Viscoelastic Substrate Research Articles

Capability of energy harvesting in cantilever piezoelectric-actuated arch structures via highly accurate semi numerical method

The use of nanoscale arch structures in vibration detection has become popular due to their ability to capture resonance in two independent directions. This study investigates the vibration behavior of a small-scale cantilever curved beam structure made of a functionally graded carbon nanotube reinforced nanocomposite core and piezoelectric surface layers on a viscoelastic substrate. The piezoelectric layers convert motion into electrical signals, allowing for the harvesting of high-frequency motions in a delicate manner. Various theories, including the first-order shear deformation theory, strain gradient theory, and nonlocal theory, are used to capture the mechanical properties of the FG nanocomposite core at both nano- and micro-scales. The equations of motion and natural boundary conditions are derived using Hamilton’s principle and solved using Akbari-Ganji’s method. An artificial intelligence method is also presented to simplify the solution procedure and calculate numerical results based on important parameters in the vibrational behavior analysis. The study demonstrates the significance of viscoelastic properties of the substrate and the volume fraction of CNT in composite core in the frequency analysis of the arch structure, as shown by the results of both the numerical and AI methods.

A semi-analytical solution to incipient sliding contact on viscoelastic layer-elastic substrate with imperfectly bonded interface

This paper presents a semi-analytical solution to the incipient sliding contact between a rigid sphere and a viscoelastic layer-elastic substrate with spring-like interface. In this solution, Papkovich–Neuber potentials in frequency domain are applied to calculate the influence coefficients (ICs) based on the surface and interface conditions; the elastic constant in the elastic solution is replaced by the creep function to cover the time-dependent characteristics of the viscoelastic layer; discrete convolution-fast Fourier transform (DC-FFT) is used to obtain the displacements and stresses caused by the external load; conjugate gradient method (CGM) is employed to compute the pressure on the top surface of the viscoelastic layer. The validity of the solution is verified by a previous method and the finite element method (FEM), where the relaxation and creep functions of the viscoelastic layer are expressed as Prony series. Influences of variations in parameters on the surface pressure, normal displacement and von Mises stress are analyzed by a parametric study of the time, relaxation time, relaxation modulus, stiffness coefficients, coating thickness and friction coefficient. The results indicate that this solution can predict the contact behaviors of viscoelastic layered half-space and may serve as a numerical experiment in research of coating materials.

Temperature-dependent vibrational behavior of bilayer doubly curved micro-nano liposome shell: Simulation of drug delivery mechanism

This article analyzes the vibrational behavior of the double-layered micro-nanosphere to simulate the drug delivery mechanism in the biological structure under the influence of the temperature environment and the viscoelastic substrate for the polar lipid fraction E (PLFE) liposome isotropic material model. In order to obtain the micro-nano structural equations of the double-layer spherical shell, the displacement-strain relations of the shell have been expressed according to the first-order shear deformation theory and the non-local strain gradient theory. The partial differential equations of motion have been obtained by applying Hamilton’s principle. The system of linear couple equations have been solved using the Galerkin method. After validating the model with the results of the articles available in the literature to determine the accuracy of the presented model, numerical results are presented to investigate the effects of various parameters such as the radius of curvature ratio to length, damping coefficient, Kelvin-Voight damping coefficient, boundary conditions and temperature on vibration frequency response are provided and discussed. Results of the current research indicates that natural frequency decreases as the damping coefficient related to the viscous effect between the liposome bilayers increase. Results of the current research can be used as a benchmark for drug delivery applications.

Nonlinear 2D-DQ volume-preservative global–local dynamic analysis of composite sandwich plates with soft hyperelastic cores and viscoelastic Winkler-Pasternak foundations

