Linear Viscoelastic Material Properties Research Articles

Dynamic mechanical analysis of PA 6 under hydrothermal influences and viscoelastic material modeling

Polyamides serve as matrix material for fiber reinforced composites and are widely applied in many different engineering applications. In this context, they are exposed to various environmental influences ranging from temperature to humidity. Thus, the influence of these environmental conditions on the mechanical behavior and the associated implications on the performance of the material is of utmost importance. In this work, the thermoviscoelastic behavior of polyamide 6 (PA 6) for two equilibrium moisture contents is investigated. To this end, dynamic mechanical analysis tests with and without humidity control of the environmental chamber were performed. In terms of relaxation tests, the experimental results reveal drying effects and increased diffusion activities when the sample’s equilibrium moisture content differs from the ambient humidity level within the testing chamber. Temperature-frequency tests quantify the humidity-induced shift of the glass transition temperature. The linear generalized Maxwell model (GMM) and time-temperature superposition are used to analyze the hydrothermal effects on the linear viscoelastic material properties and the onset of mechanical nonlinearity. Based on these investigations and findings, insight is gained on the humidity influence on the material properties and the limitations of linear thermoviscoelastic modeling. Furthermore, the computational construction of master curves and the parameter identification for a generalized Maxwell model are described in detail.

An improved method to establish continuous relaxation spectrum of asphalt materials

The relaxation spectrum plays a vital role in the study of linear viscoelastic (LVE) properties of asphalt materials; however, the current developed using methods are not accurate enough to characterize the LVE properties of asphalt materials. This paper aims to develop an improved method to determine the continuous relaxation spectrum of asphalt materials. A modified Christensen–Anderson–Marasteanu (CAM) model is first selected as the master curve model of the storage modulus, upon which the master curve model of loss modulus is then established using the numerical form of the exact Kramers-Kronig relation between the storage modulus and loss modulus. According to LVE conversions between the relaxation spectrum and storage modulus, the model of the continuous relaxation spectrum is subsequently derived and finally determined based on the same model parameters of the storage modulus and loss modulus models. This study demonstrates that the relaxation spectrum of both mixtures and binders constructed by the proposed method is compliant with LVE theory and physical causality. The generated relaxation spectrum is verified to be accurate enough to compare the storage modulus and loss modulus values recalculated by the relaxation spectrum and the corresponding values predicted by master curve models. The results also show that the approximate Kramers-Kronig relation between the storage modulus and loss modulus cannot be used to establish the relaxation spectrum of asphalt materials, especially for asphalt binders. In addition, the generated relaxation spectrum was utilized to construct the relaxation modulus of mixtures and to develop the stiffness modulus of binders, respectively. Since the relaxation modulus and creep stiffness are determined from the relaxation spectrum, both are consistent with LVE theory and physical causality.

Revisiting the basis of transient rheological material functions: Insights from recoverable strain measurements

Recent studies have shown that rheological material functions that can be linked to structural measures are defined in terms of the recoverable and unrecoverable strains [for example, Lee et al., Phys. Rev. Lett. 122, 248003 (2019)]. In this study, we explore the consequences of applying these ideas to transient nonlinear rheological tests, using new material functions including an elastic modulus and a flow viscosity defined in terms of the recoverable strain and the rate of acquisition of unrecoverable strain, respectively. These material functions, based on recoverable and unrecoverable strains (rather than total strain), are defined in the same way independent of the test protocol and provide the viscoelastic properties of a material in a clear and succinct way without requiring a priori knowledge of the constitutive model. At short times, we observe that for a self-assembled wormlike micellar solution, the new material functions exhibit a constant (plateau) modulus and a constant (zero-shear) viscosity independent of the applied shear rate, even under conditions that eventually lead to nonlinear responses. This observation quantitatively corroborates the intuitive picture of material deformation that when the material is close to equilibrium, it responds according to its linear viscoelastic material properties for both linear and nonlinear deformations. The fundamental, universal, and unifying nature of these new transient measures are showing promise in explaining a range of phenomena, including the Payne effect for filled polymers and yield stress materials, as well as suggesting new improved dimensionless groups for more accurate flow diagnosis. This work lays the foundation for measuring material functions that are directly related to the material structure and are agnostic of the testing protocol.

