Elastic Substrate Research Articles

AFM Nanoindentation of Stiff Inhomogeneous Layer onPolymeric Substrate.

Analysis of indentation data of heterogeneous material, in particular, layer on an elastic substrate requires information about the contact area that is essential for calculating mechanical properties. The actual shape of the AFM-tip is not described by simple body of revolution. In this work, the indentation of a stiff layer on a hyperelastic substrate by a truncated conical tip is studied using finite element methods. The size of the tip, elastic modulus, and thickness of the layer are varied. The obtained model dependences of loading and contact area versus the depth of indentation are used in analysis of the experimental data of AFM indentation of stiff inhomogeneous nanolayers of polyurethane surface. Thickness and elastic modulus of the layers, fracture properties of the surface are studied. The obtained results can find application in the study of mechanical properties and fracture toughness of thin flexible films on an elastic substrate.

A Stretchable Conductive Material with High Fatigue Resistance for Strain Sensors.

Intrinsically stretchable conductive materials based on elastic substrates and conductive components play important roles in biomedical applications, such as exercise rehabilitation monitoring and disease prediction. A persistent challenge is to combine high fatigue resistance with excellent mechanical properties in stretchable conductive materials. Herein, we present a stretchable conductive material with both good fatigue resistance and high tensile properties (∼3170%) based on poly(acrylic acid)-phytic acid-trehalose-polypyrrole (denoted as PPTP). The as-prepared PPTP hydrogel electrode showed no obvious cracking or delamination after 400 loading and unloading cycles and maintained good electrical signal transmission function after 1000 cycles. We further collected stable signals for human motion and handwriting using the stretchable hydrogel electrode as a strain sensor, demonstrating the potential application of the PPTP stretchable hydrogel electrode in biomedicine.

Forced vibration analysis of sandwich beam reinforced with graphene in piezoelectric medium on elastic substrate

In this study, using an analytical and precise solution, the dynamic transverse deflection of a five-layer beam with Prussian core with graphene platelet reinforced composite (GPLRC) under a moving harmonic load on a Pasternak elastic substrate is analyzed. First, the properties of the porous core materials and the piezoelectric layer and surface, which were graphene platelet reinforcements (GPLRs), were defined. The constitutive relations were extended using the Bonilla’s higher-order theory and Hamilton’s principle, relationships were extracted. Finally, using the Laplace method and analytical solution. A parametric analysis is provided to investigate impact of temperature distribution, porosity coefficient, thickness ratio, spring constant, voltage and excitation frequency on the responses.

Lubrication Prediction of Sphere‐Gradient Coated Half Space Interfaces

ABSTRACTFunctionally graded coating (FGC) has played a pivotal role in numerous engineering applications owing to its exceptional properties. This work proposes a novel elastohydrodynamic lubrication (EHL) model with FGC, in which the elastic deformation and stress are computed using influence coefficients (ICs) and discrete convolution‐fast Fourier transform (DC‐FFT) algorithm. Comparisons are made with homogeneous EHL solutions and finite element analysis (FEA) to validate its accuracy. The study systematically explores how coating elastic modulus, coating thickness and substrate elastic modulus influence contact and lubrication behaviours. The developed model is expected to establish a theoretical framework for FGC material design, enhancing the performance of friction pairs.

Experimental investigation of contact time of bouncing droplet on vibrating substrates

The observation of an elastic substrate self-driving droplet to produce a “springboard effect” provides new enlightenment to the application of elastic materials in the anti-icing area. The droplet–substrate dynamic of a water drop impacting a superhydrophobic elastic substrate is experimentally investigated at different Weber (We) numbers and beam stiffness. For water drop, the spreading dynamic is not affected by the We number and beam stiffness since the inertial action is dominant, and the elastic action of the beam is relatively small, while the receding dynamic is closely related to the parameters. For elastic substrate, the vibrating deflection increases with the increase in the We number and reduction of the stiffness, while the vibrating frequency is only dependent on its stiffness. Based on this, the rebound dynamic of the droplet is discovered dependent on the scale relationship between the droplet and substrate oscillation period. Finally, a relation of the contact time of a droplet impacting elastic substrates, which is verified to hold for a large range of We numbers, beam stiffness, and droplet sizes, is established. The discoveries may contribute to the design of a droplet–elastic substrate system to achieve desirable contact time, providing a theoretical basis to forecast the performance of droplet–substrate systems by employing elastic materials.

