Viscoelastic Substrate Research Articles

Research on Adhesion Pull-Off Behavior of Rigid Flat Punch and Viscoelastic Substrate

Interfacial adhesion is one of the key factors affecting the reliability of micro–nano systems. The adhesion contact mechanism is still unclear as the time-dependent viscoelasticity of soft materials. To clarify the adhesion interaction, the pull-off detachment between the rigid flat punch and viscoelastic substrate is explored considering the viscoelasticity of soft materials and rate-dependent adhesion. Taking the Lennard-Jones (L-J) potential characterizing interfacial adhesion and the Prony series defining the viscoelasticity of materials as references, the bilinear cohesion zone model (CZM) and standard Maxwell model are employed, and an adhesion analysis framework is established by combining finite element technology. The influence laws of the loading and unloading rates, material relaxation coefficients and size effect on adhesion pull-off behavior are revealed. The results show that the pull-off force is independent of the material relaxation effect and related to the unloading rate. When v^ ≥ 50 or v^ < 0.01, the pull-off force has nothing to do with the unloading rate, but when 0.01 < v^ < 50, the pull-off force increases with the increasing unloading rate. Also, it is controlled by the size effect, and the changing trend conforms to the MD-n model proposed by Jiang. The energy required for interfacial separation (i.e., effective adhesion work) is a result of the comprehensive influence of unloading rates, material properties and the relaxation effect, which is consistent with Papangelo1’s research results. In addition, we derive the critical contact radius of the transition from the Kendall solution to the strength control solution. This work not only provides a detailed solution for the interfacial adhesion behavior but also provides guidance for the application of adhesion in Micro-Electro-Mechanical Systems (MEMSs).

Bulk and fracture process zone contribution to the rate-dependent adhesion amplification in viscoelastic broad-band materials

The contact between a rigid Hertzian indenter and an adhesive broad-band viscoelastic substrate is considered. The material behavior is described by a modified power law model, which is characterized by only four parameters, the glassy and rubbery elastic moduli, a characteristic exponent n and a timescale τ0. The maximum adherence force that can be reached while unloading the rigid indenter from a relaxed viscoelastic half-space is studied by means of a numerical implementation based on the boundary element method, as a function of the unloading velocity, preload and by varying the broadness of the viscoelastic material spectrum. Through a comprehensive numerical analysis we have determined the minimum contact radius that is needed to achieve the maximum amplification of the pull-off force at a specified unloading rate and for different material exponents n. The numerical results are then compared with the prediction of Persson and Brener viscoelastic crack propagation theory, providing excellent agreement. However, comparison against experimental tests for a glass lens indenting a PDMS substrate shows data can be fitted with the linear theory only up to an unloading rate of about 100μm/s showing the fracture process zone rate-dependent contribution to the energy enhancement is of the same order of the bulk dissipation contribution. Hence, the limitations of the current numerical and theoretical models for viscoelastic adhesion are discussed in light of the most recent literature results.

Fabrication of flexible pressure sensor for human detection by direct-write printing concave surface

Flexible pressure sensor plays an important role in the field of human-computer interaction area due to its high flexibility and sensitivity. Convex surface of flexible electrodes provide an efficient way to enhance the sensitivity of flexible pressure sensors. However, facilely preparing controllable convex surface of flexible electrodes is still a challenge for obtaining high sensitive flexible pressure sensors. In this paper, direct-write print technique was utilized to prepare a concave structure surface with viscoelastic substrate, which could be used to prepare convex structure flexible electrode for fabricating highly sensitive flexible pressure sensors. Interaction between ink droplet and substrate was explored to generate a concave template, which could be controlled in spacing and diameter with printing spacing and nozzle diameter. Convex structure flexible surface could be prepared with the concave template, and then the convex structure flexible electrode could be realized with the evaporation of metallic silver on the surface. Furthermore, flexible pressure sensor was assembled with an interlocking structure by stacking two convex structure flexible electrodes in a face-to-face way, which could efficiently enhance flexibility and electrical property. The flexible pressure sensor presents a high sensitivity, a fast response/recovery time (<100 ms) and excellent flexibility (more than 10,000 cycles of bending), which could be applied in monitor physiological signals such as pulse detection, sound vibration, finger bending and so on. Therefore, this work provides an efficient method for preparing controllable structured surface, which has a great potential in the fabrication of flexible sensors, wearable electronics and energy devices.

