Nonlinear Viscoelastic Response Research Articles

Temperature and Strain Rate Related Deformation Behavior of UHMWPE Fiber-Reinforced Composites.

As they possess the qualities of high specific strength, high specific modulus, high specific energy absorption, and excellent designability, ultra-high molecular weight polyethylene (UHMWPE) fiber-reinforced composites have gradually replaced traditional materials such as ceramics and steel plates as the main ballistic protection materials. Using an improved test method, the uniaxial tensile tests of UHMWPE fiber-reinforced composites at two strain rates of 10-4 s-1 and 10-2 s-1 and a temperature range from -20 °C to 80 °C are carried out to study the effects of strain rate and temperature on the tensile behavior of UHMWPE fiber-reinforced composites. The experimental results indicate that the tensile responses exhibit nonlinear characteristics and the sensitivity of strain rate and temperature. The yield strength and modulus decrease with increasing temperature and increase with the increase in strain rate. A phenomenological viscoelastic constitutive model composed of a nonlinear spring and a nonlinear Maxwell element is proposed to characterize the temperature and strain rate dependent deformation behavior of UHMWPE fiber-reinforced composites before yielding. The results show that the model can accurately predict the tensile nonlinear viscoelastic responses of UHMWPE fiber-reinforced composites before yielding over a wide temperature range under quasi-static loading.

Modulation of molecular state and air-water interface adsorption behavior of ovalbumin via interference with its surrounding charge distribution

Herein, pH combined with ionic strength was employed to modulate the charge distribution around ovalbumin molecules, and the whole process (from the water phase to the interface) of film formation and stabilization of ovalbumin at the air-water interface was further analyzed. As the pH continuously rose above the isoelectric point, the molecular surface charge increased. More cations, however, reduced the surface charge through the electrostatic shielding effect. The pH and cationic strength were shown to have a remarkable effect on the aggregate size. Intrinsic fluorescence and excitation emission matrix spectroscopy indicated that the migration of tryptophan and tyrosine was accompanied by a change in the backbone structure and rearrangement of the hydrophilic/hydrophobic side chains. Interfacial adsorption kinetic analysis revealed that low pH and ionic strength generally favored the adsorption and stabilization of ovalbumin. Lissajous plots confirmed that stronger intra-interfacial interactions and viscoelastic-like solid interfaces would be generated under the above conditions. Interfacial dilatational rheology analysis illustrated that in most cases, the interfacial film formed by ovalbumin was dominated by an elastic response and produced a nonlinear viscoelastic response under strain. Overall, the combined effect of low pH (pH 5.0) and ionic strength (25 mmol/L and 50 mmol/L) on the surface charge resulted in superior foam capacity (60.00% for pH 5.0 and 50 mmol/L) and stability (97.87% for pH 5.0 and 25 mmol/L). This study detailed the mechanism by which charge influenced the molecular and interfacial properties of ovalbumin, leading the way for the development of protein-based foam systems.

Enzymatic cleaving of entangled DNA rings drives scale-dependent rheological trajectories.

DNA, which naturally occurs in linear, ring, and supercoiled topologies, frequently undergoes enzyme-driven topological conversion and fragmentation in vivo, enabling it to perform a variety of functions within the cell. In vitro, highly concentrated DNA polymers form entanglements that yield viscoelastic properties dependent on the topologies and lengths of the DNA. Enzyme-driven alterations of DNA size and shape therefore offer a means of designing active materials with programmable viscoelastic properties. Here, we incorporate multi-site restriction endonucleases into dense DNA solutions to linearize and fragment circular DNA molecules. We pair optical tweezers microrheology with differential dynamic microscopy and single-molecule tracking to measure the linear and nonlinear viscoelastic response and transport properties of entangled DNA solutions over a wide range of spatiotemporal scales throughout the course of enzymatic digestion. We show that, at short timescales, relative to the relaxation timescales of the polymers, digestion of these 'topologically-active' fluids initially causes an increase in elasticity and relaxation times followed by a gradual decrease. Conversely, for long timescales, linear viscoelastic moduli exhibit signatures of increasing elasticity. DNA diffusion, likewise, becomes increasingly slowed, in direct opposition to the short-time behavior. We hypothesize that this scale-dependent rheology arises from the population of small DNA fragments, which increases as digestion proceeds, driving self-association of larger fragments via depletion interactions, giving rise to slow relaxation modes of clusters of entangled chains, interspersed among shorter unentangled fragments. While these slow modes likely dominate at long times, they are presumably frozen out in the short-time limit, which instead probes the faster relaxation modes of the unentangled population.