Experimental study on effect of elastic-rigid composite boundary on shockwave from cavitation bubble collapse

Understanding the mechanisms behind the cavitation erosion resistance of elastic materials is the basis for the development of new cavitation erosion resistance materials. This paper employs underwater low-voltage discharge to induce cavitation bubble, combined with high-speed photography, shadowgraph methods, and transient pressure measurement systems to experimentally investigate the evolution and intensity of shockwave from bubble collapse near elastic-rigid composite boundary. Under the condition of constant elastic material thickness, with the bubble–wall distance increasing, shockwave shape evolves from multi-layers to single-layer. The peak pressure of the shockwave shows a trend of decreasing, then increasing, and finally stabilizing with increase in the bubble–wall distance. Furthermore, it was found that the elastic-rigid composite boundary causes the shockwave to reflect twice. As the material thickness increases, the intensity of the first reflected shockwave from the elastic surface decreases initially, then increases, and eventually stabilizes. However, that of the second reflected shockwave decreases. The total energy of the two reflections at the elastic interface is less than 4% of the mechanical energy of the bubble at its maximum volume. Finally, after the energy dissipation by the two reflections and material deformation, the elastic layer substrate withstands over 70% of the total mechanical energy of the cavitation bubble. There is an optimal elastic material thickness to minimize the shockwave load on the elastic layer substrate under the condition that the elastic-rigid composite boundary does not affect the evolution of cavitation bubble shape. These findings are significant for understanding bubble dynamics near elastic-rigid composite boundaries and provide theoretical support for developing cavitation erosion-resistant materials in engineering.

Dynamic of composite nanobeams resting on an elastic substrate with variable stiffness

This study introduces a novel approach by combining finite simulation and an enhanced shear deformation theory to analyze the dynamic behavior of multi-layer composite nanobeams supported by an elastic foundation. The calculation formulae are derived from nonlocal theory in order to account for the impact of size effect. An intriguing aspect of this research is the presence of intricate curved profiles in the two material layers of the beam. The elastic foundation exhibits varying stiffness throughout the beam's length, accounting for many imperfections in the beam and including the drag parameter of the material. These elements contribute to the steady evolution of the issue model towards more realistic structures. Nevertheless, the computation gets intricate and impedes the precise approach. However, our work has successfully resolved this difficult and significant difficulty using the two-node element. This research demonstrates the temporal evolution of the dynamic reactions of the point with the greatest displacement and velocity, as dictated by the law of change. Simultaneously, it also presents visual representations of every point on the beam as it undergoes temporal variations. These conclusions possess both scientific and practical value, establishing a foundation for real-world implementations.

Investigation of Cell Mechanics and Migration on DDR2-Expressing Neuroblastoma Cell Line.

Neuroblastoma is a devastating disease accounting for ~15% of all childhood cancer deaths. Collagen content and fiber association within the tumor stroma influence tumor progression and metastasis. High expression levels of collagen receptor kinase, Discoidin domain receptor II (DDR2), are associated with the poor survival of neuroblastoma patients. Additionally, cancer cells generate and sustain mechanical forces within their environment as a part of their normal physiology. Despite this, evidence regarding whether collagen-activated DDR2 signaling dysregulates these migration forces is still elusive. To address these questions, a novel shRNA DDR2 knockdown neuroblastoma cell line (SH-SY5Y) was engineered to evaluate the consequence of DDR2 on cellular mechanics. Atomic force microscopy (AFM) and traction force microscopy (TFM) were utilized to unveil the biophysical altercations. DDR2 downregulation was found to significantly reduce proliferation, cell stiffness, and cellular elongation. Additionally, DDR2-downregulated cells had decreased traction forces when plated on collagen-coated elastic substrates. Together, these results highlight the important role that DDR2 has in reducing migration mechanics in neuroblastoma and suggest DDR2 may be a promising novel target for future therapies.

