Viscoelastic Matrix Research Articles

Determination of Effective Characteristics of the Fibrous Viscoelastic Composite with Transversal and Isotropic Components

The method of determining the parameters of the integral operator of the effective longitudinal elastic modulus of the first-kind composite material is proposed. The viscoelastic transversal and isotropic composite with a periodic structure is used as an object of study. The elements of its cell are the transversal and isotropic viscoelastic matrix and the elastic fiber, which are approximated by hollow and solid cylinders, respectively. The rheological matrix characteristics are described according to the Boltzmann–Volterra hereditary theory. The axisymmetric longitudinal tension of the cell is considered. It is assumed that the radial displacements and stresses on the border between the matrix and the fiber are continuous, the lateral surface of the cell is free from stresses, and axial deformations of the matrix and the fiber coincide. The Laplace transform is applied to solve the obtained boundary value problem. The similar problem in image space is solved for the homogeneous transversely isotropic viscoelastic composite. The effective instantaneous longitudinal elastic modulus and the relaxation kernel are determined via the relation between deformation of the composite and its components, namely the equality of their axial deformations. The proposed method allows one to determine the viscoelastic composite characteristics via the corresponding characteristics of its elements and the volume fractions of the matrix and the fiber in the composite material.

Time-dependent behavior of viscoelastic three-phase composite plates reinforced by Carbon nanotubes

The recent advancement in the manufacture and analysis of Carbon nanotubes (CNT) has persuaded many researchers to use them as the reinforcing phase of a polymer matrix. Nevertheless, it should be recalled that polymers show a viscoelastic behavior, so that their mechanical properties are functions of time due to the intrinsic nature of the material. In this paper, a Maxwell rheological model is employed to describe the time-dependency of the mechanical properties of the matrix in the framework of linear viscoelasticity. The viscoelastic matrix is enriched by both CNTs and oriented fibers to obtain the so-called three-phase composite materials. Such materials represent the main constituents of the plates investigated in this paper by means of the Reissner-Mindlin theory. The transient response, which is analyzed through the Newmark’s scheme, is expressed in terms of central deflection and mechanical parameters for several configurations. The effect of the mass fraction of both reinforcing phases is discussed. The solutions are achieved numerically by means of a Finite Element (FE) code which implements the viscoelastic model and the proper homogenization technique in order to deal with three-phase composites.

Magneto-mechanical characterization of magnetorheological elastomers

This work analyses the properties and the magneto-mechanical characteristics of magnetorheological elastomers, a class of smart materials not yet broadly investigated. First, set of several samples of this material was manufactured, each one characterized by a different percentage of ferromagnetic material inside the viscoelastic matrix. The specimens were manufactured in order to create isotropic and anisotropic configurations, respectively, with randomly dispersed ferromagnetic particles or with an aligned distribution, obtained through and external magnetic field. Then, the mechanical behaviour of each sample was analysed by conducting a compression test, both with and without an external magnetic field. Moreover, a three-point bending test was also performed on the same specimens. Stiffness, deformation at maximum stress and specific energy dissipated were calculated based on the experimental data. The results were analysed considering the mechanical responses, and an analysis of variance was carried out in order to assess the statistical influence of each variable. The experimental results highlighted a strong correlation between the percentage of ferromagnetic material in each sample and its mechanical behaviour. The anisotropicity of the material, aligned in columnar structures, also affects the stiffness measured in the compression test, while the external magnetic field’s main contribution is to reduce the samples’ maximum deformation. Using analysis of variance results as guidelines, we built a simple phenomenological model which produces quite reliable predictions regarding the mechanical response of the magnetorheological elastomers under compressive stress.