Approach for accurately characterizing nonlinear viscoelastic and nonrecoverable properties of asphalt binders based on MSCR test

The multiple stress creep and recovery (MSCR) test has been widely accepted as a more practical method for accessing the rutting performance of asphalt binders than the conventional Superpave rutting factor test. Nevertheless, there still exists a major concern that 9-s recovery time in each cycle may not guarantee a sufficient recovery of the recoverable viscoelastic strain, especially for modified asphalts, and this could result in a potential inaccuracy in characterizing rutting resistance of binders. To effectively separate the recoverable nonlinear viscoelastic (NLVE) and nonrecoverable responses in the MSCR test, this paper presents a new approach that adopts an additional one-cycle low-stress creep and recovery (LSCR) test and the Schapery’s NLVE model in analyzing the MSCR test data. The LSCR test, covering the entire duration of the MSCR test (200 s), can well determine the linear viscoelastic (LVE) recoverable properties that the Schapery’s model requires for NLVE analysis. The results show that with the recoverable and nonrecoverable responses accurately isolated, the proposed approach rigorously redefines the indicators of the percent recovery R and nonrecoverable creep compliance Jnr in the MSCR test, and therefore effectively eliminates the inaccuracy of the original indicators caused by incomplete recovery of the recoverable strain component in each cycle. Also, the developed method exactly characterizes stress dependence and permanent deformation resistance of asphalt binder, thus offering an effective and accurate approach for high-temperature performance evaluation of asphalt binders.

Nonlinear time-dependent mechanical behavior of mammalian collagen fibrils.

The viscoelastic mechanical behavior of collagenous tissues has been studied extensively at the macroscale, yet a thorough quantitative understanding of the time-dependent mechanics of the basic building blocks of tissues, the collagen fibrils, is still missing. In order to address this knowledge gap, stress relaxation and creep tests at various stress (5-35 MPa) and strain (5-20%) levels were performed with individual collagen fibrils (average diameter of fully hydrated fibrils: 253±21 nm) in phosphate buffered saline (PBS). The experimental results showed that the time-dependent mechanical behavior of fully hydrated individual collagen fibrils reconstituted from Type I calf skin collagen, is described by strain-dependent stress relaxation and stress-dependent creep functions in both the heel-toe and the linear regimes of deformation in monotonic stress-strain curves. The adaptive quasilinear viscoelastic (QLV) model, originally developed to capture the nonlinear viscoelastic response of collagenous tissues, provided a very good description of the nonlinear stress relaxation and creep behavior of the collagen fibrils. On the other hand, the nonlinear superposition (NSP) model fitted well the creep but not the stress relaxation data. The time constants and rates extracted from the adaptive QLV and the NSP models, respectively, pointed to a faster rate for stress relaxation than creep. This nonlinear viscoelastic behavior of individual collagen fibrils agrees with prior studies of macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. STATEMENT OF SIGNIFICANCE: Pure stress relaxation and creep experiments were conducted for the first time with fully hydrated individual collagen fibrils. It is shown that collagen nanofibrils have a nonlinear time-dependent behavior which agrees with prior studies on macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. This new insight into the non-linear viscoelastic behavior of the building blocks of mammalian collagenous tissues may serve as the foundation for improved macroscale tissue models that capture the mechanical behavior across length scales.

