The performance and durability of solid oxide fuel cells and reversible solid oxide cells are strongly affected by the electrode-electrolyte interface, where charge transfer, ionic transport, adhesion, morphology and thermomechanical stability interact. Early-stage compatibility screening is usually based on electrochemical or compositional criteria, whereas surface-related descriptors are rarely included in a unified framework. This work proposes a surface-based methodology to assess the expected compatibility of candidate electrode-electrolyte pairings. Contact-angle measurements with water and glycerol are used to determine total, dispersive and polar surface free energy components through the Owens-Wendt-Rabel-Kaelble method. Confocal topography is used to extract ISO 25178 roughness parameters, including average roughness, peak-to-valley height, valley depth, skewness, kurtosis and surface slope. A compatibility matrix is constructed by combining energetic affinity and morphological suitability, with emphasis on the electrolyte surface, since the electrode is deposited directly onto the electrolyte substrate. The results indicate that the most promising interfaces are not necessarily those with the highest surface free energy, but those combining high adhesion work, low interfacial energy and a substrate morphology suitable for continuous electrode deposition. The proposed approach provides a rational pre-electrochemical screening tool to prioritize electrode-electrolyte combinations for subsequent validation by electrochemical impedance spectroscopy, area specific resistance, electrical contact resistance, microstructural analysis and durability testing. Although it does not replace electrochemical characterization, it offers a physically grounded way to connect surface chemistry, topography and interface formation in solid oxide cell materials.

The effect of material and geometric nonlinearity is often underestimated in contact mechanics. However, recent experiments reveal that classical linear models might fail to accurately predict key contact features, such as the contact area, in scenarios involving frictional sliding. In this study, we employ accurate yet simple plane-strain finite element simulations to investigate frictional sliding contact under finite elasticity. We consider both rigid and deformable sinusoidal indenters pressed against a flat substrate, exploring both periodic and aperiodic boundary conditions. Our results show that the transition of the contact area from the static conditions to the gross sliding is qualitatively governed by the pressure value. Indeed, at low pressure contact shrinkage is observed, in agreement with most experimental observations led under qualitatively similar pressure levels. Importantly, we also found a pressure threshold above which the sliding contact area can exceed the static one, especially for deformable sinusoids with high aspect ratio. To validate our numerical results, we perform ad hoc experiments with micro-fabricated soft sinusoids in either static or sliding contact against a microscope slide, which confirm the trend. Moreover, we also investigate the role of periodic boundary conditions, showing that this is not a key factor and aperiodic contacts behave almost the same. These novel findings provide deeper insights into rubber nonlinear contact mechanics at the sinusoid scale, which constitutes the building block of rough contact mechanics, showing that contact area increase is also possible without adhesion, with direct implications for real tribological systems such as tire-road and seal interactions, soft robotics locomotion, and biomechanics.

In this study, we investigate the tangential sliding of a rigid Hertzian indenter on a viscoelastic substrate, a problem of practical interest due to the crucial role that sliding contacts play in various applications involving soft materials. A finite element model is developed, where the substrate is modelled using a standard linear viscoelastic model with one relaxation time, and adhesion is incorporated using a Lennard–Jones potential law. We propose an innovative approach to model tangential sliding without imposing any lateral displacement, thereby enhancing the numerical efficiency. Our goal is to investigate the roles of adhesive regimes, boundary conditions (displacement and force-controlled conditions), and finite thickness of the substrate. Results indicate significant differences in the system’s behaviour depending on the boundary conditions and adhesion regime. In the short-range adhesion regime, the contact length ℒ initially increases with sliding speed before decreasing, showing a maximum at intermediate speeds. This behaviour is consistent with experimental observations in rubber-like materials and is a result of the transition from small-scale to large-scale viscous dissipation regimes. For long-range adhesion, this behaviour disappears and ℒ decreases monotonically with sliding speed. The viscoelastic friction coefficient μ exhibits a bell-shaped curve with its maximum value influenced by the applied load, both in long-range and short-range adhesion. However, under displacement control, μ can be unbounded near a specific sliding speed, correlating with the normal force crossing zero. Finally, a transition towards a long-range adhesive behaviour is observed when reducing the thickness t of the viscoelastic layer, which is assumed to be bonded to a rigid foundation. Moreover, the friction coefficient reduces when t tends to zero. These findings provide insights into the viscoelastic and adhesive interactions during sliding, highlighting the critical influence of boundary conditions on contact mechanics.