Piezoresistive and Mechanical Characteristics of Graphene Foam Nanocomposites

We report the piezoresistive and mechanical characteristics of three-dimensional (3D) graphene foam (GF)–polydimethylsiloxane (PDMS) nanocomposites processed by a facile two-step approach. A polyurethane (PU) foam with graphene embedded (and aligned) in the pore walls is pyrolyzed and then impregnated with PDMS to form a GF–PDMS nanocomposite, resulting in a slitlike network of graphene embedded in the viscoelastic PDMS matrix. The interconnected graphene network not only imparts excellent electrical conductivity (up to 2.85 S m–1, the conductivity of PDMS is 0.25 × 10–13 S m–1) to the composite but also enables ultrasensitive piezoresistive behavior. For an applied compressive strain of 10% we report a 99.94% reduction in resistance, with an initial gauge factor of 178, and note that this value is significantly higher than those reported in the literature. Cyclic compression–release tests conducted at different strain amplitudes demonstrate that both the mechanical and piezoresistive responses of the GF–...

Mechanical Load Effects on Cardiac Action Potential and Arrhythmogenic Ca2+Activitiesrevealed by a Novel Patch-Clamp-In-Gel Technology

Cardiomyocytes are under mechanical load when the heart pumps blood against peripheral resistance. However, the mechanical load effects on cells have been missed in previous patch-clamp experiments because the cells were bathed in solution under load-free condition. We have developed an innovative Patch-Clamp-in-Gel technique to embed single cells in a 3-D hydrogel made of viscoelastic polymer matrix. Experiments were performed when mouse ventricular myocytes were contracting in-gel under mechanical load. (1) Compared to load-free cells, the myocytes in-gel under mechanical load showed prolonged action potential duration (long APD), early afterdepolarization (EAD), delayed afterdepolarization (DAD), and triggered AP, indicating that mechanical load increases arrhythmogenic AP activities. (2) Simultaneous triple-signal recordings of AP, Ca2+, and contraction revealed that load-induced DAD occurs in conjunction with spontaneous Ca2+ wave. (3) The EADs, DADs, and Ca2+ tides were abolished by blocking the late Na+ current, suggesting changes in the Na+ and Ca2+ homeodynamics. (4) The load-induced arrhythmogenic activities were abolished by specific inhibition of nitric oxide synthase 1 (NOS1 or nNOS), indicating a critical role of nNOS in the mechano-chemo-electro-transduction. Our data show that mechanical load significantly affects action potential, Ca2+ signaling, and myocyte contraction. The Patch-Clamp-in-Gel technology provides a new tool to control mechanical load on single myocytes, which enables studying mechanotransduction effects on the three dynamic systems - electrical, Ca2+ signaling, and contractile systems - that control cardiac function and arrhythmogenesis.

High Frequency Active Microrheology Reveals Mismatch in 3D Tumor Intracellular and Extracellular Matrix Viscoelasticity

Tissue homeostasis and malignant transformation are modulated by the reciprocal crosstalk between cells and the surrounding extracellular matrix (ECM), which encompasses both long-term matrix organization and short-term biochemical responses. Here, I present data where broad band optical trap- active microrheology was used to probe the microscale rigidity |G∗(ω)| and viscoelasticity tan(δ(ω)) at locations inside the cell cytoplasm and in the surrounding 3D ECM. These measurements were acquired with near simultaneity and at high frequencies relevant to molecular dynamics. A mechanical mismatch wherein the tumor cells are stiffer than the surrounding ECM was observed. In the frequency regime about the terminal relaxation time, both intracellular and extracellular measurements of both |G∗| and tan(δ) relate to oscillation frequency? by monomial power laws in the range 400 Hz – 15 kHz independent of type of matrix and perturbation of the cytoskeletal dynamics. These data also extend the frequency range revealing a stronger power law dependence for both intracellular and the coupled extracellular mechanics. The exponents and coefficients of these power laws are anti-correlated and collapse onto master curves. These data suggest that there is a mismatch between cells and the ECM when cells are cultured in 3D mimetics in the frequency range at which single filament dynamics emerge.

