Nonlinear Viscoelastic Behavior Research Articles

Rheological analysis of network structure of raw natural rubber prepared by different processing techniques

The performance of raw natural rubber (NR) is dominated by its network structure, particular the levels of long chain branching (LCB) and entanglement. Here, three type of raw rubbers were prepared using different processing methods for commercial grade NRs. Linear and nonlinear viscoelastic behaviors, as well as stress relaxation, were analyzed to access their network structures. The third relative harmonic, phase angle, and first to second quarter-period integral ratio of stress curve were utilized as indicators for the nonlinearity of samples. By combining these values with flow activation energy and characteristic times, it can be confirmed that naturally coagulated NR showed higher elasticity than acid-coagulated NR due to high levels of LCB and entanglement, and hot air drying could lead to chain degradation. These findings correlated with molecular weight parameters, gel content and Mooney viscosity results. This research establishes a method for monitoring raw NR quality and predicting its properties.

The effect of starch types on extensional, linear and nonlinear rheological properties of starch cracker dough

Cracker is a popular snack, and their quality depends on the rheological properties of the dough during production. This study focused on the impact of different starch types (tapioca, corn, and potato) used in the same amount (30 g) on the rheology of starch cracker dough. Various rheological tests were conducted to assess the dough's properties. Linear viscoelastic properties were determined using oscillatory frequency and temperature sweep tests, while the nonlinear viscoelastic behavior was characterized through stress relaxation and creep recovery tests. Extensional rheological behavior was also examined. Additionally, the textural and thermal properties of the dough were monitored to understand starch gelatinization and its interactions with other components. In the linear viscoelastic region, no significant differences were found between different dough formulations. However, in the nonlinear viscoelastic region, the potato starch-containing formulation exhibited different viscoelastic and textural properties. Biaxial extensional rheological behaviors showed no significant variations between formulations. The temperature sweep test data from differential scanning calorimetry measurements were consistent with temperature sweep data. In summary, this study provides valuable insights into how different starches influence the rheological behavior of starch cracker dough, considering various degrees of deformation and temperature. These findings have implications for cracker production parameters.

A Constitutive Framework for Modeling of the Visco-Hyperelastic Materials: Application to the Mechanical Behavior of Cylinders Made of the Rate-Dependent Elastomers

In this paper, the formulation of the mechanical behavior of visco-hyperelastic materials is developed in a thermo-dynamically compatible framework. In this viewpoint, the stress power is assumed to be equal to the sum of the reversible (elastic) energy rate stored and the irreversible energy rate dissipated. Based on this assumption and using the second law of thermodynamics, the constitutive modeling framework is obtained for the rate-dependent materials. Inspired by the constitutive law of a Newtonian fluid and also, models of density strain energy of an elastic material, a framework for the dissipative energy rate related to the irreversible part is proposed for viscoelastic materials. In this framework, the reversible energy part is considered a function of the right Cauchy–Green deformation tensor, and the irreversible energy part is considered a function of the same tensor’s rate. To evaluate the proposed model for nonlinear viscoelastic behavior modeling, the results of tests performed on non-compressible materials at different rates are used, and the proposed model provided acceptable results. Finally, the proposed model is implemented to find a closed-form analytical solution for mechanical behavior modeling of the thick-walled cylindrical shells made of visco-hyperelastic materials, also, stress and stability analyses are assessed for these types of cylinders. To achieve this goal, the effect of pre-stretch on the stability of cylinders has been substantially investigated. Furthermore, based on the proposed model, the effect of the parameters such as the wall thickness and behavior of the material used in the cylinder are examined on the stability of open-ended and closed-ended cylinders.

On the Schapery nonlinear viscoelastic model: A review

Among the various models presented so far to describe the nonlinear viscoelastic behavior of materials, the model proposed by Schapery in the 1960s stands out for its wide acceptance and significant contributions to the field. Through a detailed inspection of the main articles presented by Schapery and other related studies, the present paper reviews the Schapery nonlinear viscoelastic model. One-dimensional and three-dimensional formulations of the model for both isotropic and anisotropic materials, along with model accuracy, are discussed. The present article highlights the challenges of material characterization methods, such as creep-recovery testing, stress relaxation testing, and dynamic mechanical analysis. The article also addresses the issues of characterizing the material's behavior under non-recoverable strain and varying temperatures. Finally, the future research needs in this field are outlined, emphasizing the potential for further advancements in our understanding of nonlinear viscoelasticity.