Crack initiation and propagation are fundamental problems in materials science, often leading to catastrophic failure. While fracture in elastic solids occurs instantaneously above a critical load, viscoelastic materials may sustain high loads for a finite time before cracks start to propagate. This phenomenon, known as delayed fracture, has been widely observed experimentally but is still only partially understood theoretically. In this study, we present a rigorous framework based on the Lagrange–d'Alembert principle of virtual work (PVW) to predict both the viscoelastic delay time and the subsequent crack evolution under arbitrary loading histories. We derive how the delay time depends on the applied remote load and validate the theory through quantitative comparison with experiments, using directly measured delay times together with DMA-based viscoelastic characterization of the material. Very good agreement is obtained over a broad range of loading and delay times. Our results also show that crack propagation starts at finite speed and that load-dependent steady-state conditions are soon established. Finite element analyses further support the proposed framework and clarify the role of finite-ranged adhesion forces at fixed adhesion energy, showing that shorter interaction ranges yield results in quantitative agreement with theory. We also present, for the first time, a rigorous J-integral formulation valid for linear viscoelastic solids under arbitrary, time-varying loading histories. The result restores path independence and yields a generalized Griffith criterion that naturally predicts delayed fracture initiation in non-conservative materials. Remarkably, fracture initiation can be described without specifying the detailed stress distribution within the process zone, as long as it remains small relative to the crack length.

Classical linear contact mechanics, formulated with small strain and displacement assumption, struggles to accurately describe experiments involving rubbers and elastomers. Indeed, under high loads, these materials undergo large deformations and exhibit constitutive behaviors that deviate from a linear relationship between stress and strain. In such cases, it is essential to move beyond linear elasticity to account for nonlinearity caused by large deformations and displacements. Despite efforts to develop numerical tools capable of incorporating these non-linearities in contact problems, our understanding of their impact on contact mechanical responses remains limited. In this study, we investigate the basic case of normal contact between a wavy rigid indenter and a flat, deformable substrate. We examine the influence of geometric non-linearities, arising from large deformations and displacements, alongside material non-linearities, under both frictionless and frictional interfacial conditions. To this end, we developed a finite element model, and we compared its predictions with those of Westergaard’s fully linear theoretical model. The results indicate that even in frictionless contact scenarios, non-linearities produce a mechanical response that differs significantly from predictions based on linear theory. This discrepancy becomes more pronounced as the aspect ratio of the wavy indenter increases, thereby invalidating the small-displacement assumption inherent in linear models. Moreover, the presence of friction, coupled with geometric non-linearities, induces contact hysteresis during loading and unloading cycles a phenomenon often attributed to other interfacial behaviors such as adhesion and plasticity.

This study investigates the reciprocating motion of a rigid Hertzian indenter on a viscoelastic substrate with adhesion, using a finite element-based numerical model. An innovative methodology is employed to transform the sliding contact problem into an equivalent normal contact problem, enabling the accurate simulation of adhesion effects at the contact interface. The results reveal that system behaviour is governed by the interplay between viscoelasticity and adhesion, leading to notable changes in contact pressure distribution, contact area, and energy dissipation during reciprocating motion. Specifically, viscous dissipation within the substrate material dominates at intermediate sliding speeds, where the interaction between adhesion and viscoelastic relaxation processes results in pronounced hysteresis cycles. In contrast, at low and high sliding speeds (corresponding to the rubbery and glassy regions, respectively), the material behaviour is predominantly elastic, and no hysteresis is observed. Adhesion influences contact pressure distribution and contact size, particularly in the transition regime, where its effects on viscous dissipation are measurable. Moreover, the study clarifies that adhesion alone does not induce hysteresis in elastic regimes, distinguishing reciprocating contact from normal contact, where adhesive hysteresis is typically observed. New insights are also provided into how adhesion and viscoelasticity jointly impact tribological performance, offering a deeper understanding of energy dissipation mechanisms and contact mechanics during motion reversal. Interestingly, our results also show that there is a lag period after motion reversal, where friction aligns with motion direction before eventually changing direction as pressure redistribution occurs within the system. This phenomenon highlights how changes in contact mechanics affect local tribological interactions and can lead to variations in overall system response.

