Nonlinear Viscoelasticity Research Articles

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.

Effect of Cross-Linking Density on Non-Linear Viscoelasticity of Vulcanized SBR: A MD Simulation and Experimental Study.

In recent years, there has been a growing interest in changes in dynamic mechanical properties of mixed rubber during dynamic shear, yet the influence of vulcanized characteristics on the dynamic shear behavior of vulcanized rubber, particularly the effect of cross-linking density, has received little attention. This study focuses on styrene-butadiene rubber (SBR) and aims to investigate the impact of different cross-linking densities (Dc) on dynamic shear behavior using molecular dynamics (MD) simulations. The results reveal a remarkable Payne effect, where the storage modulus experiences a significant drop when the strain amplitude (γ0) exceeds 0.1, which can be attributed to the fracture of the polymer bond and the decrease in the molecular chain's flexibility. The influence of various Dc values mainly resides at the level of molecular aggregation in the system, where higher Dc values impede molecular chain motion and lead to an increase in the storage modulus of SBR. The MD simulation results are verified through comparisons with existing literature.

A proposed approach for accurate fatigue quantification of the base asphalt binders coupling nonlinear viscoelastic effects in S-VECD theoretical framework

The nonlinear viscoelasticity (NLVE) effects at high loading amplitudes are neglected in the stiffness evolution and fatigue quantification for asphalt binders. This study is to determine the applicability of the simplified viscoelastic continuum damage (S-VECD) model considering NLVE effects to the fatigue test protocols of asphalt binders at high strain levels, and to identify the real damage degradation and fatigue life quantification. An equivalent non-linear complex modulus (|G*|NLVE) of the NLVE-based S-VECD model was proposed and quantified by incremental stress sweep testing. A refined fatigue failure criterion GRNL was proposed in the NLVE model. The effectiveness of NLVE on the released pseudo-strain energy (PSE) and failure criteria was also verified. |G*|NLVE values in NLVE region are lower than |G*|LVE values in LVE region. The linear viscoelasticity (LVE)-based S-VECD model overestimates the damage effectiveness on the stiffness degradation. A significant difference exists between the NLVE and LVE models in the damage characteristic curves of the asphalt binders. The actual damage quantified by the NLVE model is lower than that of the LVE model. For both types of binder, the GRNL parameter remains well linear with the fatigue life (Nf). The linear relationship between the released PSE shrinkage values (ΔΣWrR) and the reduced damage (ΔS) is clear when comparing the LVE and NLVE models. The NLVE model predicted a higher fatigue life for asphalt binders than that predicted by the LVE model. The fatigue life determined by the NLVE model exhibits a linear functionality to that quantified by the LVE model, which further validates the applicability and validity of the NLVE model for the diagnosis of fatigue measurement. In contrast, the NLVE-based S-VECD model predicts the fatigue life of asphalt binders under practical service conditions more closely to the mechanical response under actual traffic loads.

Recent Advances in Tissue-Engineered Cardiac Scaffolds-The Progress and Gap in Mimicking Native Myocardium Mechanical Behaviors.

Heart failure is the leading cause of death in the US and worldwide. Despite modern therapy, challenges remain to rescue the damaged organ that contains cells with a very low proliferation rate after birth. Developments in tissue engineering and regeneration offer new tools to investigate the pathology of cardiac diseases and develop therapeutic strategies for heart failure patients. Tissue -engineered cardiac scaffolds should be designed to provide structural, biochemical, mechanical, and/or electrical properties similar to native myocardium tissues. This review primarily focuses on the mechanical behaviors of cardiac scaffolds and their significance in cardiac research. Specifically, we summarize the recent development of synthetic (including hydrogel) scaffolds that have achieved various types of mechanical behavior-nonlinear elasticity, anisotropy, and viscoelasticity-all of which are characteristic of the myocardium and heart valves. For each type of mechanical behavior, we review the current fabrication methods to enable the biomimetic mechanical behavior, the advantages and limitations of the existing scaffolds, and how the mechanical environment affects biological responses and/or treatment outcomes for cardiac diseases. Lastly, we discuss the remaining challenges in this field and suggestions for future directions to improve our understanding of mechanical control over cardiac function and inspire better regenerative therapies for myocardial restoration.