Skin-inspired self-powered tactile sensing textile with high resistance to tensile interference

Tactile sensors that can mimic the sensory capabilities of human skin to perceive external static and dynamic pressure without tensile interference are essential in smart wearable electronics. Here, inspired by human skin, we report a highly stretchable and conformable self-powered tactile sensing textile capable of precisely sensing the pressure with no influence of the extension. The tactile sensing textile consists of an elastic fabric substrate and a triboelectric nanogenerator network with specific dimensionally stable triangular cross knots, providing the textile with prominent comprehensive performances (high tactile sensitivity, high stretching-insensitivity, high pressure resolution, long-time stability, and washability) superior to other reported stretching-insensitive tactile sensors. A pressure sensing system is developed based on the tactile sensing textile, which presents wide application for precise pressure detection in smart wearable conditions including athletics and healthcare facilities.

A reinvestigation on combined dry and wet adhesive contact considering surface tension

The present study theoretically explores combined dry and wet adhesive contact between a rigid sphere and elastic semi-half substrate, in which dry contact is encircled by liquid bridge. We consider threefold effects of liquid bridge on contact behavior, namely Laplace pressure induced by the curved surface of liquid meniscus, surface tension at the triple-phase junction and alternation of adhesion energy between solid surfaces ascribed to liquid immersion. A clear novelty in this study is the investigation on the effect of surface tension at the vapor-liquid-solid junction on the adhesive contact response, in contrast to previous studies. The model solution predicts that the contact behavior and adhesive strength are strongly dependent on surface wettability (manifested by contact angle), liquid volume and the contact system's rapidity in achieving thermodynamic equilibrium. It is found that the transition of the pull-off force is evidently different from Maugis-Dugdale model in terms of a couple of interesting characteristics. Moreover, it is unveiled that the jump instabilities and hysteresis of force-separation curves are highly affected by surface wettability and liquid volume. These theoretical results can not only shed lights on the mechanism of liquid-mediated adhesion employed by animals and plants, but also provide us inspiration for development of biomimetic adhesive devices.

The influence of polyacrylamide gel substrate elasticity on primary cultures of rat retinal ganglion cells

In vitro primary cell culture models of retinal ganglion cells (RGC) are widely used to study pathomechanisms of diseases such as glaucoma. The biomechanic interaction with the culture substrate is known to influence core cellular functions. RGC cultures, however, are usually grown on rigid plastic or glass substrates. We hypothesized that soft polyacrylamide gel substrates may alter survival and neurite outgrowth of primary cultured RGC.Primary retinal cultures from postnatal (day 1-6) Wistar rats were grown on glass coverslips or polyacrylamide (PA) gel substrate with different Young’s elastic moduli (0.75, 10 or 30 kPa). Substrates were coated with Poly-l-lysine and / or laminin. RGC were immunostained with anti-beta-III-tubulin. Total neurite length, growth cone morphology, RGC density, mitochondrial morphology and transport as well as pro-survival pathways (Erk1/2, Akt, CREB) were assessed.PA gel substrates of E = 10 kPa significantly increased the total neurite length by factor 1.5 compared to glass (p = 0.02). The growth cone area was significantly larger by factor 5.3 on 30 kPa gels (p = 0.01). The presence of a substrate coating was more important for neurite outgrowth and RGC survival on PA gels (poly-l-lysine > laminin) than on glass. Neither mitochondrial morphology and motility nor the activation of pro-survival pathways significantly differed between the four substrates.PA gel substrates significantly enhanced RGC neurite outgrowth. The signaling cascades mediating this effect remain to be determined.

