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New research is being conducted to better understand the relationship between mechanical characteristics and strain rate in polymeric materials. In this study, calcium phosphate nanoparticles were incorporated into polylactic acid using ultrasonic vibration-assisted melt mixing, and the samples were cast under vacuum. The normal stress difference and relaxation modulus for the Polylactic acid/Calcium phosphate nanocomposites were calculated using the experimentally measured value of viscoelastic properties. The dependency of normal stress difference and relaxation modulus on different parameters was also shown for the validation of the expressions. The first normal stress difference and relaxation modulus were predicted based on the frequency dependence viscoelastic characteristics of polylactic acid/calcium phosphate nanocomposites. The first normal stress difference increases with shear rate and reaches a plateau at lower shear rates. The value of the first normal stress differential increases with calcium phosphate nanoparticle concentration, demonstrating that calcium phosphate promotes elasticity. The relaxation modulus falls as shear rates increase while increasing with calcium phosphate nanoparticle concentration. However, the incorporation of the calcium phosphate nanoparticle to polylactic acid increases the relaxation modulus because of polymer-filler interaction. [ABSTRACT FROM AUTHOR]

In this paper, in order to reduce the indentation rolling resistance of a belt conveyor and improve its operation efficiency, the indentation rolling resistance of a belt conveyor is studied. Firstly, the theoretical calculation of the indentation rolling resistance caused by the contact between a conveyor belt and an idler is studied. Additionally, the expression of the indentation rolling resistance including the multi-element Maxwell relaxation modulus is simplified and deduced using the assumption of small deformation, and the steps of iterative calculation of the indentation rolling resistance through setting the initial values are designed. Then, the multi-component Maxwell relaxation modulus function of the conveyor belt tested in the previous work of the authors is substituted into COMSOL 5.6 finite element software, and the stress distribution caused by the contact between the conveyor belt and the idler under different working conditions is analyzed. Also, a series of measures to reduce the indentation rolling resistance are found through the laws presented by the simulation results. Finally, the experimental study of the indentation rolling resistance is carried out using the indentation rolling resistance testing device from our research group. By comparing the experimental results for the indentation rolling resistance under different working conditions with the theoretical calculation results for the indentation rolling resistance, it was found that the relative error was less than 13%, which proved the feasibility of the indentation rolling resistance and relaxation modulus testing method, as well as the theoretical calculation method for indentation rolling resistance. [ABSTRACT FROM AUTHOR]

Purpose: Prior studies have indicated an impact of cardiac muscle viscoelasticity on systolic and diastolic functions. However, the studies of ventricular free wall viscoelasticity, particularly for that of right ventricles (RV), are limited. Moreover, investigations on ventricular passive viscoelasticity have been restricted to large animals and there is a lack of data on rodent species. To fill this knowledge gap, this study aims to develop a biaxial tester that induces high-speed physiological deformations to characterize the passive viscoelasticity of rat RVs. Methods: The biaxial testing system was fabricated so that planar deformation of rat ventricle tissues at physiological strain rates was possible. The testing system was validated using isotropic polydimethylsiloxane (PDMS) sheets. Next, viscoelastic measurements were performed in healthy rat RV free walls by equibiaxial cyclic sinusoidal loadings and stress relaxation. Results: The biaxial tester's consistency, accuracy, and stability was confirmed from the PDMS samples measurements. Moreover, significant viscoelastic alterations of the RV were found between sub-physiological (0.1 Hz) and physiological frequencies (1–8 Hz). From hysteresis loop analysis, we found as the frequency increased, the elasticity and viscosity were increased in both directions. Interestingly, the ratio of storage energy to dissipated energy (Wd/Ws) remained constant at 0.1–5 Hz. We did not observe marked differences in healthy RV viscoelasticity between longitudinal and circumferential directions. Conclusion: This work provides a new experimental tool to quantify the passive, biaxial viscoelasticity of ventricle free walls in both small and large animals. The dynamic mechanical tests showed frequency-dependent elastic and viscous behaviors of healthy rat RVs. But the ratio of dissipated energy to stored energy was maintained between frequencies. These findings offer novel baseline information on the passive viscoelasticity of healthy RVs in adult rats. [ABSTRACT FROM AUTHOR]