Asphalt binder characterization using waveform-based viscoelastic measures and time-temperature superposition principle under large strains

In the United States, currently peak-to-peak oscillatory shear stress-strain data is used in the asphalt binder characterization protocols. This practice necessitates the measurement, usage, and reporting of only peak responses for material characterization and specification even though a sinusoidal waveform is applied. However, in this paper it is argued that with the proliferation of modified binding systems, it is critical to capture and examine the complete waveform data when subjected to both small and large strains. This approach will help properly differentiating between materials. In this study, four modified binders were tested at small and large strain levels while recording the complete response waveform. The recorded waveform data was then used to examine the linear and nonlinear viscoelastic characteristics of these binders. The orthogonal stress decomposition technique was used to delineate elastic and viscous contributions in the nonlinear regime. This study examined the time-temperature dependency under both linear and nonlinear regimes. The time-temperature shift factors obtained from linear regime were effectively applied in the nonlinear regime. Further, all the tested binders showed strain stiffening and shear thinning behavior under most of the testing conditions. This study provides useful insights about the material behavior under nonlinear regime and can serve as a benchmark for further investigation of nonlinear viscoelastic behavior of asphalt binders.

Nonlinear viscoelastic mechanical behavior and fatigue hysteresis loops modeling of composite laminates

Fatigue constitutive curve is the presentation of mechanical response and damage mechanism of composites. The hysteresis phenomenon in composites is essentially attributed to the viscoelastic properties of the polymer matrix, causing the strain response to lag behind the stress excitation. Combined with the fatigue damage modes of composites, the contributions of elastic, plastic and viscoelastic strains to the cumulative cyclic strain are analyzed to determine the evolution law of the hysteresis loops with cycling. The hysteresis loops and cyclic hysteresis energy models of composites under tensile-tensile fatigue loads are proposed, and the models are verified by the experimental results of four kinds of laminates under several fatigue loads.

Nonlinear viscoelasticity of Melaleuca alternifolia essential oil Pickering emulsion stabilized with cellulose nanofibrils

Pickering emulsions are suitable technological approaches to stabilize the bioactive compounds of essential oils (EOs) with economic interests for the pharmaceutical, cosmetic and food industries using atoxic and renewable stabilizers, such as cellulose nanostructures. The Melaleuca alternifolia essential oil (MaEO) is recognized for its pronounced antimicrobial performance, which has attracted your interest in developing eco-friendly antiseptic products. In this contribution, we report the nonlinear viscoelasticity behavior of MaEO-in-water Pickering emulsions stabilized by cellulose nanofibrils (CNF) using Large Amplitude Oscillatory Shear (LAOS) tests. The rheological characterizations by Fourier Transform (FT) rheology spectroscopy and Lissajous plots enabled the correlation of the viscous and elastic behaviors with the physical processes involving the deformation of the emulsion. Also, the internal structure of the emulsion was elucidated by fluorescence optical microscopy. Several findings relative to the effects of the shear deformation amplitude over the nonlinear viscoelasticity of the emulsified system are reported here, which are essential to the industrial processes used to develop technological products.

Development and Characterization of Heparin-Containing Hydrogel/3D-Printed Scaffold Composites for Craniofacial Reconstruction.