Constituent-based quasi-linear viscoelasticity: a revised quasi-linear modelling framework to capture nonlinear viscoelasticity in arteries

Arteries exhibit fully nonlinear viscoelastic behaviours (i.e. both elastically and viscously nonlinear). While elastically nonlinear arterial models are well established, effective mathematical descriptions of nonlinear viscoelasticity are lacking. Quasi-linear viscoelasticity (QLV) offers a convenient way to mathematically describe viscoelasticity, but its viscous linearity assumption is unsuitable for whole-wall vascular applications. Conversely, application of fully nonlinear viscoelastic models, involving deformation-dependent viscous parameters, to experimental data is impractical and often reduces to identifying specific solutions for each tested loading condition. The present study aims to address this limitation: By applying QLV theory at the wall constituent rather than at the whole-wall level, the deformation-dependent relative contribution of the constituents allows to capture nonlinear viscoelasticity with a unique set of deformation-independent model parameters. Five murine common carotid arteries were subjected to a protocol of quasi-static and harmonic, pseudo-physiological biaxial loading conditions to characterise their viscoelastic behaviour. The arterial wall was modelled as a constrained mixture of an isotropic elastin matrix and four families of collagen fibres. Constituent-based QLV was implemented by assigning different relaxation functions to collagen- and elastin-borne parts of the wall stress. Nonlinearity in viscoelasticity was assessed via the pressure dependency of the dynamic-to-quasi-static stiffness ratio. The experimentally measured ratio increased with pressure, from 1.03 pm 0.03 (mean pm standard deviation) at 80–40 mmHg to 1.58 pm 0.22 at 160–120 mmHg. Constituent-based QLV captured well this trend by attributing the wall viscosity predominantly to collagen fibres, whose recruitment starts at physiological pressures. In conclusion, constituent-based QLV offers a practical and effective solution to model arterial viscoelasticity.

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.

Extremely early onset of nonlinear viscoelasticity in dynamic shear of ideally monodisperse DNA

AbstractThis work reports that the rheology of ideally monodisperse lambda () phage DNA solutions is extremely sensitive to the applied strain in dynamic oscillatory experiments. DNA exhibits nonlinearity at strains far smaller than what is observed in conventional synthetic polymers. However, it is found that polydisperse calf thymus DNA does not exhibit the extreme strain sensitivity. By mixing samples of monodisperse DNA with the polydisperse calf thymus DNA, we correlate the molecular weight distribution (or polydispersity) to the onset of nonlinear viscoelasticity. We demonstrate that the strain sensitivity weakens as the polydispersity index increases. This is the first work correlating the inception of nonlinear viscoelasticity in entangled polymer system such as lambda DNA solution to the polydispersity of the samples. The experimental data suggests that ideally monodisperse polymer systems are very sensitive to the applied strain and have a very early transition to the nonlinear regime. We conclude that nominally monodisperse synthetic polymers are not sufficiently monodispersed to exhibit the early onset.

Nonlinear Viscoelasticity and Toughening Mechanisms in Nanoclay-PNIPAAm Double Network Hydrogels.

We investigate the mechanical properties of a magnetic temperature-sensitive hydrogel at varying concentrations of covalent and physical cross-linking. The hydrogel consists of covalently cross-linked poly(N-isopropylacrylamide) (PNIPAAm), physically interacting nanoclay particles, and magnetic ferric oxide nanoparticles. The physical nanoclay network exhibits strong viscoplastic behavior, and we find that increasing nanoclay content improves both strength and toughness in the double network materials. We investigate the behavior of the gels using a nonlinear viscoplasticity model with a modified rule of mixtures approach and attribute the observed trends to two factors: (a) the yield-stress behavior of the nanoclay network and (b) load-sharing interactions between the PNIPAAm and the nanoclay. Our findings indicate a strong correlation between the mass ratio of covalent cross-linker used and fractional percolation of the PNIPAAm network.

Biomimetic Design of 3D Fibrous Mesh Reinforced Hydrogel Replicating the Form and Function of the Intervertebral Disc

A Biomimetic Design of the Artificial Intervertebral Disc In article number 2200254 Wei Lei, Mingjie Liu, Yang Zhang, and co-workers fabricate biomimetic prototype of artificial intervertebral disc with nature-mimicking mechanics and structure. The design possesses an angle-ply fiber scaffold with multi-scale structural hierarchy, which exhibits osmotic behaviors, non-linear viscoelasticity and durability, enduring it with a great potential for total cervical disc replacement in future.

