Generalized Maxwell Model Research Articles

Viscoelastic Behavior and Constitutive Relation of Heavy Crude Oils.

Heavy crude oil exhibits very complex viscoelastic behaviors due to its complex composition of resins, asphaltenes, saturates, and aromatics. It has a great influence on oil production and transportation. In this work, the viscoelastic behaviors of three different heavy crude oils were measured using a rotational rheometer. In conclusion, all of these heavy crude oils display linear viscoelastic behaviors in the experimental range. The loss modulus (E″) of the three crude oils decreased as the experimental temperature increased, and the variation trends of the three crude oils were basically the same. However, the experimental temperature has almost no effect on the storage modulus (E′), which always retained a constant value of 0.4 Pa. Furthermore, the storage modulus (E′) and loss modulus (E″) increase as the angular frequency increases. To describe the physical deformation characteristics of viscoelastic materials, the generalized Maxwell model and the fractional derivative Maxwell model are used to establish the constitutive relation of heavy crude oil. In conclusion, the generalized Maxwell model and the fractional derivative Maxwell model can predict the experimental results very well. All of the square of the correlation coefficient (R2) values are greater than 0.95. However, the number of fitting parameters for the fractional derivative Maxwell model is less than that for the fourth-order generalized Maxwell model which can save the calculating time. Therefore, the fractional derivative Maxwell model is suggested to describe the viscoelastic behavior of heavy crude oil in industrial applications.

Application of the variational EIV approach to linear viscoelastic phases governed by several internal variables - Examples with the generalized Maxwell law

New developments regarding the variational approach originally proposed by Lahellec, N., and Suquet, P., Int. J. Solids Struct. 44, 507–529, 2007, also called EIV approach, are presented in the context of linear viscoelasticity. In previous work (Tressou et al., Eur. J. Mech./A Solids. 68, 104–116, 2018), we have demonstrated the efficiency of this approach as associated to different linear schemes and, as a result, its possible application to various microstructures. In the present paper, our aim is to enlarge the application domain of the EIV model in terms of constituents' viscoelastic laws that may be considered. Initially applied to linear viscoelastic phases described by a single, traceless, internal variable, the original formulation of the EIV model is here generalized to phases described by several internal variables with both spherical and deviatoric parts. The resulting generalized EIV approach is evaluated by comparison of the estimated phase average and effective responses to reference solutions obtained by full-field finite element (FE) simulations for a fiber-reinforced microstructure. Different linear viscoelastic laws with increasing complexity are considered to this aim. At first, a classical Maxwell model is considered for the matrix as in Lahellec and Suquet's original work, but now the internal variable (viscous strain) has a spherical part. Bulk and shear moduli have identical or different characteristic times, the matrix only or both constituents are viscoelastic. Then, the matrix is described by a generalized Maxwell model with two and four internal variables. Different distributions of relaxation times are studied for bulk and shear moduli in order to test the robustness of the model. In every studied situation, the agreement with reference solutions is satisfactory.

Rosin natural terpenes as processing aid for polyhydroxyalkanoate: Thermal, mechanical, and viscoelastic properties

AbstractRosin natural terpene (Dertoline) is compounded with a bacterial thermoplastic polyesters polyhydroxyalkanoate (PHA), specifically here poly(3‐hydroxybutyrate) (PHB), a biodegradable and biocompatible polymer. The compatibility of the blend is examined with differential scanning calorimetry and thermal gravimetry analysis. In the range of concentration of Dertoline, from 5 to 15 wt%, a cold crystallization peak first shifts to slightly higher then lower temperature. Dynamical mechanical analysis and tensile tests confirm that the addition of Dertoline slightly decreases the elastic modulus. The degree of crystallinity again increases then decreases with the content of Dertoline. Polarized light microscopy reveals smaller diameter spherulites for PHB/Dertoline blends and their presence is discussed in relation to tensile tests. Overall, the addition of Dertoline has limited effects on mechanical properties of the blends: the stress at break and the strain at break. In addition, oscillatory rheology at different temperatures provides the activation energies and the parameters of a generalized Maxwell model. The temperature dependence of the rheological properties follows an Arrhenius form. Finally, transient step viscosity measurements are used in order to quantify the PHB thermal degradation.