Regeneration of cartilage and bone tissues remains challenging in tissue engineering due to their complex structures, and the need for both mechanical support and delivery of biological repair stimuli. Therefore, the goal of this study was to develop a composite scaffold platform for anatomic chondral and osteochondral repair using heparin-based hydrogels to deliver small molecules within 3D-printed porous scaffolds that provide structure, stiffness, and controlled biologic delivery. We designed a mold-injection system to combine hydrolytically degradable hydrogels and 3D-printed scaffolds that could be employed rapidly (<30min) in operating room settings (~23°C). Micro-CT analysis demonstrated the effectiveness of our injection system through homogeneously distributed hydrogel within the pores of the scaffolds. Hydrogels and composite scaffolds exhibited efficient loading (~94%) of a small positively charged heparin-binding molecule (crystal violet) with sustained release over 14days and showed high viability of encapsulated porcine chondrocytes over 7days. Compression testing demonstrated nonlinear viscoelastic behavior where tangent stiffness decreased with scaffold porosity (porous scaffold tangent stiffness: 70%: 4.9MPa, 80%: 1.5MPa, and 90%: 0.20MPa) but relaxation was not affected. Lower-porosity scaffolds (70%) showed stiffness similar to lower ranges of trabecular bone (4-8MPa) while higher-porosity scaffolds (80% and 90%) showed stiffness similar to auricular cartilage (0.16-2MPa). Ultimately, this rapid composite scaffold fabrication method may be employed in the operating room and utilized to control biologic delivery within load-bearing scaffolds.

Distribution of Mechanical Properties in Poly(ethylene oxide)/silica Nanocomposites via Atomistic Simulations: From the Glassy to the Liquid State.

Polymer nanocomposites exhibit a heterogeneous mechanical behavior that is strongly dependent on the interaction between the polymer matrix and the nanofiller. Here, we provide a detailed investigation of the mechanical response of model polymer nanocomposites under deformation, across a range of temperatures, from the glassy regime to the liquid one, via atomistic molecular dynamics simulations. We study the poly(ethylene oxide) matrix with silica nanoparticles (PEO/SiO2) as a model polymer nanocomposite system with attractive polymer/nanofiller interactions. Probing the properties of polymer chains at the molecular level reveals that the effective mass density of the matrix and interphase regions changes during deformation. This decrease in density is much more pronounced in the glassy state. We focus on factors that govern the mechanical response of PEO/SiO2 systems by investigating the distribution of the (local) mechanical properties, focusing on the polymer/nanofiller interphase and matrix regions. As expected when heating the system, a decrease in Young's modulus is observed, accompanied by an increase in Poisson's ratio. The observed differences regarding the rigidity between the interphase and the matrix region decrease as the temperature rises; at temperatures well above the glass-transition temperature, the rigidity of the interphase approaches the matrix one. To describe the nonlinear viscoelastic behavior of polymer chains, the elastic modulus of the PEO/SiO2 systems is further calculated as a function of the strain for the entire nanocomposite, as well as the interphase and matrix regions. The elastic modulus drops dramatically with increasing strain for both the matrix and the interphase, especially in the small-deformation regime. We also shed light on characteristic structural and dynamic attributes during deformation. Specifically, we examine the rearrangement behavior as well as the segmental and center-of-mass dynamics of polymer chains during deformation by probing the mobility of polymer chains in both axial and radial motions under deformation. The behavior of the polymer motion in the axial direction is dominated by the deformation, particularly at the interphase, whereas a more pronounced effect of the temperature is observed in the radial directions for both the interphase and matrix regions.

Study on the nonlinear viscoelastic behavior of rubber composites filled with silica

Silica-filled rubber composites exhibit nonlinear viscoelastic behavior depending on filler dispersion and matrix interaction. This study investigated the effects of silane treatment on dynamic mechanical properties of precipitated and fumed silica-reinforced polybutadiene rubber composites. The silane coupling agent improved filler dispersion and interfacial adhesion as characterized by microscopy and bound rubber content. Payne effect measurements showed enhanced storage modulus and network stability for silanized composites due to better filler networking. Cyclic tensile loading displayed reduced stress-softening in treated composites attributable to minimized damage formation. Modeling using Kraus and damage mechanics approaches provided quantitative correlations between the microstructure and magnitude of nonlinear response. The results demonstrate that silane treatment optimizes the viscoelastic performance of silica-filled rubber composites.