Nonlinear large amplitude vibration and dynamic deformations of sandwich plates with composite face sheets and hyperelastic cores that encounter large thickness changes during the vibration are investigated here for the first time. Moreover, a new global–local zigzag hyperelastic plate theory that considers the incompressibility and large transverse deformability of the core, and employs transverse normal strains whose order is higher than that of the in-plane strains is proposed. The plate is resting on a viscoelastic Winkler-Pasternak substrate, exposed to various spatial and time distributions of loads, and experiencing a diversity of edge conditions. The governing equations of motion are obtained by using Hamilton’s principle, von Kármán’s assumptions, and the series expansion of the volume-preserving strain energy density function. A 2D differential quadrature (2D-DQ) technique is employed for the spatial discretization of a structure with both constitutive and kinematic nonlinearities, for the first time. The time-dependent combination of the nonlinear coupled motion equations and boundary conditions is treated by an iterative/updating Runge-Kutta time-marching technique and the effects of the thickness and aspect ratio of the plate, viscoelastic and shear parameters of the foundation, types of the edge conditions, constitutive parameters of the composite materials, fiber orientation angle, and magnitude and distribution pattern of the loads on the resulting dynamic lateral deflections are studied. Results reveal that while the vibration frequencies and amplitudes of the face sheets are quite different, the damping is more remarkable when stiffer cores are utilized. Moreover, the effects of the higher vibration modes are more apparent in looser edge conditions, smaller fiber angles, and special excitation frequencies.

All‐Dry Deterministic Transfer of Thin Gold Nanowires for Electrical Connectivity

AbstractMetallic nanowires (NWs) exhibit a number of interesting properties, such as high conductivity, flexibility, and cold‐weldability, making them ideal for nanocircuits. They are usually adsorbed on substrates by depositing a colloidal solution of NWs on the surface. However, they remain randomly scattered and solvent residues may contaminate/ degrade the sample. This study presents a method for forming electrical contacts with gold nanowires based on all‐dry deterministic transfer. The process begins with the adsorption of gold nanowires by drop casting the colloidal solution onto a viscoelastic substrate. These wires are transferred to selected locations on the substrate, minimizing manipulation with fabrication times a factor of 2 shorter than direct drop casting deposition, preserving surface and sample conditions, and improving the fabrication of nanocircuits. Atomic force microscopy is used to manipulate the NWs for the final connections, which have contact resistances of a few ohms. To illustrate the technique, three different examples of applicability are presented. This work is expected to be a starting point for expanding the potential of deterministic transfer that is successfully used in 2D materials. For example, to study local electrical transport in heterogeneous samples such as van der Waals heterostructures and twisted layers of 2D materials.

Detachment of a Rigid Flat Punch from a Viscoelastic Material

We show that the detachment of a flat punch from a viscoelastic substrate has a relatively simple behaviour, framed between the Kendall’s elastic solution at the relaxed modulus and at the instantaneous modulus, and the cohesive strength limit. We find hardly any dependence of the pull-off force on the details of the loading process, including maximum indentation at preload and loading rate, resulting much simpler than the case of a spherical punch. Pull-off force peaks at the highest speeds of unloading, when energy dissipation is negligible, which seems to be in contrast with what suggested by the theories originated by de Gennes of viscoelastic semi-infinite crack propagation which associated enhanced work of adhesion to dissipation.Graphical abstract

Efficient machine-learning algorithm applied to predict the transient shock reaction of the elastic structure partially rested on the viscoelastic substrate

Due to numerous applications of piezoelectric materials in the modern technologies, this study assesses the thermomechanical shock behavior of the functionally graded graphene platelets reinforced nanocomposite (FG-GPLRN) annular plate surrounded by two piezoelectric layers and partially rested on the viscoelastic substrate for different cases of boundary conditions by metaheuristic optimized machine-learning methods, for the first time. Thermal and mechanical shocks are simultaneously applied on the upper surface of the mentioned structure. Governing equations of the system are formulated in the background of three-dimensional (3D) elasticity theory. Energy balance of the system is considered based on the Lord-Shulman theorem. Differential quadrature method (DQM) is selected as the main solver to determine the spatial response of the system from the state-space form of the governing differential equations. Additionally, Laplace transform is collaborated with modified Dubner and Abate’s approach to predict the temporal response of the system. Accuracy of the applied methods is carefully examined and verified through comparative study performed between the current results and those determined in the published high-quality studies. Valuable outcomes of the current approach would be directly employed in designing process of similar structures interacting with probable thermomechanical shocks.