Direct-write printed controllable concave surface for fabricating flexible metal electrode

Structured surface of flexible substrate could generate a positive impact on flexibility of metal electrode due to the surface free energy relaxation, which could make the flexibility of metal electrode meet the performance requirement of flexible electronics. However, the preparation of controllable structured surface of flexible substrate is still a tough and challenge process. In this research work, controllable concave surface of flexible substrate was prepared by direct-write print with a viscoelastic substrate. When the controllable concave surface of flexible substrate was evaporated with a nanoscale metal layer, various metal electrodes could be obtained with a controllable morphology of concave surface. The direct-write printed concave surface efficiently enhanced the flexibility of metal electrodes. When the prepared concave surface generated a continuous connected structure with a 0.1 mm printing space, an excellently enhanced flexibility of metal electrode was achieved with an internal bending flexibility of 93.72%, external bending flexibility of 93.67%, stretchability of 85% and number of stable cyclic bending times over 12,000. Meanwhile, the direct-write printed concave surface generated a reversed convex surface, which could be used for pressure sensing as a flexible pressure sensor. Therefore, this research work provides an efficient method for fabricating flexible electrode, which has important research and application value in the area of high-performance flexible electronics.

Dynamic Wrinkling Instability of Elastic Films on Viscoelastic Substrates

Abstract The dynamic instability of stiff films on compliant substrates has received sustained attention due to the potential applications in flexible functional devices. Film/substrate system-based devices are increasingly utilized under dynamic conditions, including dynamic sensors, tunable optical components, anti-fouling surfaces, etc. To better design the dynamic characteristics of devices based on film/substrate systems, it is essential to establish a comprehensive dynamic model and find out the deterministic and non-deterministic instability domains of nonlinear dynamic wrinkling under time-varying biased loads. In this paper, a multi-level coupling time-varying parameter excitation dynamic model for films bonded on Kelvin viscoelastic substrates is developed. The damping effect on the nonlinear dynamic responses of wrinkled film/substrate systems under step, slope and biased sinusoidal axial time-varying excitations are analyzed. We revealed and analyze the nonlinear dynamic behavior of film/substrate systems, which are significantly influenced by the excitation frequency and viscous coefficients of substrates. Various response forms, such as excitation-following deterministic responses, chaotic responses, and double-period resonant responses, are observed. We analyzed the parametric excitation induced dynamic bifurcation of the time-varying energy barrier that causes the nonlinear dynamic phenomenon, and provided deterministic and non-deterministic dynamic response domains. Based on the theory and results, methods for generating responses of specific types are proposed, offering theoretical guidance for designing dynamic characteristics of devices based on film/substrate systems.

Hygrothermomechanical loading-induced vibration study of multilayer piezoelectric nanoplates with functionally graded porous cores resting on a variable viscoelastic substrate