Dedifferentiation- and aging-induced loss of mechanical contractility and polarity in vascular smooth muscle cells: Heterogeneous changes in macroscopic and microscopic behavior of cells in serial passage culture

Dedifferentiation and aging of vascular smooth muscle cells (VSMCs) are associated with serious vascular diseases, such as arteriosclerosis and aneurysm. However, how cell dedifferentiation and aging affect cellular mechanical behaviors at the single-cell and intracellular structure levels remains unclear. An in-depth understanding of these interactions is extremely important for understanding the mechanism underlying VSMC mechanical integrity and homeostatic regulation of vascular walls. Herein, we systematically investigated changes in VSMC morphology, structure, contractility, and motility during dedifferentiation and aging induced by serial passage culture using traction force microscopy with elastic micropillar substrates, laser nanodissection of cytoskeletons, confocal fluorescence microscopy, and atomic force microscopy. We found that VSMC dedifferentiation started in the middle stage of serial passage culture, accompanied by a transient cell spreading in the cell width and decrease in contractile protein expression. Dedifferentiated VSMCs showed a significant decrease in the contraction and stiffness of individual actin stress fibers; however, their overall cell traction forces were maintained. Simultaneously, a significant increase in cell motility and the number of actin fibers was observed in dedifferentiated VSMCs, which may be associated with the enhancement of cell migration and disruption of cell/tissue integrity during the early stage of vascular diseases. As cell senescence progressed in the later stage of serial passage culture, VSMCs displayed reduced cell spreading and migration with decrease in the overall cell traction forces and drastic reduction in mechanical polarity of cell structures and forces. These results suggested that cell senescence causes loss of mechanical contractility and polarity in VSMCs, which may be an important factor in vascular disease progression. The experimental systems established in this study can be powerful tools for understanding the mechanisms underlying cellular dedifferentiation and aging from a biomechanical perspective.

90-degree peeling of elastic thin films from elastic soft substrates: Theoretical solutions and experimental verification

Peeling of thin films has been widely used in adhesion measurement, film transfer and bio-inspired design. Most previous studies focused on the peeling of thin films from rigid substrates, but soft substrates are common in practical applications. Herein, we propose a two-dimensional model based on the bilinear cohesive law to characterize the 90-degree peeling of elastic thin films from elastic soft substrates, and obtain theoretical solutions expressed in terms of the Chebyshev series. The theoretical solutions match well with the finite element method results, including the load-displacement curves and the bulging deformation of soft substrates. We find that with decreasing substrate modulus, the maximum peeling force (Pmax) decreases but the steady-state peeling force remains unchanged. With the present solutions, the interfacial strength and fracture energy can be extracted simultaneously from the 90-degree peeling experiments of thin film/soft substrate systems, and then the experimentally measured Pmax for different film thicknesses can be well predicted. Furthermore, we obtain a new power scaling law of Pmax, where the scaling exponent depends on substrate elasticity. These results can help us measure the interfacial properties of thin film/soft substrate systems via peel tests, and regulate their peeling behaviors by interface design.

Love wave propagation in a smart composite structure of linear and exponential functionally graded porous piezoelectric material

Functionally graded materials (FGMs) have emerged as a promising avenue for enhancing the performance and longevity of surface acoustic wave (SAW) devices. This importance is gained due to gradual variation in functional properties of FGMs. In this paper, a mathematical model of a piezoelectric layer overlying a functionally graded porous piezoelectric (FGPP) layer resting on the elastic substrate is presented for the study of Love waves. The material parameters of the FGPP layer are considered to vary linearly and exponentially with the thickness of the layer. The solutions of governing equations corresponding to the FGPP layer are obtained by the Wentzel Kramers Brillouin (WKB) method. Dispersion equations are derived for both electrically open and shorted boundaries, linear and exponential gradation in both mechanical and electrical parameters, and for gradation in mechanical parameters alone as well. After numerical computation, dispersion curves are plotted to investigate the influence of wavenumber, type of gradation, extent of gradation, and type of boundaries on the phase and group velocity. The phase velocity decreases with wavenumber and is found more for linear gradation in comparison to exponential gradation. The electromechanical coupling factor is analyzed for different propagating modes of Love waves, in the case when gradation in mechanical properties is considered, the electromechanical coupling factor is greater than that when variation in both mechanical and electrical properties is considered. It is also observed that the tailoring of gradation can help to get the suitable value of the electromechanical coupling factor. The insights obtained from these findings can offer valuable contributions toward advancing the functionality and efficiency of SAW devices, there by bolstering their applicability in various technological domains.