Equine hoof wall: Structure, properties, and bioinspired designs

The horse hoof wall exhibits exceptional impact resistance and fracture control due to its unique hierarchical structure which contains tubular, lamellar, and gradient configurations. In this study, structural characterization of the hoof wall was performed revealing features previously unknown. Prominent among them are tubule bridges, which are imaged and quantified. The hydration-dependent viscoelasticity of the hoof wall is described by a simplified Maxwell-Weichert model with two characteristic relaxation times corresponding to nanoscale and mesoscale features. Creep and relaxation tests reveal that the specific hydration gradient in the hoof keratin likely leads to reduced internal stresses that arise from spatial stiffness variations. To better understand realistic impact modes for the hoof wall in-vivo, drop tower tests were executed on hoof wall samples. Fractography revealed that the hoof wall's reinforced tubular structure dominates at lower impact energies, while the intertubular lamellae are dominant at higher impact energies. Broken fibers were observed on the surface of the tubules after failure, suggesting that the physically intertwined nature of the tubule reinforcement and intertubular matrix improves the toughness of this natural fiber reinforced composite. The augmented understanding of the structure-mechanical property relationship in dynamic loading led to the design of additively manufactured bioinspired structures, which were evaluated in quasistatic and dynamic loadings. The inclusion of gradient structures and lamellae significantly reduced the damage sustained in drop tower tests, while tubules increased the energy absorption of samples tested in compact tension. The samples most similar to the hoof wall displayed remarkably consistent fracture control properties. Statement of significanceThe horse hoof wall, capable of withstanding large, repeated, dynamic loads, has been touted as a candidate for impact-resistant bioinspiration. However, our understanding of this biological material and its translation into engineered designs is incomplete. In this work, new features of the horse hoof wall are quantified and the hierarchical failure mechanisms of this remarkable material under near-natural loading conditions are uncovered. A model of the hoof wall's viscoelastic response, based on studies of other keratinous materials, was developed. The role of hydration, strain rate, and impact energy on the material's response were elucidated. Finally, multi-material 3D printed designs based on the hoof's meso/microstructure were fabricated and exhibited advantageous energy absorption and fracture control relative to control samples.

A method of automatically obtaining master surfaces of resin matrix composites by time–temperature superposition

AbstractThe time–temperature superposition (TTS) is a data processing method of viscoelastic mechanics, which is realized by translating and superposing the responses at different temperatures to get master curves beyond the test time or frequency. In this study, an automatic shift method is developed to obtain master surfaces of the carbon fiber reinforced plastics and epoxy resin. First step, an interpolation is used to process the dynamic mechanical analysis test data measured by frequency sweep/temperature step or continuous heating‐up method. Second step, the Prony series of the generalized Maxwell model are used to fit the storage and loss modulus at each temperature, which makes the fitting curves have physical meaning and causality. Third step, the automatic shift is achieved by minimizing the sum of squares of the vertical distances between two fitting curves. Last step, master surfaces are created by Prony series fitting and interpolation, and the storage modulus, loss modulus, loss factors, and relaxation modulus at any temperature, frequency or time can be found on the master surfaces. Both storage modulus and loss modulus are considered at same time according to the weight. The effects of different weights are studied.

Effect of asphaltene on the rheological properties of bitumen

In this paper, the rheological behavior of bitumen as a function of asphaltene concentration has been studied. Several bitumen samples having distinctly different amounts of asphaltene were prepared and characterized using differential scanning calorimetry and rheological measurements. The glass transition temperature of bitumen increases with an increase of the asphaltene concentration. This correlation can be used to estimate the asphaltene concentration of bitumen samples using DSC measurements. Small-amplitude oscillatory shear data for the bitumen-derived samples were fit by the generalized Maxwell model with good agreement. A constitutive model is proposed, where the zero-shear complex viscosity of the bitumen sample is a strong function of the asphaltene concentration, and it can be used to predict the asphaltene concentration.

