debonding of a rigid disc from a confined film, it is modified non-trivially by the elasto-capillary number for an ultra-soft film. Depending upon the degree of confinement and the spatial distribution of external stress, various analogs of the canonical instability patterns in liquid systems can also be reproduced with thin confined elastic films.