Nonlinear Viscoelasticity Research Articles

On the origin of start-up effects in ply-ply friction for UD fiber-reinforced thermoplastics in melt

Hot press forming is an attractive production technology to fulfil the increasing demand for complex fiber-reinforced thermoplastic parts. Over the years, process simulation tools on press forming have shown to be very helpful in facilitating the design stage for defect free parts production. One of the important deformation mechanisms considered in process simulations is the relative slip of successive plies or ply-ply friction, of which the underlying principles need to be better understood in order to improve the overall predictive simulation quality. In particular the use of steady-state friction values, neglecting the transient response, is questionable as experiments showed that shear stress overshoots can be as high as three times the long-time value. The phenomenon of the overshoot at start-up shear is analyzed. Possible explanations include nonlinear viscoelasticity and a slip relaxation effect giving rise to wall slip, which are discussed using relevant ply-ply friction measurements carried out on a dedicated friction test set-up. Experimental results on UD C/PEEK show that the shear stress build up and subsequent relaxation comply with nonlinear viscoelasticity. However, the long-time shear stress fails to match the matrix material’s viscosity, possibly due to a yield stress. The flow curve corrected for a yield stress resembles the effects of wall slip. A transient model according to these findings will enhance the accuracy of press forming simulation software.

Fiber-reinforced composites: nonlinear elasticity and beyond

A fiber-reinforced material comprised of a soft polymeric matrix reinforced with polymeric filaments is often modeled as an equivalent anisotropic nonlinearly elastic solid. Although the response of a single constituent polymeric material can be modeled by nonlinear thermo-elasticity over a large range of deformations and temperatures, there can be conditions requiring a theory that extends the range of application to account for other features, such as nonlinear viscoelasticity and an evolving microstructure due to a combination of mechanical and nonmechanical factors. In a multi-constituent fiber-reinforced material these effects can be expected to occur with different initial triggering and ongoing potency in the separate polymer matrix and fiber constituents. This paper summarizes a number of constitutive models for fiber-reinforced materials that include these features, discusses the connection of these models to a nonlinearly elastic scaffold, provides a framework for the incorporation of these features into the constitutive theory for an equivalent general simple solid, and shows how certain terms in the mathematical structure can be associated with the matrix constituent while other terms can associated with the fibrous constituent.

Extensional hardening of multimodal, linear PE with high amounts of UHMWPE

Until the advent of the novel Enders catalysts, the nonlinear rheological characterization of polyethylene (PE) blends, containing up to 50 wt. % of ultra-high molecular weight PE (UHMWPE, with weight average molecular weight Mw > 106 g/mol) was unattainable. In this study, by melt blending of a commercially available high-density PE (polymer matrix) and PE-reactor-blends (RBs), multimodal PE blends were prepared, and their nonlinear viscoelastic properties were investigated. The experiments revealed how extraordinarily high amount of UHMWPE content and ultra-broad molecular weight distribution characterized by well separated molecular weight modes influence the nonlinear viscoelasticity. Furthermore, in order to evaluate the strain hardening ability of the multimodal PE, an approach was proposed allowing to objectively analyze and quantify the nonlinear response of the investigated samples. Analyzing the “state diagram” of the extended specimens, which captures the melt behavior and flow instabilities during uniaxial extensional measurements, unveiled that the observed SH of multimodal PE blends, at temperatures notably higher than their melting temperature, is controlled by the stretched chains of the 2nd well separated UHMWPE molecular weight mode. Moreover, it was found that, in order to highly stretch the PE chains, a characteristic strain must be applied.

Compensation of Nonlinear Distortion in Loudspeakers Considering Nonlinear Viscoelasticity of the Suspension

Compensation of Nonlinear Distortion in Loudspeakers Considering Nonlinear Viscoelasticity of the Suspension

Characterization of polyethylene/silica nanocomposites using different rheological analyses

Polyethylene (PE)/silica polymer nanocomposites (PNCs) were investigated mainly using rheological measurements. Various PEs [linear low-density polyethylene (LLDPE), high-density polyethylene (HDPE), and low-density polyethylene (LDPE)] were selected as polymer matrices, and two comparable particulate silicas were utilized as favorable (hydrophobic, R202) or unfavorable (hydrophilic, A90) fillers. Small amplitude oscillatory shear (SAOS), large amplitude oscillatory shear (LAOS), elongational rheometry, tensile tests, and TEM were adopted to characterize PE/silica PNCs. LDPE/silica nanocomposites showed the best filler dispersion in TEM images but were the poorest in terms of rheological property enhancement. Linear viscoelasticity as determined by SAOS testing was discordant with their morphology. However, nonlinear viscoelasticity as determined by FT-rheology in LAOS testing adequately determined dispersion states. Elongational viscosity revealed LDPE/silica PNCs show strain-hardening behavior, which resulted in intense mixing conditions and best compatibilization on LDPE/silica PNCs. To quantify the strain-hardening effect, strain hardening coefficients (SHCs) were calculated for LDPE/silica PNCs and found to decrease with increasing silica concentration. In addition, tensile testing showed mechanical properties deteriorated with silica content.