Effect of Material State and Temperature on Nonlinear Viscoelastic Response: 3D Constitutive Model and Incremental Formulation for Numerical Analysis

Effect of Material State and Temperature on Nonlinear Viscoelastic Response: 3D Constitutive Model and Incremental Formulation for Numerical Analysis

Experimental characterization and phenomenological modeling of nonlinear viscoelasticity, plasticity and damage of continuous carbon fiber-reinforced thermoplastics

The presented work addresses the experimental characterization and phenomenological modeling of the complex rate dependent mechanical response of continuous fiber-reinforced thermoplastics (cFRTP). The theoretical basis is given by the concept of an equilibrium curve of the material which provides a comprehensive framework for separating the mechanical response into a rate dependent overstress and a rate independent equilibrium stress. In long-term creep and relaxation tests, it is shown that relaxation tests provide several advantages over creep tests when determining the equilibrium response. A stepwise loading–unloading relaxation (SR) test is proposed which makes it possible to extract nonlinear viscoelasticity, damage and plasticity present in the material from a single test. The application to cFRTP is exemplified by using the proposed method for the experimental characterization of a continuous carbon fiber-reinforced polycarbonate (CF-PC). Based on the obtained experimental data, a phenomenological material model is developed which describes the mechanical response of a unidirectional ply. The model consists of an overstress branch addressing the nonlinear viscoelastic material response and an equilibrium branch that utilizes a coupled damage-plasticity approach. After calibrating the model using the experimental data, it is shown that the proposed model is able to accurately reproduce the mechanical response of cFRTP.

The micromorphology and large amplitude oscillatory shear behaviors of hydrocarbon gel fuels filled with fumed silica and aluminium sub-microparticles

The gel network structure filled with attractive nanoparticles (NPs) significantly affects the viscoelasticity of the nanocomposites, which is poorly understood and troubles industrial processes. In this work, the nanoparticle gel matrices were prepared with hydrophilic fumed silica (FS), and filled with aluminium sub-microparticles (Al SMPs) loading in the range of 10%− 50%. The effects of particle content and composition on the large amplitude oscillatory shear (LAOS) behaviors are investigated by stress decomposition methods. Meanwhile, the higher harmonics and the Chebyshev harmonics coefficients were obtained. We found that the gels exhibit consistent progressive stiffening with particles filling, companying with plastic transformation and weak strain overshoot (WSO). With aluminum increasing, nonlinear viscoelastic responses gradually weaken in LAOS, severely decreasing the linear viscoelastic (LVE) region, and were validated by strain stiffening index S, T and high-order harmonics. In confocal microscopy (CFM) images, the aluminum particles were fluorescently labeled and found to be adhered together with FS clusters. This article could provide a perspective on understanding the flow mechanism of particulate network structure by combining morphological details and LAOS behaviors.

A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity.

Reactive viscoelasticity is a theoretical framework based on the theory of reactive constrained mixtures that encompasses nonlinear viscoelastic responses. It models a viscoelastic solid as a mixture of strong and weak bonds that maintain the cohesiveness of the molecular constituents of the solid matter. Strong bonds impart the elastic response while weak bonds break and reform into a stress-free state in response to loading. The process of bonds breaking and reforming is modeled as a reaction where loaded bonds are the reactants and bonds reformed into a stress-free state are the products of a reaction. The reaction is triggered by the evolving state of loading. The state of stress in strong bonds is a function of the total strain in the material, whereas the state of stress in weak bonds is based on the state of strain relative to the time that these bonds were reformed. This study introduces two important practical contributions to the reactive nonlinear viscoelasticity framework: (1) normally, the evaluation of the stress tensor involves taking a summation over a continually increasing number of weak bond generations, which is poorly suited for a computational scheme. Therefore, this study presents an effective numerical scheme for evaluating the strain energy density, the Cauchy stress, and spatial elasticity tensors of reactive viscoelastic materials. (2) We provide the conditions for satisfying frame indifference for anisotropic nonlinear viscoelasticity, including for tension-bearing fiber models. Code verifications and model validations against experimental data provide evidence in support of this updated formulation.

Computational Modeling of Polymer Matrix Based Textile Composites.