Volume expansion and TRPV4 activation regulate stem cell fate in three-dimensional microenvironments

For mesenchymal stem cells (MSCs) cultured in three dimensional matrices, matrix remodeling is associated with enhanced osteogenic differentiation. However, the mechanism linking matrix remodeling in 3D to osteogenesis of MSCs remains unclear. Here, we find that MSCs in viscoelastic hydrogels exhibit volume expansion during cell spreading, and greater volume expansion is associated with enhanced osteogenesis. Restriction of expansion by either hydrogels with slow stress relaxation or increased osmotic pressure diminishes osteogenesis, independent of cell morphology. Conversely, induced expansion by hypoosmotic pressure accelerates osteogenesis. Volume expansion is mediated by activation of TRPV4 ion channels, and reciprocal feedback between TRPV4 activation and volume expansion controls nuclear localization of RUNX2, but not YAP, to promote osteogenesis. This work demonstrates the role of cell volume in regulating cell fate in 3D culture, and identifies TRPV4 as a molecular sensor of matrix viscoelasticity that regulates osteogenic differentiation.

On internal stability loss of a row unidirected periodically located fibers in the visco-elastic matrix

In the present paper, the microbuckling or internal stability loss in the viscoelastic composites containing unidirected fibers under compression along the fibers is studied by use of piecewise homogeneous body model. In this model, it is used the 3-D geometrically non-linear exact equations of viscoelasticity theory. The composite material was considered as an infinite viscoelastic body with a row unidirected periodically located elastic fibers that have an initial infinitesimal imperfection. When the initial imperfection starts to increase and becomes indefinitely, this is taken as a stability loss criterion and co-phase microbuckling mode out of plane are taken into account. The numerical results about the influence of the interaction between the fibers on the values of the critical time are obtained and presented.

Constitutive modeling framework for residually stressed viscoelastic solids at finite strains

This article presents a novel three-dimensional constitutive modeling framework for residually stressed viscoelastic solids undergoing finite strains. Within the current of phenomenological approach, the constitutive relations are derived for a viscoelastic matrix whereas residual stresses are considered in the constitutive law in terms of a set of invariants. In particular, we analyze the bifurcation of a residually stressed viscoelastic solids using the finite element method (FEM). In-plane residual stresses are introduced in the constitutive relation that satisfy the balance of momentum. The implementation is discussed with regard to commercial finite element code Abaqus. Furthermore, the robustness of the proposed user material is illustrated emphasizing the dependence of bifurcation and viscoelastic parameters of tubes under torsion upon the residual stresses. The proposed formulation is also suitable for cord-rubber composite application like tires, airsprings, and soft tissues in biomechanics, among others, being such applications particular extensions to anisotropic materials.

Numerical multiscale homogenization approach for linearly viscoelastic 3D interlock woven composites

This work aims at modeling the homogenized behavior of a polymer matrix composite reinforced with three dimensional (3D) woven fabric. The effective warp and weft tows’ properties were determined by numerical homogenization with Abaqus considering elastic fibers, a viscoelastic matrix and periodic boundary conditions. The temperature- and cure-dependent linearly viscoelastic model previously developed by the authors for this particular polymer matrix was implemented into a subroutine using a differential strategy. A second homogenization procedure was carried out to obtain the mesoscopic structure homogenized behavior. Moreover, rectangular composite plates were manufactured by Resin Transfer Molding (RTM) and isothermal creep tests were carried out to study the material’s viscoelastic behavior at high temperatures below the resin’s glass transition temperature. Experimental results were compared to the temperature-dependent homogenized linearly viscoelastic model predictions. This model is a step forward for the accurate prediction of the residual stresses developed during the manufacturing of structural parts made out of 3D woven interlock composites.

Linear and nonlinear rheological behaviors of silica filled nitrile butadiene rubber

Nanoparticles significantly reinforce rubber and enhance nonlinear mechanical behavior while the underlining mechanisms are not clear. Herein the effects of crosslinking, filler content and filler surface chemistry on the linear and nonlinear rheological responses of silica filled nitrile butadiene rubber are investigated. A time-concentration superposition principle is employed for constructing rheological master curves. While the strain amplification and dynamics retardation contribute to the high-frequency linear rheology of the compounds, the former is crucial for the vulcanizates with matrix of similar crosslinking degree. In both the compounds and vulcanizates, the Payne effect is initiated at a similar microscopic strain of the rubber phase. A weak overshoot of loss modulus appears in compounds containing hydrophilic silica and vulcanizates containing hydrophobic silica. It is suggested that the viscoelastic matrix is highly important for the rheological responses of the filled compounds and vulcanizates.