Fatigue response and damage accumulation law of asphalt binder after nonlinear viscoelastic cyclic shear loads

This study investigated the effects of cyclic nonlinear viscoelastic (NLVE) loads on the fatigue response of asphalt binder, and the damage accumulation law of asphalt binder under NLVE-LVE combined loads. The experimental results reported the difference in the fatigue characteristics of asphalt binder under cyclic NLVE and LVE loads. It was found that NLVE loads nonlinearly reduced the remaining fatigue life of asphalt binder, which demonstrated the inapplicability of the conventional Miner’s rule. In addition, good agreement between the proposed model (Oeser and Zhang (orz) model) and the experimental results indicated the reliability and effectiveness of the established damage accumulation model.

A Nonlinear Viscoelastic Model for the Yielding of Gelled Waxy Crude Oil

We explore some rheological aspects of the yielding of gelled waxy crude oil on the basis of a fractal model for the structural description of the waxy gel and Marrucci’s model for the time evolution of the stress with mixed elastic and viscous effects. With some parameters of the model directly obtained from classic rheometry, and others by fitting the parameters to the experimental data of one shear-rate condition, the flow curves for another shear-rate condition are predicted. Both theoretical curves—the fitting and the predicted ones—share the basic features of the experimental ones. Comparison with results of Maxwell model shows that Marrucci’s model used here leads to much better results, as it incorporates nonlinear viscoelasticity of waxy crude gels in the stress evolution equation. The strain dependence of the elastic modulus also plays a relevant role on the prediction of the model, suggesting a double-network contribution for very small strain values. Due to the inertia of rheometric device, the actual shear rate is often found to depart from the setting one, and modification of shear rate history can be necessary in model validation.

Effect of interaction enhancement on rheological response of polypropylene /polybutadiene blend composites

Enhancement interaction between polybutadiene (PB) nanoparticle and polypropylene (PP) matrix by grafts via hydrogen bonding was verified and characterized by dynamic rheological analysis. The introduction of acrylamide (AM) facilitated PB uniform distribution in PP and strengthened interfacial interaction. The correlated structure based on H-bonding interaction leading to the viscoelastic nonlinearity, which restricted polymer relaxation and exhibited different rheological responses. The formation of correlated structure is an energetically favorable process driven by enthalpy, while the dynamics of construction is controlled by diffusion of the binding groups correspondingly, thus, the reconstruction and recoverability depend on the thermodynamic equilibrium distorted by either the shearing or the temperature. Therefore, the recovery ratio increases from 77.31%, 96.53%, to 98.87%, for the blend with identical composition, when increment of temperature from 180, 200–220 °C, is attributed to relaxation enhancement for both the decrement of local viscosity and the acceleration of diffusion.

Refining rheological model for description of linear and nonlinear viscoelasticity of polymer systems

The article reviews the current mesoscopic modeling of flows for polymer solutions and melts of various structures. It also demonstrates the unified structure of the rheological constitutive relation, up to a certain dissipative function. Linear and nonlinear effects are considered for the simple shear and uniaxial tension of polymer melts based on the modified Vinogradov and Pokrovskii rheological model. The model can describe with adequate accuracy the linear viscoelasticity of fluid polymer systems, as well as transient processes at the shear flow and uniaxial elongation. It was compared with other experimental data for the melt of an industrial polyethylene sample. The nonlinear viscoelastic response of a polymer material was modeled at large periodic deformations. The calculation results were obtained via the Runge-Kutta approach with in-line subprograms of MATLAB IT environment. They were later compared with the experimental data for the solution of polyethylene oxide in dimethyl sulfoxide. The nonlinear behavior of the polymer sample manifested itself in the distortion of the viscoelastic response of the material at sinusoidal oscillations. In this case the shear stresses are no longer the correct harmonics and a "step" appears at the leading edge of the response. Besides, their amplitude is not proportional to the amplitude of the shift. The paper also considers the superposition of the oscillating shear flow on the simple shear. The distortion of the viscoelastic response is observed here though, unlike the high-amplitude periodic deformation, the curvatures of the upper and lower half-waves of the response differ. Since there is still no experimental data for this case, this work expects to encourage the researchers working in the field of nonlinear viscoelastic properties of polymer solutions and melts for further endeavors.