Engineering technologies frequently draw inspiration from nature, as exemplified in bio-inspired adhesive surfaces. These surfaces present textures adorned by pillars, mimicking the topography found on the pads of certain animals renowned for their exceptional adhesive capabilities. The adhesive response is strongly influenced by the morphology of these pillars. In typical existing models, perfect bonding conditions are assumed between the pillar and the countersurface, and solely the detachment process of the pillar from the countersurface is investigated.The proposed model, based on the assumption that interactions at the interface are governed by van der Waals forces modeled by the Lennard-Jones potential law, enables the examination of the entire approach and retraction cycle, tracking the movement of the pillar towards and away from the countersurface.Our findings reveal that adhesive contact mechanics is primarily influenced by the geometry of the pillar and the potential presence of interfacial ’defects’, which in turn affect the distribution of contact pressure. Furthermore, we show that the detachment process may simultaneously involve various modes of separation, such as crack propagation from outer edge, crack propagation from inner defects, and uniform decohesion. This suggests that existing theoretical models alone cannot fully elucidate the complexity of detachment phenomena. Additionally, we anticipate the occurrence of hysteretic losses during the approach-retraction cycle, attributed to pull-in and pull-off contact jumps. Adhesive hysteresis is a phenomenon consistently observed in experiments but frequently overlooked in existing models.

Mushroom-shaped pillars have been extensively studied for their superior adhesive properties, often drawing inspiration from natural attachment systems observed in insects. Typically, pillars are modeled with linear elastic materials in the literature; in reality, the soft materials used for their fabrication exhibit a rate-dependent constitutive behavior. This study investigates the role of viscoelasticity in the adhesion between a mushroom-shaped pillar and a rigid flat countersurface. Interactions at the interface are assumed to be governed by van der Waals forces, and the material is modeled using a standard linear solid model. Normal push and release contact cycles are simulated at different approaching and retracting speeds. Results reveal that, in the presence of an interfacial defect, a monotonically increasing trend in the pull-off force with pulling speed is observed, and the corresponding change in the contact pressure distribution suggests a transition from short-range to long-range adhesion. This phenomenon corroborates recent experimental and theoretical investigations. Moreover, the pull-off force remains invariant to the loading history, due to our assumption of a flat-flat contact interface. Conversely, in absence of defects, detachment occurs after reaching the theoretical contact strength, and the corresponding pull-off force is found to be rate independent.

Modeling the elasto-plastic contact between rough interfaces may require high computational effort as real surfaces present broad roughness spectra. In this work, we propose an efficient multi-asperity model where each asperity follows Jackson and Green's equations and both coupling and coalescence of contact spots are considered. In agreement with previous studies, the contact area A is found to rise linearly with the applied load. Moreover, under the assumption of yield stress independent of the asperity size, no differences are found with respect to the elastic contact solution for nanometric root mean square (rms) roughness amplitudes hrms. On the contrary, for micrometric hrms, the slope of the area-load relation is observed to increase when reducing the yield strength crY. We have also investigated the effect of increasing the rms roughness gradient of the surface h ' rms by adding fine-scale wavelengths to the roughness spectrum. Due to plastic deformations, the contact area A is found to be independent of the high-frequency cut-off of the roughness spectrum as it converges when increasing the number of roughness scales.

Contact mechanics theories are commonly developed using the half-space approximation, which may raise concerns when dealing with contact region sizes comparable to or even larger than the size of the contacting bodies. In this study, we examine the normal adhesive contact between a rigid, wavy indenter and a viscoelastic substrate with a finite thickness. To achieve this, we utilize a recently developed finite element model that incorporates adhesive interactions based on the Lennard–Jones potential law. The results demonstrate that adhesive behavior is influenced by a combination of rate and size effects. Additionally, when considering non-negligible viscous effects, an optimal thickness can be determined to maximize the pull-off stress.

The problem of crack propagation in viscoelastic materials is of great interest given the numerous engineering applications of such materials. Due to viscoelasticity, even the study of the basic Mode I opening represents a tricky theoretical challenge. Indeed, existing theories adopt important approximations such as i) simplistic constitutive behaviour, ii) steady-state crack propagation, iii) infinite domain of the system. In this work, we revise the theory of Persson & Brener for systems of infinite domain; specifically, we propose a solution to take into account size effects in a viscoelastic plate. The theory allows to consider the realistic constitutive behaviour of viscoelastic materials and to predict the dependence of the energy release rate with the crack tip speed. Comprehensive experimental investigations are performed to corroborate our theoretical predictions. First, dynamic mechanical analysis (DMA) is performed to characterize the complex viscoelastic modulus of PolyTetraFluoroEthylene (PTFE). Second, tensile tests are carried out on cracked PTFE samples, and pictures are recorded with an image acquisition system. Moreover, a point tracking algorithm is developed to measure the crack length and opening displacement. Moving from small to high crack tip speeds, the fracture process becomes less ductile and an increase in the maximum load is observed. In addition, experimental data show that the inclusion of finite-size effects in the theory is crucial for accurately estimating the energy release rate.