Fractional cyclic cohesive zone model for time-dependent fatigue behavior of soft adhesives under mode-II loading

Soft adhesives exhibit nonlinear viscoelastic behavior during cyclic loading, suggesting that their cycle-dependent fatigue behavior can be significantly affected by the time-dependent deformation behavior. Soft adhesives are frequently subject to various cyclic conditions in practical applications, presenting potential safety risks. This paper has proposed a fractional cyclic cohesive zone model (CZM) to characterize the time-dependent fatigue behavior of soft adhesives. To capture the nonlinear evolution of fatigue damage under asymmetric stress-controlled cyclic loading, a fatigue damage model that considers the contribution of in-situ stress/strain was incorporated into fractional-order viscoelastic model. The proposed CZM was validated through single-lap shear creep tests at various stress levels and fatigue tests at various stress amplitudes and loading periods. Furthermore, the impacts of stress ratio and peak stress level on fatigue failure under different loading periods were investigated using the proposed CZM. The results indicate that under a short loading period, the failure of the soft adhesives is primarily influenced by cycle-dependent fatigue damage, while under a long loading period, it is primarily affected by time-dependent creep deformation. Overall, this work offers a numerical strategy to describe the fatigue failure of nonlinear viscoelastic soft adhesives and to understand their time-dependent fatigue failure mechanism, with implications for product design and optimization.

A thermo-mechanically coupled constitutive model for semi-crystalline polymers at finite strains: Mechanical and thermal characterization of polyamide 6 blends

In the field of material modeling, thermoplastic polymers are often studied because of their complex material behavior and their prevalence in industry applications due to their low cost and wide range of applications. Nowadays, where reusability becomes more and more important, materials which can undergo reversible thermomechanical deformations are appealing for, e.g., the construction of car body components. To predict such complex forming processes with multiple influencing factors, such as temperature, strain rate or underlying material morphology, model formulations are needed that account for these influences simultaneously and are validated against experimental data. Unfortunately, up to now only a few contributions are available which consider all these phenomena. In addition, the range of process parameters considered is often narrow due to the experimental effort required for testing. This usually results in limited predictive capabilities of the model. To overcome these limitations, in this work, a thermo-mechanically coupled material model is developed that accounts for the underlying morphology in terms of the degree of crystallinity (DOC). The model formulation is derived in a thermodynamically consistent manner, incorporating coupled nonlinear visco-elastic and elasto-plastic material behavior at finite strains. To characterize and further validate the model, mechanical as well as thermal experiments are conducted for polyamide 6 (PA6). Here, a blending strategy of PA6 together with an amorphous co-polymer is introduced during specimen production to achieve a wider range of stable DOCs(approximately 15%). The model formulation is successfully applied to experimental results and its predictions are in good agreement with experimental observations.

Performance Evaluation of Nonlinear Viscoelastic Materials using Finite Element Method

This research paper applies the finite element method as a methodology to evaluate the structural performance of nonlinear viscoelastic solids. A finite element algorithm was built and developed to simulate the mathematical nonlinear viscoelastic material behavior based on incremental constitutive equations. The derived Equation of the incremental constitutive included the complete strain and stress histories. The Schapery’s nonlinear viscoelastic material model was integrated within the displacement-based finite element environment to perform the analysis. A modified Newton-Raphson technique was used to solve the nonlinear part in the resultant equations. In this work, the deviatoric and volumetric strain–stress relations were decoupled, and the hereditary strains were updated at the end of each time increment. It is worth mentioning that the developed algorithm can be effectively employed for all the permissible values of Poisson’s ratio by using a selective integration procedure. The algorithm was tested for a number of applications, and the results were compared with some previously published experimental results. A small percentage error of (1%) was observed comparing the published experimental results. The developed algorithm can be considered a promising numerical tool that overcomes convergence issues, enhancing equilibrium with high-accuracy results.