Description of the instantaneous stress drop behavior of a cornstraw-potato residue mixture based on stress relaxation models

Studying the stress relaxation characteristics can provide important process parameters for the granulation and briquetting of biomass materials. In this study, a generalized Maxwell model and fractional model were established to describe and analyze the stress instantaneous drop behavior of a cornstraw-potato residue mixture during the stress relaxation process. Stress relaxation characteristic parameters, e.g., the stress instantaneous drop time, were obtained. Using this information, the influence of the compression speed on the stress instantaneous drop time, stress relaxation time ratio, and other parameters were analyzed. In addition, the regression model of the compression frequency and compression speed was established, which provided a method for determining the appropriate compression frequency of the molding equipment according to the compression speed.

Research on the relationship between time-dependent strains and delamination of plastic packaged devices at polymer/copper interface under thermal-hygro environments

Delamination of polymer/metal interfaces has a destructive effect on plastic packaged devices containing thin layered structures. The physics mechanisms of the delamination inside the microstructure devices are not well understood and difficult to reveal. In order to get a deeper understanding of strain variations at the interface between the viscoelastic polymer and other elastic metal bases under a thermal-hygro environment, the following researches are conducted. Firstly, by combining the generalized Maxwell model and the hygro-mechanical strain equation of bi-layer plate, the equation set for hygro-mechanical strain at the interface of bi-layer plate is established considering the viscoelasticity of epoxy resins. Secondly, two bi-layer plate test pieces are made using elastic copper plates and two different types of viscoelastic epoxy resins (diglycidyl ether of bisphenol F (DGEBF) and Cycloaliphatic epoxy resins), and the normal strains at the interface of the two bi-layer plates under a thermal-hygro environment are measured by strain gauges sealed between the epoxy resin layer and the copper plate. Thirdly, by substituting the thermal strain results into the polynomial equations for thermo-mechanical strain at the bi-layer plate interface, the coefficients of thermal expansion of the two epoxy resins at different temperatures are obtained. Finally, multi-parameter fitting of the interface hygro-mechanical strain curves are drawn through programming in MATLAB software based on the genetic algorithm, and the shear modulus and relaxation time of the two viscoelastic epoxy resins are obtained. This paper’s experiment and calculation results reveal the relationship between time-dependent strain and delamination of plastic packaged devices at polymer/copper interface under a thermal-hygro environment, and provide a valuable reference to improve the reliability of plastic packaged devices.

Viscoelastic behavior of filled silicone elastomers and influence of aging in inert and hermetic environment

This article presents a series of experimental investigations on the viscoelastic behavior of silica-filled and silver-filled silicone rubber on the unaged and aged states. The study of specific aging conditions relative to the electronics industry is proposed in this work, namely aging in a hermetic, initially inert atmosphere, at high temperatures. Viscoelastic properties of the materials are measured through DMA tests. Strain sweep tests are carried for the characterization of unaged materials, and frequency sweeps at ambient temperature are performed to characterize the aging-dependent behavior. As a result of the experimental studies, an aging-dependent generalized Maxwell model is proposed in an attempt to describe the evolution in the behavior of silicones due to aging.

EFFECT OF CONCENTRATION AND TEMPERATURE ON THE RHEOLOGICAL BEHAVIOR OF HYDROXYLETHYL CELLULOSE SOLUTIONS

The knowledge of the rheological properties of polymers makes their use interesting in various fields of applications, such as food industry, cosmetics, enhanced oil recovery or construction materials. Whatever the application, the effect of temperature and concentration on these properties is of great importance. This study covered a wide range of concentrations from 0.2 w/% to 1 w/%, and temperatures from 10 °C to 80 °C. The results obtained provide interesting information regarding the effects of the temperature and concentration of the aqueous solutions of the polymer since they reveal that the rheological properties remained practically unchanged in the temperature range considered. The impacts of shear rate, temperature and concentration on the flow behavior were analyzed. Small-amplitude oscillatory shear measurements were performed, and the results obtained show that the apparent viscosity is strongly influenced by the concentration of the aqueous solution of HEC, exhibiting a marked non-Newtonian shear-thinning behavior at different temperatures. The flow behavior is well described by several rheological models. The effect of temperature on the kinematic viscosity was fitted with the Arrhenius model; the behavior of this model in relation to experimental viscosity values was suitable and the linear fit showed good regression coefficients. The dynamic state was well described with the generalized Maxwell model.