Integrating material properties from magnetic resonance elastography into subject-specific computational models for the human brain

Advances in brain imaging and computational methods have facilitated the creation of subject-specific computational brain models that aid researchers in investigating brain trauma using simulated impacts. The emergence of magnetic resonance elastography (MRE) as a non-invasive mechanical neuroimaging tool has enabled in vivo estimation of material properties at low-strain, harmonic loading. An open question in the field has been how this data can be integrated into computational models. The goals of this study were to use a novel MRI dataset acquired in human volunteers to generate models with subject-specific anatomy and material properties, and then to compare simulated brain deformations to subject-specific brain deformation data under non-injurious loading. Models of five subjects were simulated with linear viscoelastic (LVE) material properties estimated directly from MRE data. Model predictions were compared to experimental brain deformation acquired in the same subjects using tagged MRI. Outcomes from the models matched the spatial distribution and magnitude of the measured peak strain components as well as the 95th percentile in-plane peak strains within 0.005 mm/mm and maximum principal strain within 0.012 mm/mm. Sensitivity to material heterogeneity was also investigated. Simulated brain deformations from a model with homogenous brain properties and a model with brain properties discretized with up to ten regions were very similar (a mean absolute difference less than 0.0015 mm/mm in peak strains). Incorporating material properties directly from MRE into a biofidelic subject-specific model is an important step toward future investigations of higher-order model features and simulations under more severe loading conditions. Statement of SignificanceThe study presents a method to calibrate and evaluate subject-specific finite element brain models using a combination of advanced magnetic resonance imaging (MRI) data. The imaging data is acquired in human volunteers and includes anatomical MRI, magnetic resonance elastography (MRE), and tagged MRI to generate subject-specific geometry, calibrate subject-specific material properties, and evaluate simulation response using subject-specific brain deformation. This dataset of MRE and tagged MRI allows for a unique evaluation of whether material properties from MRE can be used to create biofidelic computational models of the human brain. The study develops a calibration procedure to readily calculate linear viscoelastic material parameters from MRE data and then provides a sensitivity study of the effect of mechanical heterogeneity of the brain on simulation response. The calibrated computational models are used to simulate each subject's tagged MRI experiment; the results show good agreement between the simulated and experimental strain fields. The presented study and results will be informative in guiding the calibration of subject-specific computational brain model from experimental MRE data. The processed MRI, MRE, and tagged MRI data are publicly available at https://www.nitrc.org/projects/bbir/.

On the effective behavior of viscoelastic composites in three dimensions

We address the calculation of the effective properties of non-aging linear viscoelastic composite materials. This is done by solving the microscale periodic local problems obtained via the Asymptotic Homogenization Method (AHM) by means of finite element three-dimensional simulations. The work comprises the investigation of the effective creep and relaxation behavior for a variety of fiber and inclusion reinforced structures (e.g. polymeric matrix composites). As starting point, we consider the elastic-viscoelastic correspondence principle and the Laplace-Carson transform. Then, a classical asymptotic homogenization approach for composites with discontinuous material properties and perfect contact at the interface between the constituents is performed. In particular, we reach to the stress jump conditions from local problems and obtain the corresponding interface loads. Furthermore, we solve numerically the local problems in the Laplace-Carson domain, and compute the effective coefficients. Moreover, the inversion to the original temporal space is also carried out. Finally, we compare our results with those obtained from different homogenization approaches, such as the Finite-Volume Direct Averaging Micromechanics (FVDAM) and the Locally Exact Homogenization Theory (LEHT).