A simple approach to the multiscale analysis of a plain weave reinforced composite made of basalt fabrics bonded to a high performance epoxy resin L285 Havel is presented. This requires a thorough experimental program to be performed at the level of individual constituents as well as formulation of an efficient and reliable computational scheme. The rate-dependent behavior of the polymer matrix is examined first providing sufficient data needed in the calibration step of the generalized Leonov model, which in turn is adopted in numerical simulations. Missing elastic properties of basalt fibers are derived next using nanoindentation. A series of numerical tests is carried out at the level of yarns to promote the ability of a suitably modified Mori–Tanaka micromechanical model to accurately describe the nonlinear viscoelastic response of unidirectional fibrous composites. The efficiency of the Mori–Tanaka method is then exploited in the formulation of a coupled two scale computational scheme, while at the level of textile ply the finite element computational homogenization is assumed, the two-point averaging format of the Mori–Tanaka method is applied at the level of yarn to serve as a stress updater in place of another finite element model representing the yarn microstructure as typical of FE based multiscale approach. Several numerical simulations are presented to support the proposed modeling methodology.

Response of binder-filler systems into and beyond linear viscoelastic domain: Modeling and healing efficiency

This study is devoted to present insights into linear and nonlinear viscoelastic responses as well as the healing efficiency (HE) of binder-filler systems. To this aim, linear viscoelastic (LV) rheometric results were collected via implementing temperature and frequency sweep measurements, while for probing the nonlinear viscoelastic (NLV) response, large-amplitude oscillatory shear test was executed for various strain maxima. A parallel rheological framework assembled from 2 Yeoh models and hyperbolic-sine flow law, hereinafter abbreviated as 2Y-HS model, was explored to emulate the stress response for LV and NLV behavior of the binder-filler systems. In addition, a strain-dependent healing protocol was developed to test the HE of materials for varying strain-amplitudes. The tested binder-filler systems were blends of a plain binder and two mineral fillers, hydrated lime (HL) and silica fume (SF), added one at a time at different rates based on the best-practice limits. The binder-filler mastics undergone different behaviors into and beyond linear viscoelastic domain (LVD). The 2Y-HS model has efficiently constituted the rheometric results in a manner that elucidates the link between the stresses and strains for both LV and NLV behaviors. The proposed HE protocol showed its efficacy to evaluate the healability of materials at varying rest periods and stretch magnitudes. The damage-mending process at small-amplitude strains tended to improve better, and worst HE was attained as the strain level increases. The richer the asphalt binder with mineral filler, the less the HE is registered; however the binder-HL system is predisposed to heal much more than SF mastics.

Effect of corneal collagen crosslinking on viscoelastic shear properties of the cornea

The cornea is responsible for most of the refractive power in the eye and acts as a protective layer for internal contents of the eye. The cornea requires mechanical strength for maintaining its precise shape and for withstanding external and internal forces. Corneal collagen crosslinking (CXL) is a treatment option to improve corneal mechanical properties. The primary objective of this study was to characterize CXL effects on viscoelastic shear properties of the porcine cornea as a function of compressive strain. For this purpose, corneal buttons were prepared and divided into three groups: control group (n = 5), pseudo-crosslinked group (n = 5), and crosslinked group (n = 5). A rheometer was used to perform dynamics torsional shear experiments on corneal disks at different levels of compressive strain (0%–40%). Specifically, strain sweep experiments and frequency sweep tests were done in order to determine the range of linear viscoelasticity and frequency dependent shear properties, respectively. It was found that the shear properties of all samples were dependent on the shear strain magnitude, loading frequency, and compressive strain. With increasing the applied shear strain, all samples showed a nonlinear viscoelastic response. Furthermore, the shear modulus of samples increased with increasing the frequency of the applied shear strain and/or increasing the compressive strain. Finally, the CXL treatment significantly increased the shear storage and loss moduli when the compressive strain was varied from 0% to 30% (p < 0.05); larger shear moduli were observed at compressive 40% strain but the difference was not significant (P = 0.12).

