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Recent experiments reveal that adhesive interactions can play a key role in causing surface instability in soft lubrication. Instances of instability include fluid entrapment in isolated pockets upon a soft sphere’s normal contact with a hard substrate and surface wrinkling of a soft substrate as a hard sphere slides across it. These phenomena underscore a substantial distinction between hard and soft lubrication. They are of paramount importance from a fundamental standpoint, providing an entirely new explanation for the transition mechanism from elasto-hydrodynamic to the mixed lubrication regimes. Here, we introduce a new theory to elucidate these observations. Our theory modifies the Reynolds elasto-hydrodynamic equation by incorporating adhesive interaction across the fluid layer, investigating the interplay between adhesion, fluid flow and elastic instability. Our analysis proposes the addition of a new dimensionless parameter in lubrication theory, that compares the stiffness of the adhesive interaction to that of the substrate. When this parameter exceeds unity, the soft solid surface exhibits instability to small perturba- tions in its shape. In mathematical terms, the Reynolds equation undergoes a transition from a nonlinear diffusion equation to a nonlinear wave equation at this critical point. Post-transition, the diffusivity of the nonlinear diffusion equation turns negative, rendering the problem ill- posed. We investigate the transition using the method of characteristics and present an exact analytic solution. This solution offers insights into the occurrence of a vanishing liquid film thickness at specific locations, resulting in dry contact—initiating transition to mixed lubrication. 

Energy dissipation around a propagating crack is the primary mechanism for the enhanced fracture toughness in viscoelastic solids. Such dissipation is spatially non-uniform and is highly coupled to the crack propagation process due to the history-dependent nature of viscoelasticity. We present an experimental approach to map the dissipation field during crack propagation in soft viscoelastic solid. Specifically, we track randomly distributed tracer particles to measure the evolving deformation field. The measured deformation field is then put into a nonlinear constitutive model to determine the dissipation field. Our methodology was used to investigate the deformation and dissipation fields around a propagating crack in a Polyampholyte (PA) hydrogel. The deformation field measurements allowed us to assess whether the commonly assumed translational invariance in viscoelastic fracture theories holds true in practical experiments. Furthermore, by combining the obtained deformation fields with a nonlinear viscoelastic model, we captured the complete history of the dissipation field during crack propagation. We found that dissipation occurred even at material points that are a few millimeters away from the crack tip. The mapped dissipation field also enabled the separate determination of the intrinsic and dissipative components of fracture toughness for the viscoelastic hydrogel. 

Biology is replete with examples, at length scales ranging from the molecular (ligand–receptor binding) to the mesoscopic scale (wing arresting structures on dragonflies) where shape-complementary surfaces are used to control interfacial mechanical properties such as adhesion, friction, and contact compliance. Related bio-inspired and biomimetic structures have been used to achieve unique interfacial properties such as friction and adhesion enhancement, directional and switchable properties. The ability to tune friction by altering surface structures offers advantages in various fields, such as soft robotics and tire manufacturing. Here, we present a study of friction between polydimethylsiloxane (PDMS) samples with surfaces patterned with pillar-arrays. When brought in contact with each other the two samples spontaneously produce a Moire´ pattern that can also be represented as an array of interfacial dislocations that depends on interfacial misorientation and lattice spacing. Misorientation alone produces an array of screw dislocations, while lattice mismatch alone produces an array of edge dislocations. Relative sliding motion is accompanied by interfacial glide of these patterns. The frictional force resisting dislocation glide arises from periodic single pillar–pillar contact and sliding. We study the behavior of pillar–pillar contact with larger (millimeter scale) pillar samples. Inter-pillar interaction measurements are combined with a geometric model for relative sliding to calculate frictional stress that is in good agreement with experiments. 

Insects and small animals often utilize structured surfaces to create friction during their movements. These surfaces typically consist of pillar-like fibrils that interact with a counter surface. Understanding the mechanical interaction between such surfaces is crucial for designing structured surfaces for engineering applications. In the first part of our study, we examined friction between poly(dimethylsiloxane) (PDMS) samples with surfaces patterned with pillar-arrays. We observed that sliding between these surfaces occurs through the interfacial glide of dislocation structures. The frictional force that resists this dislocation glide is a result of periodic single pillar-pillar contact and sliding. Hence, comprehending the intricate interaction between individual pillar contacts is a fundamental prerequisite for accurately modeling the friction behavior of the pillar array. In this second part of the study, we thoroughly investigated the contact interaction between two pillars located on opposite sides of an interface, with different lateral and vertical offsets. We conducted experiments using PDMS pillars to measure both the reaction shear and normal forces. Contact interaction between pillars was then studied using finite element (FE) simulations with the Coulomb friction model, which yielded results that aligned well with the experimental data. Our result offers a fundamental solution for comprehending how fibrillar surfaces contact and interact during sliding, which has broad applications in both natural and artificial surfaces. 

An experimental and theoretical study of delayed fracture of polydimethlsiloxane (PDMS) is presented. Previous works have demonstrated that delayed fracture in single edge notch specimens is caused by time dependent damage due to chain scission. Here we study the interactions between damage and the elastic field using different specimens and crack geometries with blunt and sharp cracks. Our experiments show that initial toughness is not well defined, as stable slow crack growth can occur over a range of applied loads. Our experiments demonstrate that there is a universal relation between crack growth rate and applied energy release rate. A model coupling the nonlinear elastic deformation and rate dependent bond scission is proposed and is in good agreement with experimental data. 

The Pure Shear (PS) crack specimen is widely employed to assess the fracture toughness of soft elastic materials. It serves as a valuable tool for investigating the behavior of crack growth in a steady-state manner following crack initiation. One of its advantages lies in the fact that the energy release rate (J) remains approximately constant for sufficiently long cracks, independent of crack length. Additionally, the PS specimen facilitates the easy evaluation of J for long cracks by means of a tension test conducted on an uncracked sample. However, the lack of a published expression for short cracks currently restricts the usefulness of this specimen. To overcome this limitation, we conducted a series of finite element (FE) simulations utilizing three different constitutive models, namely the neo-Hookean (NH), Arruda-Boyce (AB), and Mooney-Rivlin (MR) models. Our finite element analysis (FEA) encompassed practical crack lengths and strain levels. The results revealed that under a fixed applied displacement, the energy release rate (J) monotonically increases with the crack length for short cracks, reaches a steady-state value when the crack length exceeds the height of the specimen, and subsequently decreases as the crack approaches the end of the specimen. Drawing from these findings, we propose a simple closed-form expression for J that can be applied to most hyper-elastic models and is suitable for all practical crack lengths, particularly short cracks.