Epoxy asphalt is a thermosetting material. Epoxy asphalt has excellent properties such as high strength, good hightemperature stability, and fatigue resistance. The application of epoxy asphalt mixture to construct pavement is considered a feasible way to achieve pavement durability. The epoxy asphalt mixture was employed as the paving material for the pavement surface layer, and the amount of epoxy component in epoxy asphalt was reduced. The mechanical parameters of the epoxy asphalt mixture were obtained through compressive rebound modulus tests and stress relaxation tests. Based on the mechanical parameters obtained in experiments, different pavement structure combinations were designed, and the epoxy asphalt pavement was subjected to structural mechanics analysis and composite optimization design using finite element simulation. The results indicate that the performance and strength of epoxy asphalt mixtures with asphalt content of 60% and 70% were significantly superior to SBS modified asphalt mixtures. Compared with other structure combinations, combination 3 (4 cm 60% EAC-13 + 4 cm AC-13), combination 5 (4 cm 70% EAC-13 + 4 cm 70% EAC-13), and combination 7 (4 cm AC-13 + 4 cm 60% EAC-13) exhibited better mechanical performance and economic feasibility [ABSTRACT FROM AUTHOR]

Viscoelastic materials are applied in several fields, and their relaxation characteristics are intricately related to the failure mechanism of sealing components and the generation of indentation rolling resistance in belt conveyors. Therefore, it is imperative to explore the relaxation characteristics of viscoelastic materials using characterization models. This article focuses on exploring these characterization models and the indentation rolling resistance of viscoelastic materials. The research comprises the following aspects: (1) A 2N + 2 element generalized Maxwell constitutive model is proposed for the relaxation behavior of viscoelastic materials to address the limitations of conventional relaxation models. (2) We conducted numerical calculations based on the relaxation modulus to solve the relaxation spectrum using several relaxation spectrum models. The findings showed that the model parameters were dependent on the testing time range. (3) The relationship between the indentation rolling resistance and relaxation model parameters was evaluated based on the theoretical foundation of the indentation rolling resistance calculation. [ABSTRACT FROM AUTHOR]

In this paper, in order to reduce the indentation rolling resistance of a belt conveyor and improve its operation efficiency, the indentation rolling resistance of a belt conveyor is studied. Firstly, the theoretical calculation of the indentation rolling resistance caused by the contact between a conveyor belt and an idler is studied. Additionally, the expression of the indentation rolling resistance including the multi-element Maxwell relaxation modulus is simplified and deduced using the assumption of small deformation, and the steps of iterative calculation of the indentation rolling resistance through setting the initial values are designed. Then, the multi-component Maxwell relaxation modulus function of the conveyor belt tested in the previous work of the authors is substituted into COMSOL 5.6 finite element software, and the stress distribution caused by the contact between the conveyor belt and the idler under different working conditions is analyzed. Also, a series of measures to reduce the indentation rolling resistance are found through the laws presented by the simulation results. Finally, the experimental study of the indentation rolling resistance is carried out using the indentation rolling resistance testing device from our research group. By comparing the experimental results for the indentation rolling resistance under different working conditions with the theoretical calculation results for the indentation rolling resistance, it was found that the relative error was less than 13%, which proved the feasibility of the indentation rolling resistance and relaxation modulus testing method, as well as the theoretical calculation method for indentation rolling resistance.

The viscoelastic stiffness of asphalt concrete is commonly represented using relaxation modulus and dynamic modulus, which are functions of loading time and loading frequency, respectively. They are typically measured via experimental testing whereby only one of the moduli is determined, and interconversion techniques can be used to obtain the other modulus if needed. Although exact approaches exist for pavement modulus interconversion, they can be difficult to implement in practice, and approximate conversion techniques have therefore been developed for conventional use. A popular approach is to approximate a direct relationship between the time and frequency domains via an equivalency factor, but there is no apparent consensus on its proper value. In this paper, a new numerical technique is applied to experimental data to ascertain the optimal value of the time-frequency equivalency factor. Approximate conversions from dynamic modulus to relaxation modulus are conducted using the optimal factor, and results are compared to popular alternative approaches. The optimal factor is determined to be $ 0.0673 \pm 0.0009 $ 0.0673 ± 0.0009 with 95% confidence. Using the mean value of 0.0673 produced conversion errors of 1.41% on average among 30 samples of hot mix asphalt. [ABSTRACT FROM AUTHOR]

In view of the influence of asphalt mixture nonlinearity on the mechanical response of pavement structure, the creep compliance of AC-16 under 0.1, 0.3, 0.5, 0.7 and 0.9 MPa is studied first. The results show that the asphalt mixture is in the linear viscoelastic region, when the load is in the 0.1-0.5 MPa interval. When the load is greater than 0.5 MPa, the creep compliance increases significantly, and asphalt mixture presents a nonlinear property. The Prony series is used to fit the creep compliance data, and the relaxation modulus is calculated based on the convolution relationship between creep compliance and relaxation modulus in viscoelastic mechanics. The relaxation modulus under different loads is introduced into the mechanical calculation of layered viscoelastic system. The calculation results show that the nonlinearity of asphalt mixture significantly affects the permanent deformation of asphalt layer, but has little effect on the fatigue problem of the asphalt base. In the design of pavement structure, attention should be paid to the nonlinearity of asphalt mixture. [ABSTRACT FROM AUTHOR]