Shear Modulus of a Fiber Composite with a Transtropic Viscolelastic Matrix and Transtropic Elastic Fiber

When solving the problems of deformation solid mechanics, the inhomogeneous composite material is modeled as homogeneous, with averaged mechanical properties − effective characteristics. The purpose of this paper is to develop a technique for determining the effective shear modulus for a viscoelastic fiber composite with a transtropic matrix and fiber. Their isotropy planes coincide and are perpendicular to the fiber axis. The effective shear modulus is defined as a function of the matrix and fiber mechanical properties and the volume content of each of them in a composite. A unidirectional composite material with a hexagonal fiber stacking scheme and a unit cell consisting of a viscoelastic matrix and elastic fiber is considered. The geometric model of a composite is a combination of two coaxial infinite cylinders: a hollow cylinder, modeling the matrix, and a solid one, modeling the fiber inserted into it. The volume of the hexagonal cell is approximated by the volume of the cylinder. The radius of the cylinder is chosen so that the fiber volume content in the hexagonal cell coincides with the value of this characteristic for the cylindrical cell. To describe the viscoelastic properties of a composite, the ratios of the hereditary Boltzmann-Volterra theory are used. The shear modulus is defined as an integral operator with a difference kernel. Two boundary problems are considered: with regard to the longitudinal shear of a transonic viscoelastic solid cylinder modeling the composite, and the joint longitudinal shear of the hollow and solid cylinders that model the matrix and fiber materials, respectively. It is assumed that the displacements and tangential stresses on the contact surface of the matrix and fiber are continuous. A tangential harmonic load is applied on the outer surface of the cylindrical cell. To solve such problems, the Laplace transform is used. As the matching condition, the equality of displacements on the outer surface of the cylinder is used for the two problems. The application of the proposed technique makes it possible to determine the characteristics of the integral operator describing the shear modulus for a viscoelastic composite material. An instantaneous shear modulus and relaxation core parameters are found as the functions of the known mechanical characteristics of the matrix and fiber. As an example, the characteristics of the shear modulus for a composite material consisting of a rubber matrix and polyamide fiber are determined.

Hydration-induced nano- to micro-scale self-recovery of the tooth enamel of the giant panda

The tooth enamel of vertebrates comprises a hyper-mineralized bioceramic, but is distinguished by an exceptional durability to resist impact and wear throughout the lifetime of organisms; however, enamels exhibit a low resistance to the initiation of large-scale cracks comparable to that of geological minerals based on fracture mechanics. Here we reveal that the tooth enamel, specifically from the giant panda, is capable of developing durability through counteracting the early stage of damage by partially recovering its innate geometry and structure at nano- to micro- length-scales autonomously. Such an attribute results essentially from the unique architecture of tooth enamel, specifically the vertical alignment of nano-scale mineral fibers and micro-scale prisms within a water-responsive organic-rich matrix, and can lead to a decrease in the dimension of indent damage in enamel introduced by indentation. Hydration plays an effective role in promoting the recovery process and improving the indentation fracture toughness of enamel (by ∼73%), at a minor cost of micro-hardness (by ∼5%), as compared to the dehydrated state. The nano-scale mechanisms that are responsible for the recovery deformation, specifically the reorientation and rearrangement of mineral fragments and the inter- and intra-prismatic sliding between constituents that are closely related to the viscoelasticity of organic matrix, are examined and analyzed with respect to the structure of tooth enamel. Our study sheds new light on the strategies underlying Nature’s design of durable ceramics which could be translated into man-made systems in developing high-performance ceramic materials. Statement of SignificanceTooth enamel plays a critical role in the function of teeth by providing a hard surface layer to resist wear/impact throughout the lifetime of organisms; however, such enamel exhibits a remarkably low resistance to the initiation of large-scale cracks, of hundreds of micrometers or more, comparable to that of geological minerals. Here we reveal that tooth enamel, specifically that of the giant panda, is capable of partially recovering its geometry and structure to counteract the early stages of damage at nano- to micro-scale dimensions autonomously. Such an attribute results essentially from the architecture of enamel but is markedly enhanced by hydration. Our work discerns a series of mechanisms that lead to the deformation and recovery of enamel and identifies a unique source of durability in the enamel to accomplish this function. The ingenious design of tooth enamel may inspire the development of new durable ceramic materials in man-made systems.

