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The question of how soft polymers slide against hard surfaces is of significant scientific interest, given its practical implications. Specifically, such sytems commonly show interesting stick-slip dynamics, wherein the interface moves intermittently despite uniform remote loading. \mt{The year 2021 marked the 50$^{th}$ anniversary of the publication of a seminal paper by Adolf Schallamach (\emph{Wear}, 1971)} that 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 on-going application of lessons learnt from Schallamach-type waves to better understand these latter phenomena., Comment: 45 pages, 12 figures

The kinematic flow pattern in slow deformation of a model dense granular medium is studied at high resolution using \emph{in situ} imaging, coupled with particle tracking. The deformation configuration is indentation by a flat punch under macroscopic plane-strain conditions. Using a general analysis method, velocity gradients and deformation fields are obtained from the disordered grain arrangement, enabling flow characteristics to be quantified. The key observations are the formation of a stagnation zone, as in dilute granular flow past obstacles; occurrence of vortices in the flow immediately underneath the punch; and formation of distinct shear bands adjoining the stagnation zone. The transient and steady state stagnation zone geometry, as well as the strength of the vortices and strain rates in the shear bands, are obtained from the experimental data. All of these results are well-reproduced in exact-scale Non-Smooth Contact Dynamics (NSCD) simulations. Full 3D numerical particle positions from the simulations allow extraction of flow features that are extremely difficult to obtain from experiments. Three examples of these, namely material free surface evolution, deformation of a grain column below the punch and resolution of velocities inside the primary shear band, are highlighted. The variety of flow features observed in this model problem also illustrates the difficulty involved in formulating a complete micromechanical analytical description of the deformation., Comment: 16 pages, 11 figures

We isolate single Schallamach waves --- detachment fronts that mediate inhomogeneous sliding between an elastomer and a hard surface --- to study their creation and dynamics. Based on measurements of surface displacement using high-speed \emph{in situ} imaging, we establish a Burgers vector for the waves. The crystal dislocation analogues of nucleation stress, defect pinning and configurational force are demonstrated. It is shown that many experimentally observed features can be quantitatively described using a conventional model of a dislocation line in an elastic medium. We also highlight the evolution of nucleation features such as surface wrinkles, with consequences for interface delamination., Comment: 24 pages, 9 figures

A theory for conduction electron scattering by inhomogeneous crystal lattice strains is developed, based on the differential geometric treatment of deformations in solids. The resulting fully covariant Schr\"odinger equation shows that the electrons can be described as moving in a non-Euclidean background space in the continuum limit of the deformed lattice. Unlike previous work, the formalism is applicable to cases involving purely elastic strains as well as discrete and continuous distributions of dislocations --- in the latter two cases it clearly demarcates the effects of the dislocation strain field and core and differentiates between elastic and plastic strain contributions respectively. The electrical resistivity due to the strain field of edge dislocations is then evaluated using perturbation theory and the Boltzmann transport equation. The resulting numerical estimate for Cu shows good agreement with experimental values, indicating that the electrical resistivity of edge dislocations is not entirely due to the core, contrary to current models. Possible application to the study of strain effects in constrained quantum systems is also discussed., Comment: 20 pages, 5 figures