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The growth in applications of Plantain Fibre Reinforced HDPE (PFRHDPE) has increased the importance of understanding the time-dependent viscoelastic properties such as creep resistance. This study focused on the determination of creep behaviour of a novel PFRHDPE designed for elevated temperatures applications. The creep responses of PFRHDPE were experimentally determined in line with ASTM D2290 and modelled for elevated temperature applications using the classical creep models, classical viscoelastic models and the time temperature superposition approach. Creep strain, creep stress, creep modulus and creep stress relaxation were modelled and analyzed. The PFRHDPE exhibited the characteristic of the unrelaxed and relaxed moduli of material to accommodate applications at elevated temperatures. The superposition method showed PFRHDPE to have moduli of 66 MPa and 2.26 MPa for one year and fifty years of operations respectively. The relaxation stresses were also evaluated as 9.24 MPa, 9.15 MPa and 12.96 MPa for the conditions investigated showing the new material as able to accommodate the constant loads of 25 MPa and 35 MPa under the elevated temperatures of 30 °C and 60 °C.

Viscoelastic parameters of viscoelastic materials should be measured to ensure their effective use. Unfortunately, devices for effective and accurate measurement of the relaxation modulus of materials are not currently available. In this study, we designed a mechanical device that can control the spherical indenter to press on the material at a uniform speed to allow measurement of the relaxation modulus of a viscoelastic material. The results showed that the device is accurate and easy to operate. The load expressions of ramp loading (the motion of the indenter is a uniform velocity) and ramp-constant loading (the motion of the indenter is stationary after uniform velocity) were derived for the spherical indenter. The relaxation modulus function of the material was calculated by measuring the displacement and load of the indenter and fitting it using the non-negative least square method. The relaxation modulus expression of viscoelastic materials calculated using the ramp loading experiment was substituted into the derived load expression of ramp-constant loading. The values were compared with the load values obtained using the ramp-constant loading experiment and the error was evaluated. The error was less than 2.5%, indicating high feasibility and practicability of the experimental device designed in this study. [ABSTRACT FROM AUTHOR]

Under the condition of small sample, the performance parameters' interval quantization and instantaneous reliability calculation of solid rocket motor grain structure are researched. Two important mechanical properties of material: Relaxation modulus and Poisson's ratio are obtained by experiments of grain material. Since the data of parameters obtained are a small sample, the method of gray theory is used to mine the experimental data. It realizes the uncertainty quantitative analysis of grain material performance parameters and obtains the quantitative interval of performance parameters. Considering that the evidence theory can directly attribute probabilistic mass to the set or interval, the instantaneous reliability of grain structure is analyzed based on the evidence theory. By establishing the relationship between failure surface and the frame of discernment, and using the belief function and plausibility function to obtain the upper and lower bound probability distribution of structural reliability and failure probability, the instantaneous reliability probability interval of structure is obtained. [ABSTRACT FROM AUTHOR]

Power-law attenuation in elastic wave propagation of both compressional and shear waves can be described with multiple relaxation processes. It may be less physical to describe it with fractional calculus medium models, but this approach is useful for simulation and for parameterization where the underlying relaxation structure is very complex. It is easy to enforce a low-frequency limit on a relaxation distribution and this gives frequency squared characteristics for low frequencies which seems to fit some media in practice. Here the goal is to change the low-frequency behavior of fractional models also. This is done by tempering the relaxation moduli of the fractional Kelvin-Voigt and diffusion models with an exponential function and the effect is that the low-frequency attenuation will increase with frequency squared and the square root of frequency respectively. The time-space wave equations for the tempered models have also been found, and for this purpose the concept of the fractional pseudo-differential operator borrowed from the field of Cole-Davidson dielectrics is useful. The tempering does not remove the singularity in the relaxation moduli of the models, but this has only a minor effect on the solutions.