Harnessing vibrations in multifunctional nanostructured plates is pivotal to next-gen microsystems but necessitates understanding scale effects under multifield loading. Investigated in this work are the forced and unforced vibrations of multilayered piezoelectric nanoplates supported on a variable viscoelastic medium and loaded hygrothermo-electromechanically with functionally graded porous (FGP) cores. The viscoelastic foundation is supposed to demonstrate non-linear changes in both stiffness and damping characteristics in the x-coordinate direction. The goal is to improve the accuracy of the results by using the nonlocal strain gradient theory (NSGT) and the third-order shear deformation assumption (TSDA), which include the effects of hardening and softening materials. The FGP core layer considers four states of porosity distribution patterns. These porosity distributions are expected to change in both the in-plane and thickness directions. The governing partial differential equations resulting from Hamilton's principle can be reduced to a system of algebraic equations by applying the Galerkin method. The parametric studies evaluate the effects of several factors, such as the initial electric voltage, viscoelastic medium parameters, moisture rise, temperature changes, porosity distributions, FG index, nonlocal and strain gradient features, and boundary conditions, on the vibration response. The novelty lies in the incorporation of advanced theories, such as the NSGT and TSDT, which capture size-dependent effects and material hardening/softening phenomena. Additionally, the consideration of four distinct porosity distribution patterns in the FGP core layer provides insights into the influence of porosity gradients on the dynamic response. The proposed model can guide the design and optimization of multifunctional nanostructured plates for applications in next-generation microsystems, energy harvesting devices, and smart structures.

Profiling contact ridge of soft substrates with metallic thin films using a novel interference technique

HypothesisAs technology moves toward flexibility, embedded systems, and miniaturization, which often have metallic elements integrated with the functional substrates, understanding the contact deformation of such soft substrates coated with thin metallic films is crucial. However, probing nanoscale deformations optically, typically in a few hundred nanometers, poses challenges. Dual Wavelength - Reflectance Interference Contrast Microscopy (DW-RICM) holds promise in unveiling nanoscale deformations. However, when paired with conventional glass probes to measure deformation of underlying soft substrates, DW-RICM faces limitations due to light reflection at the glass-air interface, impeding accurate determination of the contact zone (e.g., contact area, contact ridge). Here we hypothesize that using alternative probes to eliminate unwanted reflections can enhance understanding of soft substrate deformation with thin metallic films (bilayer substrates). ExperimentsIn this work, we investigate the deformation profile of viscoelastic soft substrates with sputter-coated gold thin films (referred to herein as bilayer substrates) using DW-RICM. We employ millimeter-sized black ink-coated glass spheres as probes, absorbing most light under DW-RICM. We focus our laser beams associated with DW-RICM at the contact zone between the probe and the underlying soft substrates. FindingsOur new technique of using black ink-coated glass probes in contact with soft bilayer substrates enables us to accurately extract the deformation profile, particularly the contact ridge. With the increase in the gold sputter coating time, the contact area and contact ridge of gold-polymer bilayer substrates decrease. Further, long-term contact analysis of gold-coated soft substrates reveals a steady increase in the contact ridge height over time, unlike the gradual decrease observed in their bare counterparts until reaching a steady state.

Understanding the Role of Loss Modulus of Viscoelastic Substrates in the Evaporation Dynamics of Sessile Drops.

Viscoelastic properties of soft substrates play a crucial role in the evaporation dynamics of sessile drops. Recent studies have revealed that the modification of the viscoelastic properties of substrates changes the dynamics of the three-phase contact line, consequently affecting the evaporation behavior of sessile drops. Notably, these modifications occur without any noticeable changes to the substrate's wetting characteristics or surface topography. However, the individual role of storage (G') and loss (G″) moduli of substrates on drop evaporation dynamics remains unexplored. In this study, we investigate the evaporation dynamics of water drops on two groups of poly(dimethylsiloxane)-based viscoelastic substrates possessing either identical G' with varying G″ or identical G″ with varying G'. Our study reveals that on a substrate with constant shear modulus (G'), a reduction of an order of magnitude in loss modulus shifts the evaporation process from the constant contact radius mode to the constant contact angle mode. We hypothesize that this observed shift in behavior stems from the varying viscoelastic dissipation influenced by the plateau modulus and characteristic relaxation time of polymer gels. Our hypothesis is further supported from the observation that the evaporation process persists on the substrate with constant loss modulus (G″). Our study advances the current understanding of drop evaporation on soft substrates that may find potential applications involving soft composites, biological entities, tissue engineering, and wearable electronics.