Modeling the adhesion of viscoelastic rough surfaces is a recent challenge in contact mechanics. Existing models have primarily focused on simple systems with smooth topography or single roughness scale due to the co-action of roughness and viscoelasticity leading to elastic instabilities and rate-dependent behavior, resulting in complex adhesion dynamics. In this study, we propose a numerical model based on a finite element methodology to investigate the adhesion between a randomly rough profile and a viscoelastic half-plane. Approach-retraction simulations are performed under controlled displacement conditions of the rough indenter. The results demonstrate that viscous effects dampen the roughness-induced instabilities in both the approach and retraction phases. Interestingly, even when viscous effects are negligible, the pull-off stress, i.e., the maximum tensile stress required to detach the surfaces, is found to depend on the stiffness modulus and maximum load reached during the approach. Furthermore, when unloading is performed from a relaxed state of the viscoelastic half-plane, both adhesion hysteresis and pull-off stress are monotonic increasing functions of the speed. Conversely, when retraction begins from an unrelaxed state of the material, the maximum pull-off stress and hysteretic loss are obtained at intermediate velocities.

It is well-known that adhesion is strongly influenced by surface roughness. Nevertheless, the literature currently contains an ongoing debate regarding which roughness scales are primarily responsible for adhesion loss. In this study, we aim to contribute to this debate by conducting numerical simulations on self-affine fractal profiles with varying fractal dimensions. Our results reveal that the long-wavelength portion of the roughness spectrum plays a crucial role in killing adhesion when considering profiles with Hurst exponent H > 0.5. Conversely, for profiles with H < 0.5 , results show a different trend, indicating that adhesive stickiness is also influenced by short wavelength roughness. These findings are corroborated by our recent experimental observations. In such case, adhesive hysteresis and pull-off force exhibit a continuous decrease with increasing roughness scales. However, for H > 0.5 , the pull-off force converges towards a finite value as the magnification increases.

Surface roughness affects several tribological phenomena like adhesion. In this work, JKR-like experimental tests were performed between Polydimethylsiloxane (PDMS) spherical samples and flat glass substrates with different surface roughness properties. Data were interpreted in the light of classical JKR theory. We find that adhesion is destroyed by roughness in agreement with the most common and well-known results in the literature. However, from the analysis of the Power Spectral Density (PSD) of the surfaces, it emerges that the smaller scales of roughness have a greater influence on the surface adhesion energy in the range of the high fractal dimensions (D > 2.5). In this range, for surfaces with the same root mean square (RMS) roughness amplitude hrms , which is mainly affected by large scale roughness, the pull-off force (i.e., the maximum tensile force reached during the retracting phase) is observed reducing by increasing the RMS slope of the surface roughness hrms′ , that is by changing the roughness content at the small scales. This result agrees with recent theoretical findings and has never been shown experimentally in the literature to the best of our knowledge.

In this paper, the peeling of elastic thin tapes from real-like viscoelastic substrates is investigated by focusing the attention on the damping properties of this kind of materials. We show that the number of relaxation times involved in the physical process, is a key factor to increase the range in frequency where energy dissipation is predominant. This entails several advantages for appropriately managing the detachment process of the elastic tape. Indeed, we show how it is possible to obtain stable release conditions at high loads, so that the peeling force can be employed as control parameter. The practical case of the PMMA (polymethyl methacrylate) is considered as example, as it exhibits high damping at low-frequencies. As a result, stable detachment of the tape occurs at very small peeling velocities, especially with relatively stiff tapes. The results of this study can be exploited in many applications where the adherence of elastic tapes on viscoelastic substrates needs to be suitably designed such as, for example, in bio-medical contexts.

Adhesion of soft compliant solids is irreversible and rate-dependent. As a result, two different paths are observed in loading-unloading adhesion experiments because of dissipation occurring in the unloading phase. An effective surface energy is usually introduced to take account of such dissipation. Here, by exploiting a recent theoretical solution developed to study the detachment of a rigid sphere from a viscoelastic substrate (Violano et al., 2021), two different approaches are considered to calculate the surface energy. The first approach is based on the phenomenological equation derived by Gent & Schultz (A. N. Gent & J. Schultz, 1972), the latter exploits Persson & Brener theory for viscoelastic crack propagation (B. N. J. Persson & E. A. Brener, 2005). In both cases, results are observed to be in good agreement with experimental data taken from the literature.

Rough contact mechanics is a challenging topic that has attracted the interest of many scientists in the past and recent years. Notwithstanding a large amount of literature on the topic, there is a lack of studies investigating the contact behaviour of rough elastic bodies exchanging heat at the interface.