Viscoelastic materials are applied in several fields, and their relaxation characteristics are intricately related to the failure mechanism of sealing components and the generation of indentation rolling resistance in belt conveyors. Therefore, it is imperative to explore the relaxation characteristics of viscoelastic materials using characterization models. This article focuses on exploring these characterization models and the indentation rolling resistance of viscoelastic materials. The research comprises the following aspects: (1) A 2N + 2 element generalized Maxwell constitutive model is proposed for the relaxation behavior of viscoelastic materials to address the limitations of conventional relaxation models. (2) We conducted numerical calculations based on the relaxation modulus to solve the relaxation spectrum using several relaxation spectrum models. The findings showed that the model parameters were dependent on the testing time range. (3) The relationship between the indentation rolling resistance and relaxation model parameters was evaluated based on the theoretical foundation of the indentation rolling resistance calculation.

The fractional Zener constitutive law is frequently used as a model of solid-like viscoelastic behavior. In this work, a class of linear viscoelastic models of Zener type, which generalize the fractional Zener model, is studied by the use of Bernstein functions technique. We prove that the corresponding relaxation moduli are completely monotone functions under appropriate thermodynamic restrictions on the parameters. Based on this property, we study the propagation function and establish the subordination principle for the corresponding Zener-type wave equation, which provides an integral representation of the solution in terms of the propagation function and the solution of a related classical wave equation. The analytical findings are supported by numerical examples. [ABSTRACT FROM AUTHOR]

Modification using elastomeric thermoplastic polymers is commonly adopted to improve the high-temperature performance of paving bitumen. The performance of modified bitumen classified under the same grade is highly variable depending on the type of base bitumen, the polymer architecture, and its dosage. The current specification parameters are insensitive to such variability. Identification of a suitable set of parameters that can quantify the changes in rheological properties due to various interaction mechanisms of bitumen with modifier thus becomes necessary. In this study, the base bitumen obtained using two different processes, namely air rectification and component blending, are considered. Though the same grade of bitumen produced using both processes is considered, the material compositions are different, and this necessitated the use of different polymer architectures (diblock and triblock SBS) for the two binders. Three different dosages are used for each modifier. A stress relaxation experiment is conducted, and the peak modulus and stress relaxation time are determined. In addition, the continuous relaxation spectrum and the associated parameters are computed. The base bitumen and the polymer architecture of the corresponding polymer influenced the stress relaxation response substantially. These factors also influenced the response of the material captured using the relaxation spectrum and exhibited interesting insights regarding the influence of temperature. [ABSTRACT FROM AUTHOR]

In this study, pure and self-healing asphalt mixture samples were obtained by adding capsules containing waste vegetable oil to mixtures at 0.25, 0.50, 0.75 and 1.00% ratios. Afterwards, creep test with a constant stress was carried out on the samples, and the resistance of asphalt mixtures against permanent deformation was investigated. Relaxation modulus values were obtained by using the creep compliance values that measured at the end of the experiment with mathematical transformations. Then, the relaxation modulus results were fitted to the Generalized Maxwell Model, which is a common model used to represent the viscoelastic properties of asphalt mixtures, and Prony series parameters were obtained. The results showed that the addition of capsule reduced the permanent deformation strength of the asphalt mixture. In addition, the curve fitting processes were successfully performed and the desired parameters were obtained with high accuracy.

As a typical viscoelastic material, solid propellants have a large difference in mechanical properties under static and dynamic loading. This variability is manifested in the difference in values of the relaxation modulus and dynamic modulus, which serve as the entry point for studying the dynamic and static mechanical properties of propellants. The relaxation modulus and dynamic modulus have a clear integral relationship in theory, but their consistency in engineering practice has never been verified. In this paper, by introducing the "catch-up factor λ" and "waiting factor γ", a method for the inter-conversion of the dynamic storage modulus and relaxation modulus of HTPB propellant is established, and the consistency between them is verified. The results show that the time region of the calculated conversion values of the relaxation modulus obtained by this method covers 10−8–104 s, spanning twelve orders of magnitude. Compared to that of the relaxation modulus (10−4–104 s, spanning eight orders of magnitude), an expansion of four orders of magnitude is achieved. This enhances the expression ability of the relaxation modulus on the mechanical properties of the propellant. Furthermore, when the conversion method is applied to the dynamic–static modulus conversion of the other two HTPB propellants, the results show that the correlation coefficient between the calculated and measured conversion values is R2 > 0.933. This proves the applicability of this method to the dynamic–static modulus conversion of other types of HTPB propellants. It was also found that λ and γ have the same universal optimal value for different HTPB propellants. As a bridge for static and dynamic modulus conversion, this method greatly expands the expression ability of the relaxation modulus and dynamic storage modulus on the mechanical properties of the HTPB propellant, which is of great significance in the research into the mechanical properties of the propellant. [ABSTRACT FROM AUTHOR]