Fragility and the rate of change of the energy landscape topography

We conduct a comparative analysis of the mechanical response of a moderately fragile sodium borate melt, juxtaposing the adiabatic complex modulus measured at GHz frequencies using Brillouin light scattering and the steady-state shear viscosity measured at zero Hz. The two data sets are perfectly compatible with one another by fitting both components of the high-frequency complex modulus using a modified Maxwell-Wiechert model, transforming the loss modulus to viscosity, and extrapolating to zero frequency. This procedure yields an excellent fit to the steady-state viscosity under the condition that the static and relaxational moduli, as well as the activation energy for viscous dissipation are temperature dependent, as modulated by the logistic function, which accounts for the structural changes in the material as it transitions from liquid to glass. Accordingly, fragility of a glass forming liquid can be regarded as a measure of the rate of change with temperature in the energy landscape topography. • Modified Maxwell-Wiechert model to describe viscoelasticity of glass forming liquids. • Brillouin light scattering yields viscosity consistent with steady state viscometry. • Probed at high frequency relaxation peaks are better dispersed on temperature scale. • Non-Arrhenius viscosity behavior due to energy landscape changing with temperature.

Efficient Analytical Model for Time-Dependent Behavior of Layered Functionally Graded Plates with Viscoelastic Interlayers

Layered functionally graded (FG) plate plays an important role in engineering constructions. In this work, an efficient analytical solution is proposed to investigate the time-dependent characters of layered FG plate with viscoelastic interlayers, in which each FG layer is described by the elasticity theory, and the interlayer viscoelasticity is simulated by the generalized Maxwell model. The constitutive equations in the interlayer are simplified, and then, the analytical solutions of stresses and displacements for the layered FG plate are solved by virtue of the efficient recursive matrix method. Some examples are analyzed to investigate the influences of geometric and material characteristics on the long-term behaviors for the FG plate.

An in vitro model of fibrosis using crosslinked native extracellular matrix-derived hydrogels to modulate biomechanics without changing composition

Extracellular matrix (ECM) is a dynamic network of proteins, proteoglycans and glycosaminoglycans, providing structure to the tissue and biochemical and biomechanical instructions to the resident cells. In fibrosis, the composition and the organization of the ECM are altered, and these changes influence cellular behaviour. Biochemical (i. e. protein composition) and biomechanical changes in ECM take place simultaneously in vivo. Investigating these changes individually in vitro to examine their (patho)physiological effects has been difficult. In this study, we generated an in vitro model to reflect the altered mechanics of a fibrotic microenvironment through applying fibre crosslinking via ruthenium/sodium persulfate crosslinking on native lung ECM-derived hydrogels. Crosslinking of the hydrogels without changing the biochemical composition of the ECM resulted in increased stiffness and decreased viscoelastic stress relaxation. The altered stress relaxation behaviour was explained using a generalized Maxwell model. Fibre analysis of the hydrogels showed that crosslinked hydrogels had a higher percentage of matrix with a high density and a shorter average fibre length. Fibroblasts seeded on ruthenium-crosslinked lung ECM-derived hydrogels showed myofibroblastic differentiation with a loss of spindle-like morphology together with greater α-smooth muscle actin (α-SMA) expression, increased nuclear area and circularity without any decrease in the viability, compared with the fibroblasts seeded on the native lung-derived ECM hydrogels. In summary, ruthenium crosslinking of native ECM-derived hydrogels provides an exciting opportunity to alter the biomechanical properties of the ECM-derived hydrogels while maintaining the protein composition of the ECM to study the influence of mechanics during fibrotic lung diseases. Statement of significanceFibrotic lung disease is characterized by changes in composition and excessive deposition of extracellular matrix (ECM). ECM fibre structure also changes due to crosslinking, which results in mechanical changes. Separating the changes in composition and mechanical properties has been difficult to date. In this study, we developed an in vitro model that allows alteration of the mechanical changes alone by applying fibre crosslinking in native lung ECM-derived hydrogels. Characterisations of the crosslinked hydrogels indicated the model mimicked mechanical properties of fibrotic lung tissue and reflected altered fibre organisation. This ECM-based fibrosis model provides a method to preserve the native protein composition while altering the mechanical properties providing an important tool, not only for lung but also other organ fibrosis.