Tendon Extracellular Matrix Assembly, Maintenance and Dysregulation Throughout Life.

In his Lissner Award medal lecture in 2000, Stephen Cowin asked the question: "How is a tissue built?" It is not a new question, but it remains as relevant today as it did when it was asked 20years ago. In fact, research on the organization and development of tissue structure has been a primary focus of tendon and ligament research for over two centuries. The tendon extracellular matrix (ECM) is critical to overall tissue function; it gives the tissue its unique mechanical properties, exhibiting complex non-linear responses, viscoelasticity and flow mechanisms, excellent energy storage and fatigue resistance. This matrix also creates a unique microenvironment for resident cells, allowing cells to maintain their phenotype and translate mechanical and chemical signals into biological responses. Importantly, this architecture is constantly remodeled by local cell populations in response to changing biochemical (systemic and local disease or injury) and mechanical (exercise, disuse, and overuse) stimuli. Here, we review the current understanding of matrix remodeling throughout life, focusing on formation and assembly during the postnatal period, maintenance and homeostasis during adulthood, and changes to homeostasis in natural aging. We also discuss advances in model systems and novel tools for studying collagen and non-collagenous matrix remodeling throughout life, and finally conclude by identifying key questions that have yet to be answered.

Wearable MMG-Plus-One Armband: Evaluation of Normal Force on Mechanomyography (MMG) to Enhance Human-Machine Interfacing.

In this paper, we introduce a new mode of mechanomyography (MMG) signal capture for enhancing the performance of human-machine interfaces (HMIs) through modulation of normal pressure at the sensor location. Utilizing this novel approach, increased MMG signal resolution is enabled by a tunable degree of freedom normal to the sensor-skin contact area. We detail the mechatronic design, experimental validation, and user study of an armband with embedded acoustic sensors demonstrating this capacity. The design is motivated by the nonlinear viscoelasticity of the tissue, which increases with the normal surface pressure. This, in theory, results in higher conductivity of mechanical waves and hypothetically allows to interface with deeper muscle; thus, enhancing the discriminative information context of the signal space. Ten subjects (seven able-bodied and three trans-radial amputees) participated in a study consisting of the classification of hand gestures through MMG while increasing levels of contact force were administered. Four MMG channels were positioned around the forearm and placed over the flexor carpi radialis, brachioradialis, extensor digitorum communis, and flexor carpi ulnaris muscles. A total of 852 spectrotemporal features were extracted (213 features per each channel) and passed through a Neighborhood Component Analysis (NCA) technique to select the most informative neurophysiological subspace of the features for classification. A linear support vector machine (SVM) then classified the intended motion of the user. The results indicate that increasing the normal force level between the MMG sensor and the skin can improve the discriminative power of the classifier, and the corresponding pattern can be user-specific. These results have significant implications enabling embedding MMG sensors in sockets for prosthetic limb control and HMI.

A network model of transient polymers: exploring the micromechanics of nonlinear viscoelasticity.

Dynamic networks contain crosslinks that re-associate after disconnecting, imparting them with viscoelastic properties. While continuum approaches have been developed to analyze their mechanical response, these approaches can only describe their evolution in an average sense, omitting local, stochastic mechanisms that are critical to damage initiation or strain localization. To address these limitations, we introduce a discrete numerical model that mesoscopically coarse-grains the individual constituents of a dynamic network to predict its mechanical and topological evolution. Each constituent consists of a set of flexible chains that are permanently cross-linked at one end and contain reversible binding sites at their free ends. We incorporate nonlinear force-extension of individual chains via a Langevin model, slip-bond dissociation through Eyring's model, and spatiotemporally-dependent bond attachment based on scaling theory. Applying incompressible, uniaxial tension to representative volume elements at a range of constant strain rates and network connectivities, we then compare the mechanical response of these networks to that predicted by the transient network theory. Ultimately, we find that the idealized continuum approach remains suitable for networks with high chain concentrations when deformed at low strain rates, yet the mesoscale model proves necessary for the exploration of localized stochastic events, such as variability of the bond kinetics, or the nucleation of micro-cavities that likely conceive damage and fracture.

Nonlinear viscoelasticity of strain rate type: an overview.