Most used laminated glass is composed of float glass plies bonded together with a viscoelastic Polyvinyl Butyral (PVB) interlayer. The shear stiffness of the polymeric interlayer is the key factor in the behavior of laminated glass. Structural engineers in the past were designing laminated glass regardless of the shear coupling of the plies. This approach with a high level of reliability led to expensive laminated glass structures due to insufficient knowledge of foil properties. Most of the current standards suggest methods that consider the shear coupling of the plies. This paper presents the experimental data from a static loading test performed on a laminated glass panel exposed to changing temperatures. The deformations were observed for 48 h. The measured results were compared with the known analytical design approaches and in addition with the finite element modeling (FEM) analysis in the available software for laminated glass design. A simplified design approach that simulates foil behavior in dependence on load duration and temperature change was adopted in this study. Design approaches that use effective thickness calculations are used with the Young and shear relaxation modulus provided by the foil producer. The imprecision of the Eurocode standards for glass design, and the propensity to change the approach to the calculation by introducing more precise parameters were expounded. The results when combining the time-temperature superposition (TTS) and the Wölfel–Bennison approach were found to be in very good agreement with the FEM analysis of 3D solid elements in Abaqus and measured data. [ABSTRACT FROM AUTHOR]

A creep model based on Kelvin–Voigt fractional-order derivative model (KVFD) with less parameters and clearer physical description is established to obtain viscous-elastic property of frozen soil using spherical indentation tests (SITs), uniaxial creep tests and triaxial creep tests. Mechanical parameters identification principal (MPIP) is presented to verify fractional-order derivative Kelvin, Maxwell, Merchant and Burgers models have unique solution of mechanical parameters. MPIP is utilized to prove cascaded model of more than two fractional-order derivative Kelvin elements and Maxwell elements bring variable solutions of parameters in following conditions: (1) More than two cascaded fractional-order derivative Kelvin elements have same fractional-order and relaxation time; (2) More than two fractional-order derivative Maxwell elements are included in cascaded model. Experimental data of SITs reveal discrepancy of deformation curve also leads to diverse solutions of parameters and discrepancy of relaxation modulus. Discrepancy of relaxation modulus decreases with the decrease in deformation discrepancy. Relaxation modulus predicted by the proposed model is closer to Hertz's solution but higher than those given by Roman's solution after 5 h of loading. Validation of test data in SITs, uniaxial and triaxial creep tests demonstrates that the proposed model agrees well with the available laboratory results of frozen sand. [ABSTRACT FROM AUTHOR]

In order to evaluate the security coefficient of certain solid rocket motor (SRM) grain under low temperature ignition, the simulation and test of SRM grain structural integrity are carried out. Based on the three-dimensional linear viscoelastic model, the structural integrity of the SRM grain under low temperature and internal pressure is analyzed by finite element software. The rapid pressure building test system is used to simulate the engine ignition boost process under low temperature, and the volume deformation and maximum principal strain of the grain are obtained. The Poisson’s ratio inversion under the corresponding conditions is completed by comparing the simulation and experimental results. The maximum elongation of the propellant under simulated low-temperature ignition is obtained by combining the low temperature fast-slow tensile test, and then the security coefficient of motor grain under low-temperature ignition is obtained.

Viscoelastic parameters of viscoelastic materials should be measured to ensure their effective use. Unfortunately, devices for effective and accurate measurement of the relaxation modulus of materials are not currently available. In this study, we designed a mechanical device that can control the spherical indenter to press on the material at a uniform speed to allow measurement of the relaxation modulus of a viscoelastic material. The results showed that the device is accurate and easy to operate. The load expressions of ramp loading (the motion of the indenter is a uniform velocity) and ramp-constant loading (the motion of the indenter is stationary after uniform velocity) were derived for the spherical indenter. The relaxation modulus function of the material was calculated by measuring the displacement and load of the indenter and fitting it using the non-negative least square method. The relaxation modulus expression of viscoelastic materials calculated using the ramp loading experiment was substituted into the derived load expression of ramp-constant loading. The values were compared with the load values obtained using the ramp-constant loading experiment and the error was evaluated. The error was less than 2.5%, indicating high feasibility and practicability of the experimental device designed in this study.