A three-dimensional multibody tire model for research comfort and handling analysis as a structural framework for a multi-physical integrated system

A tire is an extremely integrated and multi-physical system. From only a mechanical point of view, tires are represented by highly composite multi-layered structures, consisting of a multitude of different materials, synthesized in peculiar rubber matrices, to optimize both the performance and the life cycle. During the tire motion, due to the multi-material thermodynamic interaction within the viscoelastic tire rubber matrix, the dynamic characteristics of a tire may alter considerably. In the following paper, the multibody research comfort and handling tire model is presented. The main purpose of the research comfort and handling tire is to constitute a completely physical carcass infrastructure to correctly transmit the generalized forces and torques from the wheel spindle to the contact patch. The physical model structure is represented by a three-dimensional array of interconnected nodes by means of tension and rotational stiffness and damper elements, attached to the rim modeled as a rigid body. Research comfort and handling tire model purpose is to constitute a structural physical infrastructure for the co-implementation of additional physical modules taking into account the modification of the tire structural properties with temperature, tread viscoelastic compound characteristics, and wear degradation. At the stage, the research comfort and handling tire discrete model has been validated through both static and dynamic shaker test procedures. Static test procedure adopts contact sensitive films for the contact patch estimation at different load and internal pressure conditions, meanwhile the specifically developed sel test regards the tire dynamic characterization purpose at the current stage. The validation of the tire normal interaction in both static and dynamic conditions provided constitutes a necessary development step to the integration of the tangential brush interaction model for studying the handling dynamics and to the analysis of the model response on the uneven surfaces.

Micromechanical Behaviour of Asphalt Concrete Based on X-ray Computed Tomography Images and Random Generation of Heterogeneous Aggregates Skeleton

The main objective of this work is to investigate the influence of the microstructure characteristics on the mechanical behaviour of asphalt concrete. The heterogeneous microstructure of an asphalt concrete is influenced by the aggregate content, shape, orientation and contacts. In previous works, the asphalt concrete is treated as homogeneous material and its heterogeneous microstructures are ignored. While the distribution of its heterogeneous microstructure can strongly influence the intensity of deformation at local scale. Therefore, it is important to create more precisely a micromechanical model containing information on heterogeneous microstructure. A comparison study has been done between the microstructure issues from X-ray computed tomography (CT) and digital models of random aggregate generation. The dynamic modulus of the viscoelastic matrix and elastic properties of aggregates are used as input parameters in the numerical simulations. The obtained results at global scale (complex modulus and phase angle) and at local scale (local strain intensity) of each model are compared. This comparison leads to confirm the feasibility of the proposed heterogeneous random generation of aggregate skeleton at global and local scales. These results provide the basis for an interesting discussion on material design optimization in order to increase the durability of the road pavement materials.

Highly sensitive and stretchable graphene-silicone rubber composites for strain sensing

Flexible strain sensors made by conductive elastomer composites have attracted increasing attention. In this paper, the electromechanical properties of graphene-silicone rubber nanocomposites are studied systematically. First, the conductive nanocomposites composed of graphene and silicone rubber are prepared by means of co-coagulation, which shows a lower percolation threshold with 1.87 wt% (0.94 vol%). Second, the rubber nanocomposites with different graphene contents exhibit a very high strain sensitivity (gauge factor > 143) and a larger strain sensing range (>170%), also, the good recoverability and reproducibility have been found during the loading-unloading cycle. Finally, the analytical model based on the connectivity of the graphene nanosheets and the viscoelasticity of the rubber matrix is developed to describe the electromechanical properties and explain the ‘shoulder peak’ phenomenon, also a typical application example about monitoring the operate state of the rubber seal is given.