Fabrication and Characterization of novel high internal phase bigels with high mechanical properties: Phase inversion and personalized edible 3D food printing

In this paper, bigels systems were prepared by using 20 wt% palm stearin (POs) structured soybean oil oleogels and 80 wt% xanthan gum hydrogels in different ratios of polyglycerol polyricinoleate (PGPR). The proportion of PGPR in bigels was changed to explore the phase inversion and stabilization mechanism of bigels by multiple microscopy techniques, and the mechanical properties have been evaluated by the rheology analysis and 3D printability. When the PGPR content was less than 0.4 wt%, bigels presented as the O/W type. As the PGPR content was 1.0 wt% and 1.2 wt%, the bigel presented as the W/O type with a high internal phase, and a high level of droplets dispersed closely within an oil phase. The increase in PGPR content slowed down the nonlinear viscoelastic behavior under large strains. In terms of 3D printing capability, bigels (oleogels containing 20 wt% POs) showed an unsatisfactory 3D printing capability. However, with the increase of POs and PGPR content, more plastic and printable W/O high internal phase bigels were obtained due to the formation of a more stable, homogeneous, and strong ink. In addition, the bigels systems were investigated for the preparation of 3D biscuit printing, and it was found that the K′ value of W/O bigels batter (1511.39) was larger than that of O/W bigels batter (1394.82), showing greater hardness and better 3D printing performance. These findings could facilitate the broadening of bigels systems that could be applied for 3D biscuit printing.

Viscoelasticity of hydrating shotcrete as key to realistic tunnel shell stress assessment with the New Austrian Tunneling Method

The New Austrian Tunneling Method (NATM) essentially rests on observational information concerning displacements measured in selected positions at the inner surface of shotcrete tunnel shells. The combination of these measurements with advanced material and structural mechanics, in the course of so-called hybrid methods, have successfully delivered, for more than 20 years, practically relevant estimations of internal and external forces and corresponding degrees of utilization. The reliability of the latter, however, may crucially depend on the used material model. Based on a recently proposed analytical structural mechanics model [Acta Mech 233, 2989–3019 (2022)], and focusing on the benchmark example of measurement cross section MC1452 of the Sieberg tunnel, driven in the 1990s in Miocene clay marl, the present paper compares the estimations of forces and degrees of utilization arising from differently refined constitutive concepts, namely (i) aging elasticity, (ii) aging linear viscoelasticity, and (iii) aging nonlinear viscoelasticity. It turns out that only the consideration of aging nonlinear viscoelastic material behavior provides access to realistic values for the degree of utilization, being lower than one. Simpler material models would indicate local material failure, which was not observed in situ.

Coupling between viscoelasticity and soft elasticity in main-chain nematic Liquid Crystal Elastomers

Liquid crystal elastomers (LCEs) are a class of smart elastomers exhibiting unusual mechanical behavior, including large energy dissipation and soft elasticity under uniaxial tensile loading. LCEs are composed of liquid crystal molecules, called mesogens, linked by a network of polymer chains. During deformation, the mesogens orient in the direction of the loading, leading to soft elasticity, which is an increase in strain at constant stress. The combination of mesogen rotation and intrinsic polymer viscoelasticity leads to a nonlinear viscoelastic soft elastic behavior. The aim of this paper is to investigate the coupling between the viscoelastic mechanisms and soft elasticity in main chain LCEs. We propose a rheological model in which the mesogen rotation during deformation is represented by a reversible slider while viscoelastic relaxation mechanisms are modeled as series of Maxwell elements coupled or decoupled with mesogen rotation. Fitting this model to experimental data demonstrate that the coupling between polymer chain viscoelasticity and mesogen rotation is partial, i.e. the long-time relaxation mechanisms are coupled and the short-time relaxation mechanisms are decoupled from mesogen rotation. Furthermore, we show that the viscosity of mesogen rotation is not necessary to properly predict the elastic modulus during the soft elasticity but it is needed to properly predict the initiation of the phenomenon.

The damping problem in non-linear viscoelastic frames under varying temperature

A theoretical consideration of the damping problem in frame engineering structures made of functionally graded materials with non-linear viscoelastic behaviour is carried-out. The frames studied are under external mechanical load and varying temperature. In particular, damping in a two-legged frame with supports on different levels is analyzed. The frame is subjected to a cyclic side load with simultaneous variation of the temperature. The material of the frame is functionally graded in the thickness direction. Thus, the material properties change smoothly along the thickness. Equilibrium equations are used for determining the curvature and the neutral axis coordinates in the members of the frame structure. The damping energy density is integrated in the volume of the frame members in order to find-out the damping energy in the whole frame structure. A parametric investigation is performed by using the solution of the damping energy in order to clarify the influence of various factors (the frame geometry, loading, etc.) on the damping phenomenon at different temperatures.