This paper investigates the viscoelastic properties of oxidized neat bitumen and three polymer-modified binders at low temperatures. The earlier proposed interrelated expressions for the relaxation modulus and for the creep compliance of bitumen binders are further developed. The results of creep testing of the binders on a bending beam rheometer at the six temperatures from −18 °C to −36 °C are presented. The results were analyzed using the equations developed for the relaxation modulus and the relaxation time spectrum. Viscosities at the low temperatures of tested binders were estimated. Approximate interrelations between the loss modulus and the relaxation spectrum were presented. The method for the determination of the glass transition temperature of a binder in terms of the relaxation time spectrum is proposed. The glass transition temperatures of tested binders were determined by the proposed method and compared with ones determined by the standard loss modulus-peak method. [ABSTRACT FROM AUTHOR]

The effect of force amount, age, body weight and bone mineral density (BMD) on the femur's force relaxation response was analysed for 12 donors (age: 56–91 years). BMD and fracture load, FL, were estimated from clinical CT images. The 30 min force relaxation was obtained using a constant compression generating an initial force F0 between 7% and 78% of FL. The stretched decay function (F(t) = A × e(−t/τ)β) proposed earlier for bone tissue was fitted to the data and analysed using robust linear regression. The relaxation function fitted well to all the recordings (R2 = 0.99). The relative initial force was bilinearly associated (R2 = 0.83) to the shape factor, β, and the characteristic time, τ, when F0/FL was less than 0.4, although β was no longer associated with F0/FL by pooling all the data. The characteristic time τ increased with age (R2 = 0.37, p = 0.03) explaining 35% of the variation of τ in the entire dataset. In conclusion, the relative initial force mostly determines the femur's force relaxation response, although the early relaxation response under subcritical loading is variable, possibly due to damage occurring at subcritical loading levels.

This paper deals with an experimental study of a relaxation behaviour of fibreglass/epoxy composite material subjected to tensile stress. The small tensile testing machine including the heating chamber with the temperature controller is designed and manufactured to perform the stress relief testing at different operating conditions. The influence of the operating temperature onto both the relief time and the number of the loading cycles is considered. The test specimens having a different number of layers of fibreglass tissues are prepared in the laboratory. The effect of the fiberglass tissue volume fraction on the relief behaviour of the fibreglass/epoxy composite is investigated. The constant of the relief time is evaluated for various operating temperature. The obtained results showed that the relief time and the number of relaxation cycles are highly increased by increasing the fibreglass layers. The total number of relief cycles was increased by about 34% when increasing the volume fraction of the fibreglass tissue by about 15%. The relief time of the first cycle was increased by about 83% when increasing the volume fraction of the fibreglass tissue from 30% to 45 % at operating temperature equal to 〖60〗^o C. The time taken to fracture the specimens decreased significantly by increasing the operating temperature as it decreased by about 88% and 73% for volume fraction 30% and 40% respectively when raising the operating temperature by about〖30〗^o C. The material relief time constant is strongly affected by both the operating temperature and the volume fraction of the fibreglass tissue.

To predict traumatic injuries using a computational model, accurate mechanical properties of biological materials are required. Especially, soft tissue is a viscoelastic and rate sensitive material that exhibits the decaying stress response when a constant displacement is applied. Thus, it is important to precisely formulate the phenomenon of a stress relaxation, which is readily applicable to computational models. In the current work, we newly developed an identification method of time constants and Young’s moduli for the stress relaxation response of biological soft tissues by assuming that soft tissues can be described by a generalized Maxwell model. Firstly, the decaying stress response was decomposed into a set of slow-to-fast stress components using a low-pass filter. Subsequently, we identified the time constants and Young’s moduli for slow and fast variations independently by solving the optimal problem, in which the correlation coefficient was maximized between each stress component and a corresponding normalized stress component. This method is computationally cost efficient and can semi-automatically determine the number of springs of Maxwell model. By applying the newly proposed method to the experimental data obtained for neural fiber bundles and skeletal muscle fiber bundles subjected to uniaxial stretching, we successfully demonstrated that the stress relaxation response can be well predicted for the mechanical change even in the short time range (0.1–1 s) in addition to the long time range (10–100 s).

An exact solution to the creep and long-term strength problem for pressurized thick-walled tubes consisting of several layers of physically nonlinear viscoelastic materials obeying the Rabotnov constitutive equation with two arbitrary material functions for each layer (creep compliance and a function that governs the physical nonlinearity) was constructed and studied. All layer materials are homogeneous, isotropic, and incompressible, and the tube is loaded by internal and external pressures creating a plain strain state, i.e., zero axial displacements are given on the edge of tube cross sections. Closed expressions were found for displacement, strain, and stress fields in relation to the single unknown function of time and integral operators involving this function, pairs of (arbitrary) material functions of each tube layer, preset pressure values and ratios of tube layers radii, and an integral equation to determine this unknown function was derived. Expressions and three creep failure criteria with three measures of damage (the effective shear strain, the maximum shear strain, or the maximum principal strain) were used to derive formulas for the creep fracture time of a tube to mark the layer in which the fracture will occurs earlier and to find a simple strength parameter for the tube (depending on layers thicknesses and their fracture strains) which should be increased to enhance its long-term strength. Assuming that the relaxation moduli of layer materials are proportional to a single (arbitrary) function of time and the material functions that govern the nonlinearity coincide with a power function with a positive exponent, an exact solution of the resolving functional equation was constructed. All integrals involved in the general representation of the tube stress field were calculated and reduced to simple algebraic formulas convenient for an analysis. Explicit formulas were derived for the creep fracture time of the tube, and closed equations for the long-term strength curves based on three creep failure criteria mentioned above were found. The general properties of the long-term strength curves were studied for arbitrary material functions of the constitutive relation and compared with each other. It is proved that the long-term strength curves (fracture time as a function of pressures difference) are decreasing and convex down and that their shape is controlled mainly by the compliance functions of layer materials rather than by the radii of tube layers and the nonlinearity of the governing physical function, because they influence only the factor responsible for the long-term strength in tension along the pressure axis. [ABSTRACT FROM AUTHOR]