Friction in Rolling a Cylinder on or Under a Viscoelastic Substrate with Adhesion

In classical experiments, it has been found that a rigid cylinder can roll both on and under an inclined rubber plane with a friction force that depends on a power law of velocity, independent of the sign of the normal force. Further, contact area increases significantly with velocity with a related power law. We try to model qualitatively these experiments with a numerical boundary element solution with a standard linear solid and we find for sufficiently large Maugis–Tabor parameter λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document} qualitative agreement with experiments. However, friction force increases linearly with velocity at low velocities (like in the case with no adhesive hysteresis) and then decays at large speeds. Quantitative agreement with the Persson–Brener theory of crack propagation is found for the two power law regimes, but when Maugis–Tabor parameter λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document} is small, the cut-off stress in Persson–Brener theory depends on all the other dimensionless parameters of the problem.

An Improved First-Order Shear Deformation Theory for Wave Propagation Analysis in FG-CNTRC Beams Resting on a Viscoelastic Substrate

This paper aims to analyze the wave propagation in functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams placed on a viscoelastic foundation utilizing an improved first-order shear deformation theory (FSDT). The material properties are derived from the mixture rule. Four carbon nanotube distribution patterns are considered in the analysis. The extended Hamilton’s Principle is utilized to derive the governing wave equations for the CNTRC beam. A comparison between the present theory results and those in the literature is conducted for validation. The wave dispersion investigation is mainly based on the phase and group velocities. The results illustrate the wave propagation responses for the different CNT configurations. In addition, the influence of the CNTs volume fraction, foundation stiffness parameters, and damping coefficient on the wave characteristics is examined.

Pull-off of a rigid cone from a viscoelastic substrate

The pull-off of a sphere from an elastic substrate follows the well-known JKR solution, and a similar but less known solution is valid for a cone. The two differ qualitatively in the parametric dependences of the pull-off load, so we study the case of a viscoelastic substrate using a well-known Gent and Schultz approach for the effective work of adhesion, with the assumption that the elastic modulus in the bulk of the specimen is the relaxed one. The rate of peeling of the contact line (for given remote withdrawing speed) depends on elastic modulus for the spherical case, and not for the cone. However, for the spherical geometry, we predict that the highest load amplification should be actually smaller than the highest work of adhesion amplification, while for the cone the opposite is true, although of a smaller factor.

Morphology and stability of droplets sliding on soft viscoelastic substrates.

We show that energy dissipation partition between a liquid and a solid controls the shape and stability of droplets sliding on viscoelastic gels. When both phases dissipate energy equally, droplet dynamics is similar to that on rigid solids. When the solid is the major contributor to dissipation, we observe an apparent contact angle hysteresis of viscoelastic origin. We find excellent agreement between our data and a non-linear model of the wetting of gels of our own that also indicates the presence of significant slip. Our work opens general questions on the dynamics of curved contact lines on compliant substrates.

Dynamics of the interaction of a pair of thin evaporating droplets on compliant substrates

The dynamics of the interaction of a system of two thin volatile liquid droplets resting on a soft viscoelastic solid substrate are investigated theoretically. The developed model fully considers the effect of evaporative cooling and the generated Marangoni stresses due to the induced thermal gradients, while also accounting for the effect of the gas phase composition and the diffusion of vapour in the atmosphere of the droplets. Using the framework of lubrication theory, we derive evolution equations for both the droplet profile and the displacement of the elastic solid, which are solved in combination with Laplace's equation for the vapour concentration in the gas phase. A disjoining-pressure/precursor-film approach is used to describe contact-line motion. The evolution equations are solved numerically, using the finite-element method, and we present a thorough parametric analysis to investigate the physical properties and mechanisms that affect the dynamics of droplet interactions. The results show that the droplets interact through both the soft substrate and the gas phase. In the absence of thermocapillary phenomena, the combined effect of non-uniform evaporation due to the increased vapour concentration between the two droplets and elastocapillary phenomena determines whether the drop–drop interaction is attractive or repulsive. The Marangoni stresses suppress droplet attraction at the early stages of the drying process and lead to longer droplet lifetimes. For substrates with intermediate stiffness, the emergence of spontaneous symmetry breaking at late stages of evaporation is found. The rich dynamics of this complex system is explored by constructing a detailed map of the dynamic regimes.