Evaluation of a Hybrid Underwater Sound-Absorbing Metastructure by Using the Transfer Matrix Method.

In this study, we designed a novel hybrid underwater sound-absorbing material of the metastructure that contains a viscoelastic substrate with a microperforated panel. Two types of sound-absorbing metastructures were combined to achieve satisfactory sound absorption performance in the low-frequency range. A homogenized equivalent layer and the integrated transfer matrix method were used to theoretically evaluate the sound absorption performance of the designed nonhomogeneous hybrid metastructure. The theoretical results were then compared with the results obtained using the finite-element method. The designed hybrid sound-absorbing metastructure exhibited two absorption peaks because of its different sound-absorbing mechanisms. The acoustic performance of the developed metastructure is considerably better than that of a traditional sound absorber, and the sound absorption coefficient of the developed metastructure is 0.8 in the frequency range of 3-10 kHz. In addition, an adjustment method for the practical underwater application of the designed metastructure is described in this research. Further studies show that the sound absorption coefficient of the adjusted metastructure still has 0.75 in the frequency range of 3-10 kHz, which indicates that this metastructure has the potential to be used as an underwater sound-absorbing structure. The results of this study can be used as a reference in the design of other novel hybrid underwater sound-absorbing structures.

Effects of matrix viscoelasticity and geometrical constraint on cell migrations: A multiscale bio-chemo-mechanical model

Cells actively sense the extracellular matrix (ECM) biophysical properties and respond by changing migration phenotypes. The regulatory roles of the ECM viscoelasticity and geometrical constraint were separately validated in different experimental studies. However, the extension of the study to more complex microenvironments that combines all these biophysical factors is challenging due to the difficulty of manipulating 3D ECM scaffolds. In this study, we proposed a multiscale model that enabled the sensing of the ECM mechanical properties and contact interactions between a highly deformed cell with the constricted wavy microchannels. The model is validated against experimental data and quantitatively replicates the effects of ECM viscoelasticity and confinement on cell area and speed. We observe a linearly increasing migration speed on stiff substrates with increasing cell aspect ratios in the narrower channels. The reason can be attributed to the increasing net propulsive force as traction forces become progressively polarized and the decreasing viscous drag resulting from the suppressing spreading. Notably, we predict that, on soft viscoelastic substrates, cells concurrently achieve the maximum speed and the largest spreading in which the substrate relaxation time is comparable to the clutch binding timescale. The model also shows the influence of contact guidance by the geometric curvature at the sidewall boundary on cell spreading, morphology, and migration speed. Together, our multiscale model captures varying mechanosensitive migration phenotypes with the underlying mechanism explained from the sub-cellular dynamics and provides experimentally testable predictions on cell migrations in a microenvironment that better mimic the tissue microenvironment.

Rate-dependent evolution of wrinkling films due to growth on semi-infinite planar viscoelastic substrates

A mechanistic understanding of morphogenesis in biology, the fabrication of advanced meta surfaces with specific functionalities and structures with enhanced energy dissipation often have in common that the combined effects of energy dissipation due to viscoelasticity and a loss of stability govern both their mechanical response and their final forms. In this paper we show that the interplay between viscoelasticity and multistability crucially influences the evolution of deformations in viscoelastic structures undergoing large deformations. The influence is studied on a prototypical system of a uniaxially growing film on a semi-infinite planar viscoelastic substrate, where it is shown that during the evolution of deformation the choice of multiple developing modes is greatly affected by this interplay. For the analysis of the underlying mechanics of the mode competition in the post-buckling regime, when the system undergoes large deformations, a 3D general finite-strain visco-hyperelastic theory is built. It includes kinematic and material nonlinearities in the film and in the substrate. For the case of ramp-loading time functions the phase space of the solutions is characterized and the evolution of a deformation pattern is analyzed. We find that the interaction between multistability and viscoelasticity greatly increases the evolution time of the system and that the growth rate and viscoelastic stress-relaxation rate influence the choice of the final equilibrium deformation state of the structure. This shows that viscoelastic structures can evolve into (meta)stable equilibrium states that are unattainable using purely elastic structures. The nonlinear problem is solved numerically with the use of the finite-element method. In parallel, we develop analytical solutions for a simplified problem that is based on Föppl–von Karman plate kinematics to describe the mechanics of the film and substrate that is modeled as a 2D linear-viscoelastic continuum. A remarkably good match between the analytical and the numerical results was obtained.