Dynamics of irregular hyperelastic substrate under the impact of moving load

This work delves into the study of stresses induced in a non-homogeneous pre-stressed nearly incompressible elastic substrate with irregularity as a result of a normal load moving on its rough surface. The irregularity on the free surface of the substrate is considered in the form of parabolic irregularity. The solution methodology features the applicability of perturbation method along with substitution method to obtain the displacement components. The expressions of the induced shear and normal stresses have been established in closed form, and their expressions for special cases of the considered problem have also been deduced, which concur well with the existing literature. The influences of affecting parameters viz., non-homogeneity, frictional coefficient, irregularity factor, irregularity depth, hydrostatic stress and depth of the substrate on shear and normal stresses have been depicted graphically by means of numerical computation. The computational results have been manifested for distinct cases of irregularity zone involving parabolic as well as rectangular irregularities present in the considered geometrical model. It has been figured out that the presence of non-homogeneity in the irregular substrate has significant impact on the developed stresses.

Elastic interactions compete with persistent cell motility to drive durotaxis

Many animal cells that crawl on extracellular substrates exhibit durotaxis, i.e., directed migration toward stiffer substrate regions. This has implications in several biological processes including tissue development and tumor progression. Here, we introduce a phenomenological model for single-cell durotaxis that incorporates both elastic deformation-mediated cell-substrate interactions and the stochasticity of cell migration. Our model is motivated by a key observation in an early demonstration of durotaxis: a single, contractile cell at a sharp interface between a softer and a stiffer region of an elastic substrate reorients and migrates toward the stiffer region. We model migrating cells as self-propelling, persistently motile agents that exert contractile traction forces on their elastic substrate. The resulting substrate deformations induce elastic interactions with mechanical boundaries, captured by an elastic potential. The dynamics is determined by two crucial parameters: the strength of the cellular traction-induced boundary elastic interaction (A), and the persistence of cell motility (Pe). Elastic forces and torques resulting from the potential orient cells perpendicular (parallel) to the boundary and accumulate (deplete) them at the clamped (free) boundary. Thus, a clamped boundary induces an attractive potential that drives durotaxis, while a free boundary induces a repulsive potential that prevents antidurotaxis. By quantifying the steady-state position and orientation probability densities, we show how the extent of accumulation (depletion) depends on the strength of the elastic potential and motility. We compare and contrast crawling cells with biological microswimmers and other synthetic active particles, where accumulation at confining boundaries is well known. We define metrics quantifying boundary accumulation and durotaxis, and present a phase diagram that identifies three possible regimes: durotaxis, and adurotaxis with and without motility-induced accumulation at the boundary. Overall, our model predicts how durotaxis depends on cell contractility and motility, successfully explains some previous observations, and provides testable predictions to guide future experiments.

Substrate stress relaxation regulates monolayer fluidity and leader cell formation for collectively migrating epithelia.

Groups of cells must coordinate their movements in order to sculpt organs during development and maintain tissues. The mechanical properties of the underlying substrate on which cells reside are known to influence key aspects of single and collective cell migration. Despite being a nearly universal feature of biological tissues, the role of viscoelasticity (i.e., fluid-like and solid-like behavior) in collective cell migration is unclear. Using tunable engineered biomaterials, we demonstrate that sheets of epithelial cells display enhanced migration on slower-relaxing (more elastic) substrates relative to faster-relaxing (more viscous) substrates. Building our understanding of tissue-substrate interactions and collective cell dynamics provides insights into approaches for tissue engineering and regenerative medicine, and therapeutic interventions to promote health and treat disease.