General analysis of the dissipation of strain energy in circular columns

This theoretical paper is concerned with general analysis of the strain energy dissipation in columns of circular cross-section. The columns are under longitudinal displacements that vary continuously with time. The columns exhibit non-linear viscoelastic behavior that is studied by mechanical models constructed by using non-linear springs and dashpots. Besides, the columns are functionally graded along the radius of the cross-sections. A simple expression for the dissipated strain energy in the columns under consideration is derived. The expression holds for columns having portions with different radius of the cross-section. Also, the expression derived is applicable for columns built-up by concentric layers. Results indicating how the dissipated strain energy is influenced by various factors (distribution of material properties, geometry of the columns and loading) are presented. These results are found by using a non-linear viscoelastic model with one spring and one dashpot. A check-up is performed by determining the dissipated strain energy through subtracting the strain energy in the spring of viscoelastic model from the whole strain energy in the column.

Modeling viscoelasticity and cyclic creep of PEEK by parallel rheological framework (PRF)

Although creep is usually regarded as a quasistatic phenomenon, in multiple engineering applications the load is not constant, hence creep under cyclic loading conditions should be considered. The current work presents the theoretical and experimental study on the viscoelasticity and cyclic creep of PEEK (Polyether ether ketone) – the polymer with good chemical and thermal stability. Among other demanding applications, PEEK is used in bearings industry for the fabrication of cages, which main function is to isolate and to guide rolling elements. In this application the polymer cage is subjected to the long-term load alternating in time, meaning that classical creep (under constant load) cannot be presumed. In the current study, the non-linear viscosity is included into the generalized Maxwell model, employing the Eyring equations which postulate that the viscosity coefficient is not constant but is dependent on stress. The model is implemented with the Parallel Rheological Framework (PRF) (the numerical technique recently implemented in the commercial software ABAQUS), used to construct the generalized Maxwell model with hyper-elastic springs and dashpots of non-linear viscosity. Initially, the viscoelastic material parameters are identified from the uniaxial test, and later these parameters are used to simulate the PEEK response under cyclic loading, to predict the time to creep/fatigue failure. Eventually, the numerical predictions are compared to the test results. The comparison indicates that the developed method and its numerical implementation by PRF can be successfully used to model the non-linear viscoelastic behavior of PEEK under uniaxial load. It is also found, that the simulation of cyclic creep can be reasonably performed by using the current material model and PRF.

Viscoelastic constitutive artificial neural networks (vCANNs) – A framework for data-driven anisotropic nonlinear finite viscoelasticity

The constitutive behavior of polymeric materials is often modeled by finite linear viscoelastic (FLV) or quasi-linear viscoelastic (QLV) models. These popular models are simplifications that typically cannot accurately capture the nonlinear viscoelastic behavior of materials. For example, the success of attempts to capture strain (rate)-dependent behavior has been limited so far. To overcome this problem, we introduce viscoelastic Constitutive Artificial Neural Networks (vCANNs), a novel physics-informed machine learning framework for anisotropic nonlinear viscoelasticity at finite strains. vCANNs rely on the concept of generalized Maxwell models enhanced with nonlinear strain (rate)-dependent properties represented by neural networks. The flexibility of vCANNs enables them to automatically identify accurate and sparse constitutive models of a broad range of materials. To test vCANNs, we trained them on stress-strain data from Polyvinyl Butyral, the electro-active polymers VHB 4910 and 4905, and a biological tissue, the rectus abdominis muscle. Different loading conditions were considered, including relaxation tests, cyclic tension-compression tests, and blast loads. We demonstrate that vCANNs can learn to capture the behavior of all these materials accurately and computationally efficiently without human guidance. Our source code is available at https://github.com/ConstitutiveANN/vCANN.