A layer-wise formulation for vibration performance of nanocomposite structure by introducing a novel viscoelastic substrate involving friction force

The vibration of different structural members is highly dependent on the external forces and environment they are moving in it. The stiffness and mass properties of the structure are the main factors in determining the frequency responses. However, situations commonly occur in which the structures are exposed to perpetual external loading conditions. In the present study, a novel model for investigating the effects of friction between structure and substrate is proposed and applied in small-scale cylindrical structures. In this regard, nanocomposite materials made of epoxy and reinforced by graphene oxide particles in an axial direction are used as the main material of the cylinder. The classical formulation of elasticity for anisotropic materials in a polar coordinate system is derived and presented. Moreover, the homogeneous properties of the nanocomposite are evaluated using Halpin–Tsai formulation. The core idea of the current study is to develop and present a new concept of the frictional substrate to incorporate friction forces into consideration along with visco-elastic reactions. Both finite element and analytical solutions are provided to examine the effects of different parameters on the vibrational behavior of the structure. The results of the study are presented using graphs for a detailed presentation of the effects of different parameters.

On energy absorption and low-velocity impact response of functionally graded graphene oxide powders-reinforced nanocomposite panel on the viscoelastic substrate

Curved panels are used for ships due to complex situations that can be under external loading. So, it is very important to know about the stability related to the curved system under Low-Velocity Impact (LVI). To improve the stability of this kind of structure, graphene oxide powders (GOPs) are added to its matrix. In addition, the contact force between the impactor and shell is evaluated by implementing Hertz contact theory. So, in the current work, as a first attempt, energy absorption and low-velocity impact response of functionally graded graphene oxide powders-reinforced nanocomposite panel on the viscoelastic substrate is presented. Higher-order shear deformation theory (HSDT), which has twelve factors, is employed to determine the displacement domains. Also, the minimum potential energy technique is designated to obtain the governing equations and end conditions. Moreover, Galerkin and Newmark methods are chosen to solve the relationships. The governing equations related to the curved system under external excitation aimed at achieving the LVI and dynamic outputs are determined by the connection of Galerkin and Newmark methods. The uniqueness of this research is considering the impacts associated with HSDT and various Boundary Conditions (BCs) in addition to considering FG oxide powder reinforcement. The outputs segment displays the effects related to the BCs, the radius of the impactor, mass, and velocity, as well as the weight fraction related to the GOPs on contact force, the indentation, and the indenter velocity.

Application of DQHFEM for free and forced vibration, energy absorption, and post-buckling analysis of a hybrid nanocomposite viscoelastic rhombic plate assuming CNTs’ waviness and agglomeration

Vibrations and stability responses are two mechanical characteristics of engineering materials that are highly important for designing new engineering structures. This numerical research deals with investigating the effects of reinforcing a hybrid nanocomposite viscoelastic rhombic plate with Carbon Nano-Tubes (CNTs) and Carbon Fibers (CFs) on the post-buckling behavior, free and forced vibration as well as energy absorption characteristics. The structure is located on a viscoelastic torsional fractional substrate. In addition, the influence of random distribution, waviness, and agglomeration of CNTs is analyzed using the Halpin-Tsai theory. The structural damping is based on the Kelvin-Voigt method and the structure model is created according to the first-order shear deformation theory. Four types of boundary conditions such as fixed, simply, and free-supported are considered for the structure model. To solve the governing equations, a novel approach known as the Differential Quadrature Hierarchical Finite Element Method (DQHFEM) is applied. The numerical achievements revealed that by reducing the skewness angle to 30°, decreasing the aspect ratio to 1, and increasing the CNTs weight percentage up to 0.4, dimensionless frequency improved by 101%. Application of FFFF boundary conditions has dramatically effect since the amplitudes of the dynamic deflection sharply raised (about 91.78% higher than CCCC rhombic plate) and led to deteriorated energy absorption. The dynamic deflection of the structure is increased by nearly 29.36% when both waviness and random distribution (agglomeration) parameters are considered for CNTs. Besides, the random distribution factor is more effective than waviness on post-buckling behavior, energy absorption, and stability of the rhombic plate. It is also worth mentioning that the weight percent of the CNTs affects the number of oscillations and changes the vibration pattern so that with increasing the CNTs content, the number of oscillations is enhanced.