Gear mesh stiffness of polymer-metal spur gear system using generalized Maxwell model

Polymer-metal gears become increasingly interesting to manufacturers and researchers for their advantages to combine the two material's efficiencies. Despite the variety of studies in the literature, there is a significant drop in the number of studies concerning the Gear Mesh Stiffness (GMS). The variation of the GMS by time has a major influence on the dynamic response of transmission. Therefore, this study proposes to take into consideration the viscoelastic behavior of polymer in order to model effectively the GMS of a gear system. The suggested rheological model is the Generalized Maxwell Model (GMM). It is first used to model the viscoelastic behavior of the plastic material of the pinion. Then, Pole Zero Formulation (PZF) is employed to identify parameters of the proposed model. A numerical simulation is then carried out to illustrate the results of this new approach adopted on a pure Nylon 6,6-steel pinions. The evolution of the GMS is illustrated to highlight the viscoelastic behavior's model presented in this paper. Finally, the influence of the change in the temperature is investigated.

Damping optimization of viscoelastic cantilever beams and plates under free vibration

The goal of this work is to significantly enhance the damping of linear viscoelastic structures under free vibration by relying on optimal design. Homogeneous cantilever slender beams and plates satisfying, respectively, the Euler-Bernoulli and Kirchhoff-Love assumptions are considered. A sizing optimization of the beam or plate thickness is proposed, as well as a coupled optimization of the thickness and geometry of the plate applying Hadamard’s boundary variation method. The isotropic linear viscoelastic material is modeled by a classical generalized Maxwell model, well suited for polymers. Gradients of the objective functions are computed by an adjoint approach. Optimization is performed by a projected gradient algorithm and the mechanical models are evaluated by the finite element method. Numerical tests indicate that the optimal designs, as well as their damping properties, strongly depend on the material parameters.

Modified tuned Maxwell–Wiechert model for improving seismic performance of base-isolated structures

Major earthquakes that occurred earlier in this century, including the 2011 Great East Japan Earthquake, caused severe damage to nonstructural components in low-frequency structures; hence, there is a need for novel technology to address the challenges arising from low-frequency ground motions. Because a conventional velocity-dependent damper may perform insufficiently against low-frequency responses, an energy-dissipating device that efficiently dampens low-frequency components must be developed. Rate-independent linear damping (RILD), which is an ideal linear equivalent model for hysteretic damping, can generate higher control forces than conventional velocity-dependent dampers at low frequencies, providing a promising option for the efficient response control of low-frequency structures.Among the known causal RILD models in the literature, the tuned Maxwell–Wiechert (TMW) model offers a viable option for the physical realization of constant loss stiffness. However, a challenge remains when a TMW-model-based device is incorporated into a base-isolated structure: undesired storage stiffness that compromises the flexibility of the isolation layer is introduced.To address this issue, this study proposes methods to modify a TMW model by adding stiffness-adjusting components that are capable of eliminating undesired storage stiffness. The proposed devices include negative stiffness-tuned Maxwell–Wiechert (NSTMW), inerter-tuned Maxwell–Wiechert (ITMW), and inerter-negative stiffness-tuned Maxwell–Wiechert (INSTMW) devices. Numerical analysis of base-isolated structures equipped with these modified TMW devices demonstrated their efficiency in improving the performance of base-isolated structures.

Study on dynamic viscoelastic constitutive model of nonwater reacted polyurethane grouting materials based on DMA

Abstract Nonwater reacted polyurethane grouting materials are new materials developed to make up for the shortcomings of water-reactive materials in emergency rescue. However, its viscoelastic properties and constitutive model under dynamic loads have not been systematically studied. Based on dynamic thermal mechanical analysis (DMA), the dynamic viscoelastic indexes such as storage modulus, loss modulus, and loss factor of nonwater reacted polymer grouting material were obtained, and the frequency spectrum of polymer with different densities were analyzed. In addition, comparing and analyzing the classical viscoelastic constitutive models such as Maxewell model, Kelvin model, and Fractional model, the fourth-order generalized Maxwell model (GMM) was selected to construct the viscoelastic constitutive model of polyurethane grounding materials. Then, the parameters of the viscoelastic constitutive model of polyurethane grounding materials were obtained by using multi-objective shared parameter fitting method, and dynamic viscoelastic constitutive model of nonwater reacted polyurethane grouting materials was established. Furthermore, the viscoelastic constitutive model with different densities was verified by the DMA test. The results show that the dynamic viscoelastic constitutive model of nonwater reacted polyurethane grouting materials in the article can accurately and efficiently describe the dynamic viscoelastic properties of polyurethane grounding materials, which lays a foundation for the dynamic response analysis of polymer structures.