Rheo-viscoelastic behaviour of fresh cement-based materials: Cement paste, mortar and concrete

The viscoelasticity of fresh fine cement-based material can be investigated by rheological means using dynamic shear rheometry, hence, the term rheo-viscoelasticity. However, readily available classical rheometers are limited to the study of paste due to the aggregate size associated with mortar and concrete. This study, therefore, sets out to experimentally investigate the rheo-viscoelastic behaviour of cement-based materials containing rheology modifiers, by progressively evaluating the viscoelasticity of cement paste-mortar-concrete. The tests carried out include strain sweep, shear rate sweep, creep and creep recovery, stress relaxation and three interval thixotropy test (3ITT). The results show a trend of improved linear viscoelastic properties of the control fresh cement-based materials due to progressive inclusion of aggregate (increasing volume fraction and size). However, the rheology modifiers widely varied this trend, tending to make it difficult to approximate the rheo-viscoelastic behaviour of mortar and concrete from that of the cement paste as generally suggested in literature. The increase in the coarse volume fraction improved the stability of the cement-based materials microstructure to varying shearing rates. The study suggests that the liquid phase has a role in improving the creep recovery and stress relaxation of the mixes. Furthermore, pseudo-strain hardening was observed for the cement-based materials and flocculation-driven structuration was found to be reduced for the cement paste due to the progressive inclusion of aggregates leaving hydration as the main driving source of concrete’s structuration.

A three-scale asymptotic analysis for ageing linear viscoelastic problems of composites with multiple configurations

• A novel three-scale asymptotic analysis is proposed. • Composite materials with multiple periodic configurations are considered. • Ageing linear viscoelastic problems of composites are investigated. • Numerical results are given in detail to validate the proposed method. A novel three-scale asymptotic expansion is proposed in this work to investigate ageing linear viscoelastic problems of composites with multiple periodic configurations. Here, the composite structures are established by periodical distribution of local cells on microscale and mesoscale. The new three-scale asymptotic expansion formulas based on classical homogenized methods in time domain are constructed at first, and the microscale and mesoscale functions are also derived in detail. Further, two distinct homogenized parameters defined on microscale and mesoscale domains are obtained by upscaling methods, and the newly developed homogenized equations are given on whole structure in time domain. Then, the three-scale strain and stress solutions are constructed by assembling the unit cell solutions and homogenized solutions. Also, the efficient finite element algorithms based on the three-scale asymptotic expansion and homogenized method are brought forward. Finally, some representative numerical examples are evaluated to verify the proposed methods. They show that the three-scale asymptotic expansions developed in this work are effective and valid for predicting the ageing linear viscoelastic properties of the composite materials with multiple configurations.

До задачі розрахунку релаксації напружень у тонкостінних трубчастих елементах із лінійно- в’язкопружних матеріалів

The relaxation of isotropic homogeneous and non-aging linear-viscoelastic materials under conditions of complex stress state is considered. Thin-walled tubular specimens of High Density Polyethylene (HDPE) for creep under a single-axial stretching, with a pure twist and combined load tension and torsion are considered as base experiments, tests. The solution is obtained by generalizing the initial one-dimensional viscoelasticity model to a complex stressed state, constructed using the hypothesis of the proportionality of deviators. The heredity kernels are given by the Rabotnov’s fractional-exponential function. The dependence between the kernels of intensity and volumetric creep is established, which determine the scalar properties of linear viscoelastic materials in the conditions of a complex stressed state in the defining equations of the type of equations of small elastic-plastic deformations, and the kernels of longitudinal and transverse creep defining the hereditary properties of linear-viscoelastic materials under the conditions of the uniaxial tension. The problems of stress relaxation calculation of thin walled tubes under combined tension with torsion have been solved and experimentally approved.

Combined Numerical and Analytical Determination of Poisson’s Ratio for Viscoelastic Isotropic Materials

The Laplace–Carson integral transform method and numerical inversion of the solutions are used to establish the relationship between hereditary kernels that define the scalar properties of isotropic linear viscoelastic materials in combined stress state. The hereditary creep kernel characterizing the behavior of the viscoelastic Poisson’s ratio with time is identified. The calculation of shear creep strains and transverse creep under uniaxial loading with allowance for the time-dependent Poisson’s ratio are experimentally validated.