Viscoelastic model for analysing the behaviour of adhesive-bonded FRP-to-steel joints in civil engineering applications

Adhesively bonding fibre reinforced polymer (FRP) plates have been a mainstream method for strengthening civil engineering structures. The effectiveness of bonding strengthening is dependent on the performance of the adhesive layer. This study examines the time-temperature dependent viscoelasticity of a typical structural epoxy adhesive and develops a linear viscoelastic material model that can be used for numerical analysis. An accelerated test method involving dynamic mechanical analysis (DMA) and time-temperature superposition principle (TTSP) were used to characterise the structural adhesive. The corresponding limitations of this method were discussed, including decomposition effect, nonlinear viscoelasticity, applicability of TTSP, and further curing of the sample. The numerical study of the long-term behaviour of the single lap-shear FRP-to-steel joint found that a slightly warmer temperature (30 °C for this study) is beneficial for the bonded joint as it can reduce the concentrated shear stress with negligible increase in the shear strain. However, a higher temperature (50 °C for this study) that near the adhesive’s glass transition temperature (Tg) could be detrimental as it can lead to significant shear strain in the adhesive joint within the first year of service life.

Selection of geometry for nonlinear rheology using large amplitude oscillatory shear: Poly (vinyl alcohol) based complex network systems

AbstractOscillatory rheology is a common technique to characterize the linear and nonlinear mechanical response of complex materials. The present work studies two crosslinked systems of poly(vinyl alcohol) (PVA): physically crosslinked PVA‐Borax, and glutaraldehyde (GA) based chemically crosslinked PVA‐hyaluronic acid (HA) gel. Both exhibit nonlinear viscoelasticity with characteristic intracycle mechanisms during large amplitude oscillatory shear (LAOS), owing to H‐bonding (physical) and covalent (chemical) interactions respectively, unlike PVA solutions/vinyl polymer melts. Parallel plate (PP) geometry is commonly utilized for rheology of crosslinked systems due to flexible gaps, and ease to retain exact material shapes. Unlike the widely employed cone and plate (CP) geometry for LAOS analysis, the inherent deformation and flow fields are not uniform in PP, which manifests as qualitative difference in the response of the material within the two geometries. A quantitative dissimilarity in the response of PVA based crosslinked systems is demonstrated in this work. Three approaches for PP correction from literature are explored to obtain a geometry independent response of the systems. Therein, the true stresses are computed from the apparent stresses via torque balance, their harmonics, and harmonic ratios based single‐point correction. The first two are shown to have limited application, owing to their implicit assumption of geometry independence in the linear regime. The third approach is found to be effective upto medium strain amplitudes. We outline these shortcomings, and present guidelines to analyze PP LAOS results for the two PVA systems. The analysis can be generalized for the broader class of complex network systems' nonlinear rheology.

A Modified Constitutive Model for Shape Memory Polymers Based on Nonlinear Thermo-Visco-Hyperelasticity with Application to Multi-Physics Problems

Shape memory polymers (SMPs) as a class of smart material have provided diverse attributes recently used in different applications. Raising the usage of SMPs, especially in more sensitive environments, such as the human body or similar high-risk circumstances, highlights the necessity of more accurate simulations. Suitable constitutive modeling is the foundation of an accurate simulation. Not only should such modeling consider precise details to diminish errors, but also it must provide a robust and powerful procedure to calibrate the material parameters. To achieve these goals, in this paper a modified constitutive model for SMPs based on the concept of internal state variables and rational thermodynamics is proposed in large deformation. Taking its basis from the nonlinear hyperelasticity and viscoelasticity, the model can provide a more accurate prediction of SMPs response. In comparison to other available constitutive models based on viscoelastic approach, the number of material parameters is smaller. Furthermore, performing a new approach for material parameters extraction, two different SMP materials were calibrated. The proposed model’s capability was assessed by comparing the model outputs with experimental results in diverse conditions such as different temperature rates and applied stretch ratios. The user-friendly implementation process of this model in multi-physics software based on the finite element method can be counted as another advantage of the proposed model. Hence, to simulate smart systems containing SMP elements, three multi-physics analyses in various fields and conditions were performed, and the importance of conducting such multi-physics phenomena has been discussed.

Effect of specific surface area on the rheological properties of graphene nanoplatelet/poly(ethylene oxide) composites

The rheological properties of poly(ethylene oxide) containing graphene nanoplatelets (GNPs) having different specific surface areas (SSAs) are studied using steady shear and small amplitude oscillatory shear experiments. A series of GNPs having SSAs ranging from 175 ± 5 to 430 ± 13 m2/g was prepared using a thermomechanical exfoliation process. The complex viscosity, moduli, and yield stress of the composites increase with SSA, whereas electrical and rheological percolation threshold concentrations decrease, suggesting that higher SSAs promote filler network formation. Modeling of small amplitude oscillatory shear data using a two-phase model confirms that hydrodynamic effects dominate at low concentrations below 8 wt. %, where the particles are noninteracting. At higher concentrations, the response is dominated by filler-phase contributions. We demonstrate that the two-phase model parameters can be used to track the exfoliation of graphite into GNPs. Fitting of rheological percolation curves using Utracki and Lyngaae–Jørgensen models at low concentrations (noninteracting regime) resulted in aspect ratios between 19 and 76. At high concentrations (interacting particles), the aspect ratios determined by the Krieger–Daugherty model ranged between 5 and 24 due to aggregation. The highest aspect ratios (defined as the ratio of major dimension to minor dimension) were associated with GNPs that had the highest SSA of 430 m2/g. Strain sweeps revealed that the critical strain for the onset of nonlinear viscoelasticity scaled with SSA above the percolation threshold. The scaling relationships of the critical strain and storage modulus with volume fraction were used to infer the fractal dimensions of filler networks.