Pulmonary Visceral Pleura Biomaterial: Elastin- and Collagen-Based Extracellular Matrix.

Objective: The goal of the study is to determine the structural characteristics, mechanical properties, cytotoxicity, and biocompatibility of the pulmonary visceral pleura (PVP). Background: Collagen and elastin are the major components of the extracellular matrix. The PVP has an abundance of elastin and collagen that can serve as a potential biomaterial for clinical repair and reconstructions. Methods: The PVP was processed from swine and bovine lungs. Chemical analyses were used to determine collagen and elastin contents in the PVPs. Immunofluorescence microscopy was used to analyze the structure of the PVP. The stress–strain relationships and stress relaxation were determined by using the planar uniaxial test. The cytotoxicity of the PVP was tested in cultured cells. In in vivo evaluations, the PVP was implanted in the sciatic nerve and skin of rats. Results: Collagen and elastin contents are abundant in the PVP with larger proportions of elastin than in the bovine pericardium and porcine small intestinal submucosa. A microstructural analysis revealed that the elastin fibers were distributed throughout the PVP and the collagen was distributed mainly in the mesothelial basal lamina. The incremental moduli in stress–strain curves and relaxation moduli in the Maxwell–Wiechert model of PVP were approximately one-tenth of the bovine pericardium and small intestinal submucosa. The minimal cytotoxicity of the PVP was demonstrated. The axons proliferated in the PVP conduit guidance from proximal to distal sciatic nerves of rats. The neo-skin regenerated under the PVP skin substitute within 4 weeks. Conclusions: The PVP is composed of abundant collagen and elastin. The structural characteristics and mechanical compliance of the PVP render a suitable biological material for repair/reconstruction.

Optimization of a ring-like phononic crystal structure with bonding layers for band gap

In this paper, the band gap (BG) properties of the phononic crystal (PC) involving bonding layers described by the ring-like structure are investigated. Based on the generalized Maxwell model, the effect of the bonding layers on BGs dependence is analyzed. Combing the numerical simulation and physical experiment, BG characteristic of the ring-like PC structure involving bonding layers is proved to be more suitable for the practical application. The effects of several parameters such as the thickness of bonding layers, the height of cuboid scatterer, the height of the elastic beams, and the width of the elastic beams onto BGs are analyzed by numerical simulation, and the last three parameters are demonstrated to be the critical factors for BGs. Based on the response surface method (RSM), three factors and seven levels experiments are designed to determine the relationships between the three key factors and BGs. The optimal BGs of the proposed PC structure involving bonding layers can be opened from 60 Hz to 300 Hz. It is established that the research results can provide possibilities to boost the development and design of PCs involving bonding layers.

Viscoelastic analysis of mussel threads reveals energy dissipative mechanisms.

Mussels use byssal threads to secure themselves to rocks and as shock absorbers during cyclic loading from wave motion. Byssal threads combine high strength and toughness with extensibility of nearly 200%. Researchers attribute tensile properties of byssal threads to their elaborate multi-domain collagenous protein cores. Because the elastic properties have been previously scrutinized, we instead examined byssal thread viscoelastic behaviour, which is essential for withstanding cyclic loading. By targeting protein domains in the collagenous core via chemical treatments, stress relaxation experiments provided insights on domain contributions and were coupled with in situ small-angle X-ray scattering to investigate relaxation-specific molecular reorganizations. Results show that when silk-like domains in the core were disrupted, the stress relaxation of the threads decreased by nearly 50% and lateral molecular spacing also decreased, suggesting that these domains are essential for energy dissipation and assume a compressed molecular rearrangement when disrupted. A generalized Maxwell model was developed to describe the stress relaxation response. The model predicts that maximal damping (energy dissipation) occurs at around 0.1 Hz which closely resembles the wave frequency along the California coast and implies that these materials may be well adapted to the cyclic loading of the ambient conditions.