Mechanics of ultrasound elastography

Ultrasound elastography enables in vivo measurement of the mechanical properties of living soft tissues in a non-destructive and non-invasive manner and has attracted considerable interest for clinical use in recent years. Continuum mechanics plays an essential role in understanding and improving ultrasound-based elastography methods and is the main focus of this review. In particular, the mechanics theories involved in both static and dynamic elastography methods are surveyed. They may help understand the challenges in and opportunities for the practical applications of various ultrasound elastography methods to characterize the linear elastic, viscoelastic, anisotropic elastic and hyperelastic properties of both bulk and thin-walled soft materials, especially the in vivo characterization of biological soft tissues.

Identification of the Hereditary Kernels of Isotropic Linear Viscoelastic Materials in Combined Stress State. 2. Proportional deviators

The relationships between the hereditary and creep kernels are established. The hereditary kernels define the scalar properties of isotropic linear viscoelastic materials in a combined stress state. The creep kernels are obtained in uniaxial-tension and pure-torsion tests. The constitutive equations are chosen so as to meet the hypothesis of proportional deviators. The problems of analyzing the creep deformation and stress relaxation of thin-walled tubular specimens under combined tension and torsion are solved and tested experimentally

Linear and nonlinear viscoelastic and viscoplastic analysis of asphalt binders with warm mix asphalt additives

ABSTRACTWarm-Mix Asphalt (WMA) is a widely used product, which proved a contribution to the reduction in asphalt mixing and compaction temperatures. This reduction leads to lower fuel consumption and smoke emission in asphalt plants. Most of the characterisation of binders used in WMA has focused in the past on measuring linear viscoelastic properties and associated Superpave parameters. Several studies have shown that the average stresses and strains of the asphalt mixture remain mostly within the linear viscoelastic response. However, localised strains in the binder phase of the mixture could reach values high enough to induce nonlinear viscoelastic and viscoplastic deformations. Therefore, this study focuses on an experimental and analytical evaluation of linear, nonlinear viscoelastic and viscoplastic responses of selected binders modified for use in WMA. The first part of the paper analyses the linear viscoelastic material properties and their ability to evaluate permanent deformation resistance. Then, the non-recoverable creep compliance parameter obtained from the Multiple Stress Creep Recovery (MSCR) test is analysed to assess the nonlinear response and permanent deformation of asphalt binders. The paper utilises a nonlinear plasto-viscoelastic (NPVE) approach to assess and quantify the nonlinear plasto-viscoelastic response of binders by separating the recoverable and irrecoverable strains measured in the MSCR test. Two WMA additives were included in this study by mixing them with polymer-modified and unmodified asphalt binders. Analysis of results showed that the NPVE approach captured a higher percentage of recovery than the NLVE approach. However, binder’s performance evaluation and ranking did not change by adopting the NPVE approach. The nonlinear viscoelastic parameters provided insight on the behaviour of asphalt binders mixed with WMA additives during loading cycles. Sasobit showed higher influence than Advera on binders in resisting permanent deformation by increasing the recoverable strain during the unloading phase.

Broadband ultrasonic spectroscopy for the characterization of viscoelastic materials

In this study, non-destructive experimental method based on acoustic through transmission technique along with broadband spectroscopy is proposed in order to determine the linear viscoelastic material properties in 20–400kHz range. Material properties such as phase velocity and attenuation coefficient of longitudinal and shear waves are measured. Diffraction correction developed for focused transducers is used to eliminate the spreading error due to the spherical wave generated by the hydrophone which is used as a transmitter. Method is validated on polymethyl methacrylate (PMMA). Both longitudinal wave velocity, shear wave velocity and attenuation coefficient of longitudinal wave of PMMA are in agreement with the previously reported values which are given in the literature. Attenuation coefficient of shear wave in PMMA is measured successfully and in agreement with the theoretical predictions. Longitudinal wave velocity and corresponding attenuation coefficient of gelatine gel are also measured.