There are some materials in nature that experience deformations that are not elastic. Viscoelastic materials are some of them. We come across many such materials in our daily lives through a number of interesting applications in engineering, material science and medicine. This article concerns itself with modelling of the nonlinear response of a class of viscoelastic solids. In particular, nonlinear viscoelasticity of strain rate type, which can be described by a constitutive relation for the stress function depending not only on the strain but also on the strain rate, is considered. This particular case is not only favourable from a mathematical analysis point of view but also due to experimental observations, knowledge of the strain rate sensitivity of viscoelastic properties is crucial for accurate predictions of the mechanical behaviour of solids in different areas of applications. First, a brief introduction of some basic terminology and preliminaries, including kinematics, material frame-indifference and thermodynamics, is given. Then, considering the governing equations with constitutive relationships between the stress and the strain for the modelling of nonlinear viscoelasticity of strain rate type, the most general model of interest is obtained. Then, the long-term behaviour of solutions is discussed. Finally, some applications of the model are presented.

On the thermodynamic consistency of Quasi-linear viscoelastic models for soft solids

Originating in the field of biomechanics, Fung’s model of quasi-linear viscoelasticity (QLV) is one of the most popular constitutive theories employed to compute the time-dependent relationship between stress and deformation in soft solids. It is one of the simplest models of nonlinear viscoelasticity, based on a time-domain integral formulation. In the present study, we consider the QLV model incorporating a single scalar relaxation function. We provide natural internal variables of state, as well as a consistent expression of the free energy to illustrate the thermodynamic consistency of this version of the QLV model. The thermodynamic formulation highlights striking similarities between QLV and the internal-variable models introduced by Holzapfel and Simo. Finally, the dissipative features of compressible QLV materials are illustrated in simple tension.

Nonlinear viscoelastic properties of human dentin under uniaxial tension

ObjectiveDentin is a viscoelastic tissue that contributes to the load distribution in human teeth and leads to their fracture resistance. Despite previous researches on the time-dependent behavior of dentin, it is not very clear whether the viscoelastic behavior of this tissue is linear or nonlinear, and what viscoelastic constitutive equations mechanically characterize it. Therefore, the aim of this study was to describe the viscoelastic behavior of human dentin and determine the best-fitting viscoelastic model for this tissue. MethodsAfter preparation of human dentin specimens from 50 subjects, tensile stress relaxation tests were performed at 1%, 3%, 5% and 7% strain amplitudes. We first evaluated the viscoelastic linearity of this tissue and then fitted the experimental data using different constitutive models, namely, 2-, 3- and 4-term Prony series for linear viscoelasticity, Fung’s quasilinear viscoelastic model, and also Schapery and modified superposition models for nonlinear viscoelasticity. ResultsDespite an almost linear trend at small strains up to 5%, the relaxation rate generally depended on strain amplitude, indicating some degree of nonlinearity in dentine viscoelasticity. According to the results of data fitting using different models, the modified superposition formulation could best capture the viscoelastic behavior of human dentin. SignificanceIn this study, we have quantitatively examined the viscoelastic behavior of human dentin, using a large number of samples. We have obtained the coefficients of various viscoelastic formulations, which can be utilized in subsequent researches on human dentin assuming linear, quasilinear or nonlinear viscoelasticity for this tissue.

Tailoring composite materials for nonlinear viscoelastic properties using artificial neural networks

Polymer matrix composites exhibit nonlinear viscoelastic behavior over a wide range of temperatures and loading frequencies, which requires an elaborate experimental characterization campaign. Methods are now available to accelerate the characterization process and recover elastic modulus from storage modulus ( E′). However, these methods are limited to the linear viscoelastic region and need to be expanded to nonlinear viscoelastic problems to enable materials design. The present work aims to build a general machine learning based architecture to accelerate the characterization and materials design process for nonlinear viscoelastic materials using the E′ results. To expand outside the linear viscoelastic region, general relations of viscoelasticity are first developed so the master relation of E′ considering nonlinear viscoelasticity can be transformed to time domain relaxation function. The transform starts with building the master relation by optimizing the artificial neural network (ANN) formulation using Kriging model and genetic algorithm. Then the master relation is transformed to a relaxation function, which can be used to predict the stress response with a given strain history and to further extract the elastic modulus. The transform is tested on high density polyethylene matrix syntactic foams and the accuracy is found by comparing the predicted materials properties with those obtained from tensile tests. The good agreements indicate the transform can predict the elastic modulus under a wide range of temperatures and strain rates for any composition of the composite and can be used for material design problems.