ON THE AFFERRANTE-CARBONE THEORY OF ULTRATOUGH TAPE PEELING

In a simple and interesting theory of ultratough peeling of an elastic tape from a viscoelastic substrate, Afferrante and Carbone find that there are conditions for which the load for steady state peeling could be arbitrarily large in steady state peeling, at low angles of peeling - what they call "ultratough" peeling (Afferrante, L., Carbone, G., 2016, The ultratough peeling of elastic tapes from viscoelastic substrates, Journal of the Mechanics and Physics of Solids, 96, pp.223-234). Surprisingly, this seems to lead to toughness enhancement higher than the limit value observed in a very large crack in an infinite viscoelastic body, possibly even considering a limit on the stress transmitted. The Afferrante-Carbone theory seems to be a quite approximate, qualitative theory and many aspects and features of this "ultratough" peeling (e.g. conformity with the Rivlin result at low peel angles) are obtained also through other mechanisms (Begley, M.R., Collino, R.R., Israelachvili, J.N., McMeeking, R.M., 2013, Peeling of a tape with large deformations and frictional sliding, Journal of the Mechanics and Physics of Solids, 61(5), pp. 1265-1279) although not at “critical velocities”. Experimental and/or numerical verification would be most useful.

A multiscale theory for spreading and migration of adhesion-reinforced mesenchymal cells.

We present a chemomechanical whole-cell theory for the spreading and migration dynamics of mesenchymal cells that can actively reinforce their adhesion to an underlying viscoelastic substrate as a function of its stiffness. Our multiscale model couples the adhesion reinforcement effect at the subcellular scale with the nonlinear mechanics of the nucleus-cytoskeletal network complex at the cellular scale to explain the concurrent monotonic area-stiffness and non-monotonic speed-stiffness relationships observed in experiments: we consider that large cell spreading on stiff substrates flattens the nucleus, increasing the viscous drag force on it. The resulting force balance dictates a reduction in the migration speed on stiff substrates. We also reproduce the experimental influence of the substrate viscosity on the cell spreading area and migration speed by elucidating how the viscosity may either maintain adhesion reinforcement or prevent it depending on the substrate stiffness. Additionally, our model captures the experimental directed migration behaviour of the adhesion-reinforced cells along a stiffness gradient, known as durotaxis, as well as up or down a viscosity gradient (viscotaxis or anti-viscotaxis), the cell moving towards an optimal viscosity in either case. Overall, our theory explains the intertwined mechanics of the cell spreading, migration speed and direction in the presence of the molecular adhesion reinforcement mechanism.

Chaotic dynamics of fractional viscoelastic PET membranes subjected to combined harmonic and variable axial loads

Nonlinear chaotic vibrations of fractional viscoelastic PET (polyethylene terephthalate) membranes subjected to combined harmonic and variable axial loads is investigated in this paper. Axial tension variations arise from the machine disturbances of the processing line of roll-to-roll manufacturing. The viscoelasticity of PET membrane is characterized by the fractional Kelvin-Voigt model. Based on the Hamilton principle, the equation of motion of the membrane is established with the consideration of geometric nonlinearity, and the Galerkin procedure is employed to discretize the resulting governing equation. For the solution, the finite difference method is utilized in conjunction with the Caputo-type fractional derivative to reliably estimate the nonlinear response of fractional viscoelastic PET membrane. The reliability of this numerical strategy is proved by the available results of the fractional system and comparison examples. The influence of system parameters on chaotic behaviors is described by the bifurcation diagram and the detailed responses at the set bifurcation parameters. The fractional model together with the analysis provides a fundamental framework for the control of viscoelastic substrates in flexible manufacturing.