We considered relaxation, creep, dissipation, and hysteresis resulting from a six-parameter fractional constitutive model and its particular cases. The storage modulus, loss modulus, and loss factor, as well as their characteristics based on the thermodynamic requirements, were investigated. It was proved that for the fractional Maxwell model, the storage modulus increases monotonically, while the loss modulus has symmetrical peaks for its curve against the logarithmic scale log(ω), and for the fractional Zener model, the storage modulus monotonically increases while the loss modulus and the loss factor have symmetrical peaks for their curves against the logarithmic scale log(ω). The peak values and corresponding stationary points were analytically given. The relaxation modulus and the creep compliance for the six-parameter fractional constitutive model were given in terms of the Mittag--Leffler functions. Finally, the stress--strain hysteresis loops were simulated by making use of the derived creep compliance for the fractional Zener model. These results show that the fractional constitutive models could characterize the relaxation, creep, dissipation, and hysteresis phenomena of viscoelastic bodies, and fractional orders a and β could be used to model real-world physical properties well. [ABSTRACT FROM AUTHOR]

Plant fibres (PFs) are preferred reinforcements of bio-composites. Knowledge of their lifespan requires a study of their viscoelastic behaviour. In this paper, a stress relaxation analysis of kenaf fibres was performed at a constant rate of deformation at room temperature. A method for extracting the relaxation modulus in the deferred zone was proposed. This method was compared, using simulation, with the Zapas-Phillips method and experimental data via three predictive models: the stretched exponential function or KWW, the inverse power law of Nutting and the prony series. The results indicate that the relaxation modulus obtained by the method proposed is in good agreement with the experimental modulus. In addition, the estimated error is of the same order of magnitude as in the case of the Zapas-Phillips method. The parameters estimated from the KWW function (β = 0.4) and prony series model showed an important contribution in the study of the delayed response of kenaf fibres. These results can have a significant impact on the use of kenaf fibres in midterm and long-term loading applications. [ABSTRACT FROM AUTHOR]

The standard linear solid model (SLSM) is a typical and useful model for analyzing stress relaxation and creep behaviors of viscoelastic solids for obtaining the corresponding viscoelastic properties. However, the analysis results cannot be directly compared to the parameters commonly adopted for defining the mechanical properties of viscoelastic solids in the finite element simulation package such as the modulus of elasticity (Ee) and the two parameters in the dimensionless form of the relaxation modulus (g and τ1). The purpose of this paper is to introduce an alternative form of SLSM in terms of Ee, g, and τ1 for characterizing stress relaxation and creep behaviors. A series of stress relaxation and creep curves with different Ee, g, and τ1 was simulated by finite element simulation. The derived alternative form of SLSM was used to curve fit the simulated stress relaxation and creep curves to obtain the corresponding values of Ee, g, and τ1. The results showed that the values of Ee, g, and τ1 obtained from the simulation were approximately equal to the theoretical ones (i.e., those set in the simulation), showing that the alternative form of SLSM can accurately evaluate the corresponding Ee, g, and τ1. In conclusion, the alternative form is formulated in terms of the parameters used to define the mechanical properties in the finite element simulation package, so that the parameters obtained by curve fitting can be directly compared to those set in the finite element simulation package. It was also found that the physical meaning of g is associated with the ratio of viscous fluids to solids of a viscoelastic solid.