Free volume based nonlinear viscoelastic model for polyurea over a wide range of strain rates and temperatures

A series of quasi-static and dynamic uniaxial compression experiments over a wide range of temperatures were conducted on polyurea elastomer. The stress-strain response of polyurea exhibits extreme nonlinearity, temperature and strain-rate sensitivity. How to comprehensively describe these complex behaviors regulated by the unique micro-structure of polyurea is still an open question. In this paper, a nonlinear viscoelastic constitutive model for polyurea is developed. The nonlinear viscoelasticity, entropic and energetic elasticity are taken into account, correlated with the interaction of chain segments, the stretch of molecular chains and covalent bonds from the perspective of molecular structure. The viscoelastic response is formulated by the hereditary integral of relaxation modulus and strain rate with time. The real time is accelerated by shift factor, which depends on the free volume. A new mechanism of shear-induced increase of free volume, which gives rise to the nonlinearity of viscoelasticity, is proposed, and the corresponding rate-dependent evolution equation of fractional free volume is developed. Parameters in the model are determined through the compression experiments and DMA test. Comparison with experimental data, as well as the data from references, verifies the ability of the model to predict the nonlinear stress-strain response of polyurea over a wide range of temperatures and strain rates.

A finite deformation gradient-enhanced damage model for nanoparticle/polymer nanocomposites: An atomistically-informed multiscale approach

To analyze the experimentally observed failure process in nanoparticle/polymer nanocomposites, a variety of factors, including nonlocal characteristics of damage mechanism and nonlinear viscoelasticity, are required to be investigated. This work presents the development and numerical implementation of a finite deformation gradient-enhanced damage model for boehmite nanoparticle (BNP)/epoxy nanocomposites. The parameters identification of the nonlocal constitutive description is realized using a framework based on molecular simulations and experimental tests. In this context, molecular simulations are performed to parameterize the Argon model of viscoelasticity, while damage and nonlocal parameters are determined using experimental data obtained from compact-tension tests. The nonlocal constitutive model integrated into a nonlinear FE analysis is validated by comparing the numerical results of compact-tension tests of BNP/epoxy samples with experimental data. The experimental–numerical validation confirms the predictive capability of the modeling framework. The proposed procedure can be extended to other types of nanoparticle reinforced thermosetting polymers.

A variational multiscale method with linear tetrahedral elements for multiplicative viscoelasticity

We present a computational approach to solve problems in multiplicative nonlinear viscoelasticity using piecewise linear finite elements on triangular and tetrahedral grids, which are very versatile for simulations in complex geometry. Our strategy is based on (1) formulating the equations of mechanics as a mixed first-order system, in which a rate form of the pressure equation is utilized in place of the standard constitutive relationship, and (2) utilizing the variational multiscale approach, in which the stabilization parameter is scaled with the viscous energy dissipation.

Characterization of nonlinear viscoelasticity of magnetorheological grease under large oscillatory shear by using Fourier transform-Chebyshev analysis

Magnetorheological (MR) grease, which is a type of magneto-sensitive smart material, exhibits complex viscoelastic behavior under different magnetic fields. Storage and loss moduli from oscillatory test are commonly used to characterize such field-dependent viscoelastic behavior. However, they are not able to represent the higher harmonic nonlinearity appeared in oscillatory responses under large amplitude oscillatory (LAOS) shear. In this paper, an investigation is conducted on the characterization of the filed-dependent nonlinearity of MR grease under LAOS by utilizing of Fourier transform (FT)-Chebyshev analysis. To capture the higher harmonic nonlinearity for the modeling and analysis, a comprehensive test program has been conducted. Firstly, MR grease with 70% weight percentage of carbonyl iron particles (MRG-70) is prepared and the stress response of MRG-70 under the oscillatory shear from small to large strain amplitudes with different magnetic field are measured. Then the higher harmonics in stress response signal are used to detect the intercycle nonlinearity of MRG-70 and compare with the traditional analysis method of dynamic modulus. Further, the elastic and viscous measures from FT-Chebyshev analysis are obtained to capture the inter-/intracycle nonlinear behaviors, that is, strain stiffening/softening, shear thickening/thinning, of MRG-70 under LAOS. It is found that, in the presence of magnetic fields, the onset of the intercycle nonlinearities of MRG-70 is originated from shear thickening of MR grease. With the further increase of the shear strain, MRG-70 exhibits the nonlinearities with different combinations of strain stiffening/softening and shear thickening/thinning.