Modeling nonlinear viscoelastic responses of flexible composites for soft robotics applications

This study examines the deformation of soft composites comprising stiff elastic unidirectional fibers and soft matrix, such as silicone elastomer, rubber and PDMS (Sylgard 184) with potential applications for soft robots. In some soft robotic applications, precise controls of shape reconfigurations are necessary. To design soft robots with high precision motions, it requires a detailed understanding of material responses. In this study, we formulate a constitutive model for the nonlinear viscoelastic response for soft isotropic materials, which is used for the soft matrix in the composites. We examine mechanical deformations of soft composite laminas with two different matrices i.e., Ecoflex 00-30 and PDMS (Sylgard 184), which differ significantly in their extensibility, and different fiber orientations. The initial fiber orientation and matrix extensibility govern the shape reconfigurations of the laminas. The viscoelastic response of the soft matrix causes continuous shape reconfigurations associated with the creep behaviors, which influence the final shapes of the lamina. We also present the design and analyses of soft composite structural components, incorporating the nonlinear viscoelastic responses of the matrix.

Large-deformation constitutive modeling of viscoelastic foams: Application to a closed-cell foam material

Elastomeric foams display a nonlinear viscoelastic mechanical response, which is relevant to impact protection applications. In this paper, we present a methodology for the experimental characterization and constitutive modeling of the rate-dependent, large-deformation mechanical behavior of isotropic, viscoelastic foam materials under quasi-static and moderate loading rates. We conduct large-deformation, homogeneous simple compression/tension experiments under quasi-static and moderate strain rates for a closed-cell elastomeric foam to inform a phenomenological, isotropic constitutive model. The model is based on a multi-mechanism strategy, consisting of a rate-independent, hyperelastic contribution and several rate-dependent, viscoelastic contributions. This structure is motivated by the rheological concept of a hyperelastic spring in parallel with several nonlinear Maxwell elements. The hyperelastic modeling utilizes the invariants of the logarithmic strain and accounts for high compressibility and strong volumetric–distortional coupling. For the rate-dependent mechanisms, we employ the framework of the multiplicative decomposition of the deformation gradient into non-equilibrium elastic and viscous parts. Validation experiments that involve inhomogeneous deformation and deformation-rate fields are conducted, which include spherical indentation, simple-shear-like deformation both without and with a fixed pre-compression, and tension of a specimen with circular holes at different deformation rates. The responses from the validation experiments are compared against model predictions obtained from finite-element-based numerical simulations, demonstrating that the experimental results are accurately captured by the proposed model.

Characterization and prediction of the nonlinear creep behavior of 3D-printed polyurethane acrylate

While the potential application of 3D-printed polymers is remarkable because of the favorable mechanical properties of these materials and their feasibility for producing customized structural components, 3D-printed polymer materials are rarely used in load-bearing structures due to a lack of understanding of the mechanical behaviors of a printed part over a long service life. In this study, the creep behaviors of ultraviolet-curable polyurethane acrylate (UV-PUA) fabricated by using a digital light processing 3D printer was investigated through experimental testing and finite element simulations. Digital image correlation was used to monitor the creep deformations under various thermomechanical conditions. A one-dimensional creep constitutive model was developed to characterize the nonlinear viscoelastic responses of the 3D-printed UV-PUA by decoupling temperature and stress effects. The constitutive model was further implemented in an ABAQUS UMAT subroutine. The simulation results show that the numerical creep model describes well the creep deformations and predicts a reasonable creep life at low temperatures. The sensitivity of the creep behavior of the printed specimens to various types of initial damage was also studied using the developed constitutive model, and the model results were validated by the tensile test results. The results are in good agreement, which verifies the feasibility of numerical method implemented in UMAT for studying the mechanical properties of 3D printed polymers. • Creep behavior of a 3D-printed polymer was monitored using DIC technology. • A nonlinear temperature-dependent viscoelastic model was developed. • 3D constitutive models were developed and implemented in finite element analysis. • The developed model predicts well the creep behavior of the 3D-printed polymer.