Direct writing concave structure on viscoelastic substrate for loading and releasing liquid on skin surface

Droplet deposition on deformable matrix has a broad application prospect. Regular deposition and diffusion of droplet on the substrate is the key to prepare flexible concave structure. Direct writing technique is an advanced method for depositing ink droplet on various substrates, which could produce a variety of deposition forms. Meanwhile, direct writing technique has the characteristics of simplicity, convenience and strong controllability. In this work, patterned concave structure was fabricated with viscoelastic substrate by direct writing technology, depositing behavior of ink droplet, formation condition and shape control of concave structure were studied with viscoelastic substrate, and practical application of the patterned concave structure was explored in loading and releasing liquid on skin surface. This study provides an efficient method for the preparation and application of controllable concave surface.

Nonlinear dynamics of fractional viscoelastic PET membranes with linearly varying density

In this paper, the nonlinear dynamics of fractional viscoelastic polyethylene terephthalate (PET) membranes with linearly varying density are elaborated. The viscoelasticities of the PET membranes are characterized with the fractional Kelvin–Voigt model, and the density distribution is considered a linear fluctuation in the lateral direction. The geometrically nonlinear formulation is established with the von-Karman theory and the Hamilton principle. The Bubnov–Galerkin method is used to solve the resulting fractional differential equations, and a refined numerical scheme combining the finite difference with a discrete Caputo-type fractional derivative approximation is developed. Comparison examples are provided to substantiate the accuracy and effectiveness of the present method. A detailed parametric analysis is performed to illuminate the effects of the fractional order, density coefficient and various system parameters on the time response of the viscoelastic PET membranes. This study paves the way for fractional modelling and vibrational analysis of viscoelastic substrates in flexible electronics manufacturing.

Spreading of a thin droplet on a soft substrate

A thin liquid droplet spreads on a soft viscoelastic substrate with arbitrary rheology. Lubrication theory is applied to the governing field equations in the liquid and solid domains, which are coupled through the free boundary at the solid–liquid interface, to derive a set of reduced equations that describe the spreading dynamics. Fourier transform techniques and the finite difference method are used to construct a solution for the dynamic liquid–gas and solid–liquid interface shapes, as well as the macroscopic contact angle. Substrate properties affect the spreading dynamics through the contact angle and internal droplet flow fields, and these mechanisms are revealed. Increased substrate softness increases the spreading rate, whereas increased viscoelasticity decreases the spreading rate. For the case of a purely elastic substrate, the spreading power-law exponent recovers Tanner's law in the rigid limit and increases with substrate softness.

Cell Activities on Viscoelastic Substrates Show an Elastic Energy Threshold and Correlate with the Linear Elastic Energy Loss in the Strain‐Softening Region

Energy‐sensing in viscoelastic substrates has recently been shown to be an important regulator of cellular activities, modulating mechanical transmission and transduction processes. Here, this study fine‐tunes the elastic energy of viscoelastic hydrogels with different physical and chemical compositions and shows that this has an impact on cell response in 2D cell cultures. This study shows that there is a threshold value for elastic energy (≈0.15 J m−3) above which cell adhesion is impaired. When hydrogels leave the linear stress–strain range, they show softening (plastic) behavior typical of soft tissues. This study identifies a correlation between the theoretical linear elastic energy loss in the strain‐softening region and the number of cells adhering to the substrate. This also has implications for the formation of vinculin‐rich anchorage points and the ability of cells to remodel the substrate through traction forces. Overall, the results reported in this study support that the relationship between cell activities and energy‐sensing in viscoelastic substrates is an important aspect to consider in the development of reliable ex vivo models of human tissues that mimic both normal and pathological conditions.