MODELING AND RESEARCH OF PROCESSES FOR CREEP COMPLIANCE AND RELAXATION BASED ON FADING MEMORY CONCEPT

Using of rheonomic materials in engineering structures is one of the most important issues in determining strength and durability. The main task of the mechanics of a deformable solid is to simulate the processes of deformation of viscoelastic materials. Currently, there are quite well-developed theories and methods of viscoelasticity that allow to determine and describe the viscoelastic properties of materials. They differ between linear and nonlinear viscoelasticity. In the linear and nonlinear theory of viscoelasticity, such a task is reduced to finding creep and relaxation kernel. Creep and relaxation kernel are interconnected by a known integral relationship that establishes a relationship between stress, strain and time. The work is devoted to modeling of stress relaxation and sttrain of hereditary materials. Stress relaxation is described by a nonlinear integral equation with an Abel’s kernel. New efficient method has been proposed for determining of parameters (α, δ). Bisection method is used for obtaining of parameter α. Algorithm have been developed for calculating of parameters of α and δ.

Characterization of the nonlinear viscoelastic constitutive model of asphalt mixture

Asphalt mixtures are generally considered viscoelastic materials that exhibit time and frequency dependency and have been the subject of numerous studies. However, some studies have shown that the performance of asphalt mixtures changes with the magnitude of stress/strain, which is considered nonlinear viscoelasticity. Concurrently, the accurate establishment of an asphalt mixture constitutive model is the basis of the accurate prediction of the asphalt pavement mechanical response. Hence, the nonlinear viscoelastic constitutive in asphalt mixtures is analyzed and established. First, the uniaxial compressive creep experiment was conducted for three types of asphalt mixtures subjected to 0.1–1.1 MPa. The Schapery, Findley and multiple creep integral models were adopted to characterize the nonlinear viscoelastic performance of asphalt mixtures. The results showed that it was difficult to establish the multiple creep integral model due to its complex kernel function. The processes of establishing the Schapery and Findley models were similar, and the fitting degree of the Schapery model was superior to that of the Findley model. Finally, a Schapery nonlinear viscoelastic model of asphalt mixtures was proposed at 20 and 35 ℃.

Laboratory Evaluation of the Relationship of Asphalt Binder and Asphalt Mastic via a Modified MSCR Test

Asphalt mastic, which consists of an asphalt binder and a mineral filler, provides critical adhesion and viscoelasticity to an asphalt mixture. The rheological response of the asphalt mastic is mainly derived from its asphalt binder. In this study, a simple laboratory test method is proposed to estimate the relationship of asphalt binder and its mastic. Two modified binders (3.5% and 4.0% styrene–butadiene–styrene (SBS) of asphalt binder by mass) were blended with a limestone filler at six different mineral filler contents to produce mastic samples. A modified multiple stress creep-recovery (MSCR) test was conducted on both the asphalt binder and its mastic with the same testing protocols, and the stress conditions and rheological response of asphalt binder in the mastic with linear or nonlinear viscoelasticity were both investigated. The results show that the stress of the asphalt binder in its mastic decreased with increasing filler contents. However, for the linear-viscoelasticity mastic, the decrease rate of the stress began to slow down when the filler content had reached 100% or 120%. For the rheological properties of the asphalt binder in the mastic, the %R of the asphalt binder was improved by adding filler, especially for the nonlinear-viscoelasticity mastic. The asphalt binder of the linear-viscoelasticity asphalt mastic also showed a linear viscoelastic response and a good recovery property. The performance of the asphalt mastic and rheological properties of its asphalt binder were highly related to its filler content.