Nonlinear viscoelastic rheological behavior of bentonite and sepiolite drilling fluids under large amplitude oscillatory shear

Common models used to describe rheological behavior of drilling fluids are built on pure viscous flow assumption. Full rheological characterization of drilling fluid under this assumption is not feasible since drilling fluids are viscoelastic materials and exhibit both elastic and viscous features. Gel strength development, yield stress value at near zero shear rates, and sag tendency in drilling fluids are the strong function of viscoelastic responses. Linear and nonlinear viscoelastic responses should be measured to provide complete viscoelastic analysis. Two water-based drilling fluids, sepiolite and bentonite drilling muds, each in four states, were subjected to testing using rheometer. Nonlinear viscoelastic parameters and their indications for both fluid systems were characterized for the first time. Large amplitude oscillation sweep tests were conducted as a function of strain and strain rate at four temperatures and frequencies. Stress response was decomposed through Fourier transform into elastic and viscous stress components. Lissajous-Bowditch loops were assessed as rheological fingerprints to detect the initiation of nonlinear region and the nature of nonlinearity. Results revealed that bentonite fluid systems provided stronger gel strength, a more stable network, and high mechanical stability compared to sepiolite fluid samples up to 50 °C. However, the sepiolite fluid systems outperformed at high temperatures (100 and 150 °C). The elastic nonlinear response was determined to be strain/strain rate softening, and the nonlinear viscous response was shear rate thinning at large strain rates for both fluid systems. Contrary to common knowledge found in literature (shear rate thinning), it was revealed that both fluid systems demonstrated shear rate thickening behavior at low to moderate strain rates. This finding is of importance in understanding gel strength development and evaluating sag tendency in drilling operations. • Nonlinear viscoelastic properties of drilling fluids under LAOS were investigated for the first time. • Thermo-structural stability of drilling fluids was evaluated regarding nonlinear viscoelasticity. • Lissajous-Bowditch curves were established to visualize nonlinear viscoelastic characters of drilling fluids. • LAOS parameters quantified nonlinearity based on LAOS protocols for drilling fluids.

Nonlinearity in large amplitude oscillatory shear of drilling fluid: A comparative study on the oil and water base muds behavior

A viscoelastic material exhibits both fluid (viscous) and solid (elastic) like properties simultaneously. The rheological behavior of drilling fluids is customarily measured under the assumption of pure viscous flow, yet they exhibit both viscous and elastic characteristics when subjected to deformation. Some imperative properties of drilling fluids such as gel strength, yield stress, and sag tendency at near-zero shear rate region are categorically under the influence of viscoelastic behavior and have not yet been completely understood due to the lack of appropriate measurement methods. Characterizing the complete rheological profile of material requires measuring linear and nonlinear viscoelastic responses at a wide range of stress/strain levels. The viscoelastic nonlinearity can be characterized under Large Amplitude Oscillatory Shear (LAOS) tests. This study presents a large amplitude oscillatory shear rheology investigation of two water-base (Lignosulfonate and KCl/polymer) and two oil-base (low and high temperature) drilling fluids each in three states; unweighted, weighted, and weighted-contaminated. The viscoelastic nonlinearities of four fluid samples were investigated experimentally as a function of strain amplitude and strain-rate space at different temperatures. The results were described using Lissajous-Bowditch (L-B) plots and local nonlinear viscoelastic dynamic moduli through an oscillatory shear cycle. Structural stability of fluid samples was also studied using the creep-recovery test. The nonlinear viscoelastic behavior of drilling fluids was comprehensively compared and distinguished to understand their nonlinear shear mechanism. As a result of the creep-recovery test at 150 °C, high-temperature oil base mud provided higher thermo-structural stability and zero shear viscosity than those of Lignosulfonate, KCl/polymer, and low-temperature oil-base muds. While the elastic nonlinearity was found to be strain/strain rate softening, the nonlinear viscous character was recorded as shear/shear rate thinning at large strain rates for all drilling fluid systems. Quite a different shear mechanism was detected at low and moderate strain rates. Shear rate thinning was found to be the dominant mechanism for all fluids except Lignosulfonate mud samples that demonstrated shear-thickening behavior at moderate strain rates at 25 °C. At high temperatures (100 °C and 150 °C), shear rate thickening followed by shear rate thinning behavior was governing mechanism under the low and moderate strain rates in all mud samples except KCl/polymer muds. An inverse behavior (shear rate thinning followed by shear rate thickening) was observed through low and moderate strain rates in KCl/polymer muds at 100 °C and 150 °C. Therefore, as revealed from the LAOS test results, shear rate thickening behavior at low to moderate strain rates is in contradiction of the commonly known shear thinning behavior for a drilling fluid undergoing viscous deformation. This finding explains the facts underlying some important properties of drilling fluids such as gel structure formation, hole cleaning ability, and sag tendency.