Mechanical behaviour of a hydrogel film with embedded voids under the tensile load

The behaviour of alginate gel film in response to the tensile load is analysed in this paper. The bubbles of 0.5 mm diameter were embedded in the film by the fluidic method prior to gelation, thus providing uniform voidage over the entire film. Further, the intrinsic porosity of the gel matrix around the voids was varied by removing water through either evaporation under vacuum, or employing lyophilisation. The Poisson’s ratio and the modulus of elasticity were estimated from direct measurements. The viscoelasticity of the gel matrix was characterized from stress-relaxation measurement. The transient response to tensile loading and the evolution of stress contours were studied through numerical simulation in ANSYS. The ultimate strength was studied for the gel films with embedded voids of different sizes. The numerical simulations were validated by experimental measurements.

Interface/interphase effects on scattering of elastic P- and SV-waves from a circular nanoinclusion embedded in a solid viscoelastic matrix

This study aims to present an analytical investigation of the dynamic effects of the interfacial region on scattering of elastic P- and SV-waves by a circular nanoinclusion. The nanoinclusion is assumed to be surrounded by an interphase region and embedded in a polymer viscoelastic matrix. Wave function expansion method is utilized to solve the Navier wave equation in all three phases (fiber-interphase-matrix) and for the viscoelastic regions, the features of Havriliak-Negami model are used to account for the frequency-dependent material properties. Dynamic Stress Concentration Factor (DSCF) and Scattering Cross Section (SCS) results are obtained for both cases of incident waves. To focus on the interfaces, Gurtin-Murdoch model of surface elasticity is applied in modeling the interfaces. Additionally, effects of interphase inhomogeneity and viscoelasticity on the results are studied. The results indicate that considering the simultaneous effects of nanoscale interface parameter and inhomogeneity and viscoelasticity of the interphase has a considerable impact on the dynamic behavior of the nanoinclusion.

ECIS based wounding and reorganization of cardiomyocytes and fibroblasts in co-cultures

The crosstalk of two major heart cell groups, cardiomyocytes and fibroblasts, relies on direct electromechanical cellular coupling as well as indirect mechanical signal transmission through the surrounding viscoelastic extracellular matrix. Upon injury of cardiac tissue, this communication becomes unbalanced: fibrosis is initiated leading to increased collagen deposition, accompanied by an activation of fibroblasts – the key players of fibrosis. They undergo a reorganization or partial transformation to myofibroblasts during this process, which precedes scar formation within the infarcted heart in vivo. Here, we induce wound formation in an in vitro system as a model for these fibrotic conditions: we assessed the dynamics of wound healing in co-cultures of fibroblasts and myocytes upon targeted wound initiation using Electric Cell Substrate Impedance Sensing (ECIS) under optical control. We discovered distinct wound closure dynamics for mono- and co-cultures of myocytes and fibroblasts and observed a cessation of the contractile behavior for recovering cardiomyocyte cultures. We furthermore identified a change of cellular impedance for recovering fibroblasts and the presence of α-SMA, suggesting a partial transformation into myofibroblasts. This was concomitant with a modulation of connectivity, cell-substrate dynamics and membrane capacitance of all wounded cell cultures. Qualitatively, connexin 43 observation confirmed the ECIS trend found for cell-cell connectivity. Finally, we were able to validate the ECIS based wounding approach against an ECIS based barrier assay – the so-called electric fence. In particular the cell-cell connectivity and thus cell layer integrity dominates the healing dynamics within the two intrinsically different assays.

Differential Quadrature Method for Dynamic Buckling of Graphene Sheet Coupled by a Viscoelastic Medium Using Neperian Frequency Based on Nonlocal Elasticity Theory

In the present study, the dynamic buckling of the graphene sheet coupled by a viscoelastic matrix was studied. In light of the simplicity of Eringen's non-local continuum theory to considering the nanoscale influences, this theory was employed. Equations of motion and boundary conditions were obtained using Mindlin plate theory by taking nonlinear strains of von Karman and Hamilton's principle into account. On the other hand, a viscoelastic matrix was modeled as a three-parameter foundation. Furthermore, the differential quadrature method was applied by which the critical load was obtained. Finally, since there was no research available for the dynamic buckling of a nanoplate, the static buckling was taken into consideration to compare the results and explain some significant and novel findings. One of these results showed that for greater values of the nanoscale parameter, the small scale had further influences on the dynamic buckling.