Adaptive fractional order non-singular terminal sliding mode controller for underwater soft crawling robots with parameter uncertainties and unknown disturbances

Unknown disturbances and nonlinear properties of materials bring challenges to the precise trajectory tracking control of underwater soft robots. An underwater soft crawling robot with high adaptability and mobility in a disturbed underwater environment is proposed. A dynamic model that can characterize asymmetric hysteresis, creep and rate-dependent hysteresis behaviours is presented to solve the problem of electromechanical nonlinear coupling and viscoelasticity affecting the modelling accuracy. Moreover, an adaptive fractional order non-singular terminal sliding mode trajectory tracking controller is proposed to eliminate the influence of underwater uncertain disturbance. The adaptive trajectory tracking controller can achieve fast switching gain and avoid over-tuning, which can effectively improve the accuracy and robustness of the controller. Finally, the stability of the controller is verified according to Lyapunov theory, and the superiority and effectiveness of the control method proposed are proven by numerical simulation and experiment.

Nonlinear viscoelasticity and crystallization behavior of anhydrous milk fat/palm stearin/oleogel blends

The crystallization behavior of anhydrous milk fat (AMF)/palm stearin (POs)/diacetyl tartaric acid ester of mono(di)glycerides (DATEM) oleogel blends was investigated, moreover, the linear and nonlinear rheological behavior of systems was analyzed by small amplitude oscillatory shear (SAOS) and large amplitude oscillatory shear (LAOS). The addition of DATEM oleogels inhibited the growth rate of crystals of blends at 4 °C and reduced the average size of crystalline nanoplatelet. Moreover, the DATEM oleogels promoted the transition of blends to more stable β polymorphism. The nonlinear rheological response of blends was qualitatively analyzed by normalized Lissajous-Bowditch curves. The addition of DATEM oleogels made blends more resistant to large deformations and slowed down viscous losses while reducing the rearrangement behavior of the crystal microstructure under high strain. These findings could open up the possibility of developing low-saturated fat products and further broaden the application of oleogels.

Nonlinear vibrations of earth structures

This article offers a detailed analysis of the current state of plane structure dynamics, addressing the complexities posed by non-homogeneous materials exhibiting nonlinear elastic and viscoelastic properties during real-life operations. The study proposes a comprehensive mathematical model and algorithm to investigate the dynamic behavior of such structures, employing the non-linear hereditary Boltzmann-Volterra theory to describe viscoelastic material properties accurately. Nonlinear oscillatory systems are analyzed using Lagrange equations based on the d’Alembert principle. The problem is approached through a multi-step process. Initially, the linear elastic problem of the structure’s natural oscillations is solved to determine its natural frequencies and modes of oscillations. Subsequently, these eigenmodes are employed as coordinate functions to address forced nonlinear oscillations in viscoelastic non-homogeneous systems. The complexity of the problem necessitates solving a Cauchy problem comprising a system of nonlinear integrodifferential equations. To illustrate the methodology, the study examines the Gissarak earth dam, considering real operational conditions and nonlinear, viscoelastic material properties near resonant modes of vibrations. Utilizing numerical methods, the dynamic behavior of the structure is analyzed, assessing displacements and stress components at different time points under non-stationary kinematic action. Stress concentration regions within the structure are identified for resonant vibrations, allowing the evaluation of its strength. Furthermore, the impact of nonlinear elasticity and viscoelasticity on the structural dynamics is quantified. This research provides valuable insights into the behavior of plane non-homogeneous structures, considering real-world scenarios and material complexities, ultimately contributing to an improved understanding of structural dynamics and facilitating the identification and mitigation of potential structural challenges.

Non-linear response of colloid monolayers at high-frequency probed by ultrasound-driven microbubble dynamics.

High-frequency interfacial rheology of complex interfaces remains challenging yet it is central to the performance of multiphase soft matter products. We propose to use ultrasound-driven bubble dynamics to probe the high-frequency rheology of a colloid monolayer used as model system with controlled interactions and simultaneous monitoring of the microstructure. We hypothesize that by comparing the response of colloid-coated bubbles with that of a bare bubble under identical experimental conditions, it is possible to detect the non-linear response of the monolayer and use it to extract interfacial rheological properties at 104s-1. Using high-speed video-microscopy, the dynamics of colloid-coated bubbles were probed to study the micromechanical response of the monolayer to high-frequency deformation. Protocols analogous to stress-sweep and frequency-sweep were developed to examine the stress-strain relationships. A simple model, motivated by the observed non-linear responses, was developed to estimate the interfacial viscoelastic parameters. The estimated elastic moduli of colloid monolayers at 104s-1 are about an order of magnitude larger than those measured at 1 s-1. The monolayers exhibit non-linear viscoelasticity for strain amplitudes as small as 1%, and strain-softening behaviour. These findings highlight the applicability of acoustic bubbles as high-frequency interfacial probes.