Seven-Parameter Linear Viscoelastic Model Applied to Acoustical Damping Materials

In this paper, linear viscoelastic rheological properties of acoustical damping materials are predicted. A rheological model, based on a mechanical element approach, is presented. It consists of a combination of two springs, two parabolic elements, and one dashpot (2S2P1D). This model is applied to different acoustical damping materials. Its specificity comes from the fact that elements might be linked to structural and physical features. Parameters might be experimentally determined by tests. Application of the 2S2P1D linear viscoelastic model can adequately predict the behavior of acoustical damping materials with good accuracy. If the material verifies the time–temperature superposition principle (TTSP), the proposed model can predict the behavior on a wide frequency range, even with a small number of available data.

Effective properties of linear viscoelastic microcracked materials: Application of Maxwell homogenization scheme

The present paper focuses on the effect of microcracks on the overall properties of viscoelastic materials. For this goal we extend Maxwell homogenization scheme to the case of viscoelasticity and derive explicit formulas for components of the anisotropic creep operator in dependence on scatter parameter characterizing orientation distribution of cracks. Microcracks can have any orientation distribution with randomly oriented and strictly parallel being the limiting cases. Viscoelastic behavior is described using fraction-exponential operators. The results are illustrated on example of microckracked polymethylmethacrylate (PMMA).

The Material Anisotropy Influence on Modelling of Rutting Test with Application of Linear Viscoelasticity Constitutive Equations

In the paper a general approach to modelling of anisotropic linear viscoelastic material properties is presented. Rychlewski's (1983) spectral decomposition theorem is used and one dimensional relaxation functions of linear viscoelasticity model is adopted to eigenvalues of stiffness tensor and named Kelvin relaxation functions. Proposed model was implemented in the FEM system Abaqus on the example of transversely isotropic and isotropic material. On the basis of experimental data available in literature, models were calibrated and verified. Constitutive relations were used in the complex boundary value problem modelling standard rutting test used in road sector to assess the resistance of asphalt mixtures to rutting.

A micromechanical procedure for viscoelastic characterization of the axons and ECM of the brainstem

In this study, the optimal viscoelastic material parameters of axon and extracellular matrix (ECM) in porcine brain white matter were identified using a genetic algorithm (GA) optimization procedure. The procedure was combined with micromechanical finite element analysis (FEA) of brain tissue and experimental stress relaxation tests on brainstem specimens to find the optimal material coefficients of axon and ECM. The stress relaxation tests were performed in tension on 10 brainstem specimens at 3% strain level. The axonal volume fraction in brainstem was measured from the Scanning Electron Microscopy images of the brain tissue. A square periodic volume element was selected to represent the microscale homogenized brainstem tissue. Periodic boundary conditions were applied on the square volume element to mimics the repetitive nature of the volume element. Linear viscoelastic material properties were assumed for the brain tissue constituents under small deformation. The constitutive behavior was expressed in terms of Prony series. The GA procedure searched for the optimal material parameters by fitting the time-dependent tissue stresses of brain tissue FEA to the stresses of relaxation tests under the same loading conditions. The optimization procedure converged after 60 iterations. The initial elastic modulus of axon was found to be 12.86kPa, three times larger than that of ECM. The long-term elastic modulus of axon was 3.7kPa, while for ECM this value was 1.03kPa. The concordance correlation coefficient between FEA estimated elastic modulus of brainstem tissue using the optimal material properties and the experimental elastic modulus of brainstem specimens was 0.952, showing a strong agreement. The optimal material properties of brain tissue constituents can find applications in micromechanical analysis of brain tissue to gain insight into diffuse axonal injures (DAIs).

Why Is CA3 More Vulnerable Than CA1 in Experimental Models of Controlled Cortical Impact-Induced Brain Injury?