Effect of energy dissipation on a viscoelastic substrate on the dissolution of surface nanobubbles

Based on the analogy between the process of spreading a liquid droplet on a hydrophobic surface and the diffusion dissolution of surface nanobubbles (SNB), the shape of the wetting ridge, deformed by capillary forces of the substrate surface area adjacent to the contact line of the three phases, is calculated within the framework of linear elasticity theory. It is shown that the energy dissipation in viscoelastic substrates on the wetting ridge can cause the pinning of the triple line and the termination of the diffusion dissolution of the SNB. Keywords: surface nanobubble, pinning, viscoelasticity.

Propagation of shear waves in viscoelastic layered structure

• Shear wave through orthotropic material on functionally graded viscoelastic substrate. • Analytical dispersion relation. • Influence of material parameters on dispersion. The presented analytical study deals with the propagation of shear waves (S waves) in the layered structure containing an orthotropic material layer bonded with an heterogeneous viscoelastic half-space. Separate governing differential equations are applied while obtaining the analytical solution of transverse displacement in the respective media. The dispersion relation (complex form separated into real and imaginary parts) is finally derived in the closed form for the considered system employing suitable boundary conditions and the derived displacements. The obtained results are also shown to match with the classical Love waves equation (for isotropic media case). The phase- and damping velocity terms are plotted against the wavenumber (all quantities in dimensionless form) for the different values of material parameters. The effect of heterogeneity parameter, viscoelastic parameter, and the layer thickness on the wave propagation is graphically presented that can be used while exploring the nature of S wave propagation through similar composite structures.

Viscous fingering instabilities in spontaneously formed blisters of MoS2 multilayers.

The viscous fingering in the Hele-Shaw cell can be suppressed by replacing the upper-bounding rigid plate with an elastic membrane. Recently, graphene multilayers while polymer-curing-induced blistering showed the dynamical evolution of viscous fingering patterns on a viscoelastic substrate due to their thickness-dependent elasticity. Under certain conditions, the elastic solid-based instability couples with the viscoelastic substrate-based instability. The mechanisms underlying such a coupling in the blisters of 2D materials and the dynamical evolution of the viscous fingering patterns underneath the blisters are yet to be addressed. Herein, we investigate the viscous fingering instabilities in spontaneously formed blisters of MoS2 multilayers, and provide thorough analytical and experimental insights for the elucidation of the dynamical evolution of the viscous fingering patterns and the coupled instabilities in the blisters. We also estimate the interfacial adhesion energy of the MoS2 flakes over a (poly)vinyl alcohol (PVA) substrate and the confinement pressure inside the MoS2 blisters using a conventional blister-test model. It is observed that the presence of instability gives rise to anomalies in the modeling of the blister test. The adhesion mechanical insights would be beneficial for fundamental research as well as practical applications of 2D material blisters in flexible optoelectronics.

Substrate viscoelasticity affects human macrophage morphology and phagocytosis.

Viscoelasticity is an inherent characteristic of many living tissues and, in an attempt to better recapitulate this aspect in cell culture, hydrogel biomaterials have been engineered to exhibit time-dependent energy-dissipative mechanical behavior. Viscoelastic hydrogel culture platforms have been instrumental in understanding the biological effects of viscoelasticity. Although viscoelasticity has been shown to regulate fundamental cell processes such as spreading and differentiation in adherent cells, the influence of viscoelasticity on macrophage behavior has not been explored. Here, we use a tunable viscoelastic polyacrylamide hydrogel culture system to demonstrate that viscoelasticity is an important biophysical regulator of macrophage function. After biologically validating our system with HS-5 fibroblasts to show behavior consistent with existing reports, we seed human THP-1 monocytes on these viscoelastic substrates and differentiate them into macrophages. THP-1 macrophages become smaller and rounder, and less efficient at phagocytosis on more viscous polyacrylamide hydrogel substrates. Since macrophages play key roles in mounting responses such as inflammation and fibrosis, these results indicate that viscoelasticity is an important parameter in the design of immunomodulatory biomaterials.