Nonlinear active stress – Principal strain relation during pulsation of human iPS cell derived cardiomyocyte sheet

Recently, a technique for differentiating human iPS cells into cardiomyocytes has been established and therefore, human iPS cell derived cardiomyocytes (hiPS-CM) can be utilized for the biomechanical study of myocardial tissues. In the present study, a sheet structure of hiPS-CM was fabricated using cell sheet technology and the pulsation behavior was measured using a high speed imaging system. The minimum principal strain was then evaluated using the digital correlation method and the active stress was calculated on the basis of the theoretical model proposed by Guccione et al. It was found that the active stress-strain behavior clearly exhibited a nonlinear viscoelastic response characterized by a hysteresis loop. This nonlinear response was also found to be effectively predicted by the constitutive equation derived from the viscoelastic Maxwell model. A microscopic mechanism involved in the hysteresis loop was also proposed on the basis of the sarcomere structure and mechanical behavior.

The Nonlinear Viscoelastic Response of Suspensions of Vacuous Bubbles in Rubber: I — Gaussian Rubber with Constant Viscosity

The Nonlinear Viscoelastic Response of Suspensions of Vacuous Bubbles in Rubber: I — Gaussian Rubber with Constant Viscosity

A theoretical model for studying the nonlinear viscoelastic response of an active fluid undergoing oscillatory shear

In this work, a nonlinear phenomenological model for neutrally buoyant force-free active suspension of nematodes is proposed and tested. Just a few limited studies were found linked with nonlinear viscoelastic response of the active suspension investigated in this paper. The stress is decomposed through Fourier transform into elastic and viscous stress contributions. The stress response at large strain deviates drastically from the harmonic forcing in a nonlinear regime. In this case, the standard linear viscoelastic moduli cannot describe the nonlinear response of the fluid. Lissajous–Bowditch loops are used as rheological fingerprints to examine the behavior of nonlinear response of the investigated active fluid. The results show time-strain separable nonlinearity, therefore providing a new physically meaningful interpretation. When self-propelled particles interact with each other (i.e., a collective effect), they produce stresses that result in dynamic self-organization at spatial and temporal scales much larger than those of single particles. Complex rheological behavior in active matter depends on the interplay between the external forcing and the circulating flow induced by active agents. The active matter examined in this work is based on the nematode Caenorhabditis elegans motion, whose shape is defined by a dynamic balance between elastic, hydrodynamic, and muscular forces. The orientational instabilities of the active suspension of C. elegans observed in recent experiments carried out by the authors are considered in the present theoretical study. A new time evolution equation for the active stress tensor is proposed in terms of an Oldroyd–Maxwell upper convected material derivative for a dilute active suspension in the absence of thermal or active fluctuations. On the other hand, the Gordon–Schowalter material derivative is used in order to modify the model for the case of non-diluted suspensions. The constitutive equations are nondimensional, and the results are addressed on both linear (small amplitude oscillatory shear) and nonlinear (large amplitude oscillatory shear) regimes. We show results of the viscoelastic moduli as a function of strain in the linear region and in the nonlinear region. The associated Lissajous loop curves illustrating the nonlinear response and the transitions of elastic to viscous behavior of the material at high strain are also presented. The dissipated energy over oscillation cycle is associated with the area enclosed by the closed Lissajous loops curves. Lissajous–Bowditch loops are also computed for the first normal stress differences using our theoretical model, and the results are compared with experimental work that was previously published by the authors.