Tensile-endurable nanolayered polypyrrole templated by liquid crystal for high-performance stretchable supercapacitors

Ordered architectures favorable for energy storage are hard to build and preserve on stretchable electrodes owing to the elongation-induced variation in morphology. Herein, we demonstrate the construction of nanolayered polypyrrole (PPy) on stretchable polymeric electrodes via lyotropic liquid crystal (LLC) template for the first time. In situ graft polymerization of PPy onto swollen polyacrylamide-co-poly(2-hydroxy ethyl acrylate) in an aqueous Lα LLC gives stretchable electrodes with nanolayered PPy rooted in expandable wrinkles. The nanolayered PPy electrode could be stretched up to 330 % strain and keep intact after 2,000 stretch-release cycles owing to reversible unfolding of wrinkles. By virtue of the well-arranged PPy nanolayers, the stretchable electrode exhibits a high electrical conductivity of 154 S cm−1 and gives a capacitance of 1143 mF cm−2 after assembled into a supercapacitor with H2SO4 polyacrylamide hydrogel. In addition, the capacitance retention remains 94.6 % after 2,000 stretch-release cycles accompanied by galvanostatic charge–discharge. The LLC templating graft polymerization of conjugated polymers on elastic substrates paves a way to develop nanostructured stretchable electrodes for high-performance wearable supercapacitors.

Enhanced Piezoelectric Performance of PVDF-TrFE Nanofibers through Annealing for Tissue Engineering Applications.

This study investigates bioelectric stimulation's role in tissue regeneration by enhancing the piezoelectric properties of tissue-engineered grafts using annealed poly(vinylidene fluoride-trifluoroethylene) (PVDF-TrFE) scaffolds. Annealing at temperatures of 80°C, 100°C, 120°C, and 140°C was assessed for its impact on material properties and physiological utility. Analytical techniques such as Differential Scanning Calorimetry (DSC), Fourier-Transform Infrared Spectroscopy (FTIR), and X-ray Diffraction (XRD) revealed increased crystallinity with higher annealing temperatures, peaking in β-phase content and crystallinity at 140°C. Scanning Electron Microscopy (SEM) showed that 140°C annealed scaffolds had enhanced lamellar structures, increased porosity, and maximum piezoelectric response. Mechanical tests indicated that 140°C annealing improved elastic modulus, tensile strength, and substrate stiffness, aligning these properties with physiological soft tissues. In vitro assessments in Schwann cells demonstrated favorable responses, with increased cell proliferation, contraction, and extracellular matrix attachment. Additionally, genes linked to extracellular matrix production, vascularization, and calcium signaling were upregulated. The foreign body response in C57BL/6 mice, evaluated through Hematoxylin and Eosin (H&E) and Picrosirius Red staining, showed no differences between scaffold groups, supporting the potential for future functional evaluation of the annealed group in tissue repair.

Myotube formation on micropatterns guiding by centripetal cellular motility and crowding

The physical microenvironment, including substrate rigidity and topology, impacts myoblast differentiation and myotube maturation. However, the interplay effect and physical mechanism of mechanical stimuli on myotube formation is poorly understood. In this study, we utilized elastic substrates, microcontact patterning technique, and particle image velocimetry to investigate the effect of substrate rigidity and topological constraints on myoblast behaviors. Our findings suggested the interplay of substrate stiffness and cellular confinement improved the myotube formation by inducing centripetal cellular motility. These results shed light on the impact of the topological substrate on myoblast differentiation and emphasize the critical role of asymmetrical cell motility during this process, which is highly correlated with cell movement and crowding. Our research provides insights into the intricate interplay between substrate properties, cell motility, and myotube formation during myogenesis. Understanding these mechanisms could trigger tissue engineering strategies and therapies to enhance muscle regeneration and function.