Frequency of the composite shell rested on the complex non-polynomial viscoelastic media involving friction force

In this study, a 3D-flexibility theory is employed in order to investigate the frequency behavior of the composite cylindrical shells on the elastic substrate. The current composite structure is reinforced by functionally graded graphene oxide powders (FG-GOPs). It is assumed that the system is resting on an elastic foundation, in which friction force in the horizontal direction, as well as viscoelastic substrate, are taken into account. The results are extracted by the differential quadrature method (DQM). Additionally, the results are validated by COMSOL Multi-physics software. Lastly, the effect of in-plane boundary conditions, Biot’s coefficient, circumferential as well as initial radial stresses, and FG-GOP’s weight fraction on the frequency responses of the FG-GOPRC cylindrical shells on the elastic substrate is studied. Also, when Biot’s coefficient intensifies, the negative impact of the geometry parameter on the frequency response is more significant than the positive influence from the geometry parameter.

Dynamic stability, and absorbed energy measurements in a sandwich structure resting on the novel frictional viscoelastic torsional substrate and horizontal friction force

Like metallic materials, fiber metal laminate (FML) lets the material has a simple metal structure behavior but with such advantages as specialized strength properties, impact, fire resistance, weight savings, corrosion resistance, and metal fatigue. The main focus of this article is to indicate the dynamic response of circular size-dependent circular plates made of FML material via 3D-elasticity theories. The size-dependent structure is simulated by coupling the modified nonlocal couple stress and 3D-elasticity theories (MNCS-3DET). For accurate modeling of the elastic substrate, torsional and linear spring and Pasternak foundation are modeled using the equations of horizontal friction force and torsional interaction. Harmonic differential quadrature method and Chebyshev–Gauss–Lobatto grid distribution points are coupled for solving the partial differential equations of the current micro/nano-structure. Novelties of this work consider the effects of MCS-3DET, torsional interaction, horizontal friction force, and FML material in the construction of the circular micro/nanoplate. In the results section, the outputs are verified with other published articles, and the outcomes show that the MCS-3DET parameter, elastic foundation coefficient, horizontal friction force coefficient, and geometry have an essential role in the dynamic stability of the FML micro/nano-structure.

A multiscale whole-cell theory for mechanosensitive migration on viscoelastic substrates

Increasing experimental evidence validates that both the elastic stiffness and viscosity of the extracellular matrix regulate mesenchymal cell behavior, such as the rational switch between durotaxis (cell migration to stiffer regions), anti-durotaxis (migration to softer regions), and adurotaxis (stiffness-insensitive migration). To reveal the mechanisms underlying the crossover between these motility regimes, we have developed a multiscale chemomechanical whole-cell theory for mesenchymal migration. Our framework couples the subcellular focal adhesion dynamics at the cell-substrate interface with the cellular cytoskeletal mechanics and the chemical signaling pathways involving Rho GTPase proteins. Upon polarization by the Rho GTPase gradients, our simulated cell migrates by concerted peripheral protrusions and contractions, a hallmark of the mesenchymal mode. The resulting cell dynamics quantitatively reproduces the experimental migration speed as a function of the uniform substrate stiffness and explains the influence of viscosity on the migration efficiency. In the presence of stiffness gradients and absence of chemical polarization, our simulated cell can exhibit durotaxis, anti-durotaxis, and adurotaxis respectively with increasing substrate stiffness or viscosity. The cell moves toward an optimally stiff region from softer regions during durotaxis and from stiffer regions during anti-durotaxis. We show that cell polarization through steep Rho GTPase gradients can reverse the migration direction dictated by the mechanical cues. Overall, our theory demonstrates that opposing durotactic behaviors emerge via the interplay between intracellular signaling and cell-medium mechanical interactions in agreement with experiments, thereby elucidating complex mechanosensing at the single-cell level.