One interesting finding of controlled cortical impact (CCI) experiments is that the CA3 region of the hippocampus, which is positioned further from the impact than the CA1 region, is reported as being more injured. The current literature has suggested a positive correlation between brain tissue stretch and neuronal cell loss. However, it is counterintuitive to assume that CA3 is stretched more during CCI injury. Recent mechanical studies of the brain have reported on a level of spatial heterogeneity not previously appreciated-the finding that CA1 was significantly stiffer than all other regions tested and that CA3 was one of the most compliant. We hypothesized that mechanical heterogeneity of anatomical structures could underlie the proposed heterogeneous mechanical response and hence the pattern of cell death. As such, we developed a three-dimensional finite element (FE) rat brain model representing detailed hippocampal structures and simulated various CCI experiments. Four groups of material properties based on recent experiments were tested. In group 1, hyperelastic material properties were assigned to various hippocampal structures, with CA3 more compliant than CA1. In group 2, linear viscoelastic material properties were assigned to hippocampal structures, with CA3 more compliant than CA1. In group 3, the hippocampus was represented by homogenous linear viscoelastic material properties. In group 4, a homogeneous nonlinear hippocampus was adopted. Simulation results demonstrated that for CCI with a 5-mm diameter, flat shape impactor, CA3 experienced increased tensile strains over a larger area and to a greater magnitude than did CA1 for group 1, which best explained why CA3 is more sensitive to CCI injury. However, for groups 2-4, the total volume with high strain (>30%) in CA3 was smaller than that in CA1. The FE rat brain model, with detailed hippocampal structures presented here, will help to engineer desired experimental neurotrauma models by virtually characterizing brain biomechanics before testing.

A Nonlinear Finite Element Framework for Viscoelastic Beams Based on the High-Order Reddy Beam Theory

A weak form Galerkin finite element model for the nonlinear quasi-static and fully transient analysis of initially straight viscoelastic beams is developed using the kinematic assumptions of the third-order Reddy beam theory. The formulation assumes linear viscoelastic material properties and is applicable to problems involving small strains and moderate rotations. The viscoelastic constitutive equations are efficiently discretized using the trapezoidal rule in conjunction with a two-point recurrence formula. Locking is avoided through the use of standard low-order reduced integration elements as well through the employment of a family of elements constructed using high-polynomial order Lagrange and Hermite interpolation functions.

Analytic derivation of the Cox–Merz rule using the MLD “toy” model for polydisperse linear polymers

A general constitutive formalism, the “naive” polydisperse MLD model, has been developed by Mead et al. (Macromolecules 31:7895–7914, 1998) and Mead (Rheol Acta 46:369–395, 2007) at both the tube coordinate level and the mathematically simplified “toy” level independent of the tube coordinate. The model includes constraint release generated by convection-driven chain retraction (which is equivalent to “convective constraint release” (CCR)), reptation, and tube contour length fluctuations. The properties of the mathematically simplified naive polydisperse “toy” MLD model are explored in linear and nonlinear steady shear flows where we analytically derive the Cox–Merz rule relating the steady shear viscosity to the modulus of the linear viscoelastic dynamic viscosity. The Cox–Merz rule relating the linear viscoelastic material properties and the nonlinear material properties is shown to be a direct consequence of convective constraint release. The specific feature of CCR that leads to this result is that the relaxation rate due to convective constraint release is proportional to the shear rate, \(\dot{{\gamma }}\), independent of molecular weight. The viability of this well-known empirical relationship is a direct consequence of a coincidence in the mathematical structure of the linear viscoelastic material properties and convective constraint release. There is no physical analogy or relationship between the molecular relaxation mechanisms operative in linear (diffusive relaxation) and nonlinear (convective relaxation) flow regimes. The polydisperse MLD model predictions of the individual molecular weight component contributions to the flow curve, and interpretations thereof, are effectively identical to those first postulated by Bersted (J Appl Polym Sci 19:2167–2177, 1975, J Appl Polym Sci 20:2705–2714, 1976). Following the theoretical developments, a limited experimental study is executed with a commercial polydisperse polystyrene melt. Nearly quantitative agreement between the polydisperse MLD theory and experimental measurements of steady-shear viscosity and dynamic moduli is achieved over a wide range of shear rates.