A nested analytical method, a product of combining two micromechanical models is developed in this study. The proposed micromechanical method predicts the relaxation properties of polymer hybrid nanocomposites containing linearly visco-elastic matrix, transversely isotropic elastic carbon fibers, and graphene nanoplatelets. Calculations performed in this model are of two scales. The small scale, which is the domain of epoxy resin and graphene nanoplatelet interactions, and the large scale, which assumes the small scale as a homogenized isotropic matrix. In the large scale, the prescribed matrix is then reinforced by the unidirectional CFs. Each scale calculation gives the properties of the underlying material. Secant moduli and the field fluctuation techniques are adopted in this study. Resulting explicit formulae allows one to calculate the overall relaxation moduli of the graphene nanoplatelet/carbon fiber-reinforced polymer hybrid nanocomposites. By comparing the data obtained by experiments and the results extracted by the proposed micromechanical approach, the accuracy of the model becomes apparent. Addition of graphene nanoplatelets into the fibrous composites leads to an improvement in the relaxation properties of the hybrid nanocomposites. Also, the elastic properties of graphene nanoplatelet/carbon fiber-reinforced epoxy hybrid nanocomposites are reported. The role of graphene nanoplatelet agglomeration, frequently encountered in real engineering situations, in the mechanical response of unidirectional hybrid nanocomposites is examined. The effects of volume fraction of graphene nanoplatelets and CFs on the overall mechanical properties are investigated. [ABSTRACT FROM AUTHOR]

To obtain the viscoelastic parameters of asphalt mixtures and analyze the effect of temperatures and modifiers on viscoelastic properties of asphalt mixtures, the creep compliances of the neat asphalt mixture (AM), compound diatomite and basalt fibers reinforced asphalt mixture (DBFAM), and styrene-butadiene-styrene modified asphalt mixture (SBSAM) were tested and calculated by the static creep tests. And the creep compliances of the three asphalt mixtures at −20 °C, −10 °C, and 0 °C are deducted by the time–temperature equivalence principle (TTEP) and Arrhenius equation. Further, the relaxation modulus of the three asphalt mixtures from −20 °C to 50 °C at 10 °C increments are calculated by the convolution integral and Simpson method. Subsequently, the Burgers model, the generalized Kelvin model, and the generalized Maxwell model are applied to analyze the viscoelastic properties of the three asphalt mixtures at different temperatures. The results show that the generalized Kelvin model and the generalized Maxwell model are superior to the Burgers model in describing the variation of viscoelastic properties of asphalt mixtures with loading time. At low temperatures, asphalt mixtures have excellent properties in resisting permanent deformation and releasing internal stress. Besides, the addition of SBS modifier and compound diatomite and basalt fibers modifier can significantly raise the viscosity η1 and the elastic modulus E1 of the asphalt mixture, respectively. [ABSTRACT FROM AUTHOR]

• This study determines the creep compliance of AC from field sensors. • Obtained material parameters were incorporated in an FE model and validated. • Sensor obtained in-situ dynamic modulus were compared with the laboratory results. • This method can be used in any instrumented pavement to obtain material properties. This study demonstrates a methodology to determine the viscoelastic properties of Asphalt Concrete (AC) through embedded sensors such as strain gages. Determination of AC viscoelastic parameters are very quick, easy and efficient if the pavement is instrumented. Numerical interconversion method is applied to convert sensor data to relaxation modulus and dynamic modulus. Field obtained relaxation modulus are used in a finite element model to study whether the field instrumentation sensor obtained material properties can accurately represent the pavement response or not. The actual response of the pavement at different layers under 9-kip FWD load is compared with the developed FE model responses. From the results, it is observed that the developed numerical model can accurately predict the AC, base, subbase and subgrade layer responses. The validated model can be used for studying pavement performances, which can be done in a future study. [ABSTRACT FROM AUTHOR]

Highlights • Interactions of MBP gels were evaluated by using the relaxation modulus method. • Relaxation modulus of MBP was affected by salt ions, EDTA, and urea. • Calcium ions play a key role in the formation of MBP gel. • Hydrogen and ionic bonds play important roles in the formation of MBP gel. Abstract In this study, the relaxation modulus was used to elucidate the gelling mechanism of polysaccharides from Mesona blumes. The pH of Mesona blumes polysaccharides (MBP) was adjusted could significantly change the relaxation modulus of MBP. The results showed that the hydrogen bonds and electrostatic interaction existed in during the formation of MBP gel. The addition of salt ions (sodium ions and calcium ions), EDTA and urea have different effects on the relaxation modulus of MBP. Result showed that the hydrogen bond was the main force maintaining the MBP gel network structure, followed was calcium ions. And electrostatic interaction was not the decisive role of gel formation. The small molecules with active hydrogen-bond donors and/or acceptors were added into MBP, which proved −COOH was involved in the hydrogen bonds formation of MBP gel. In addition, the entanglement network number (ENN) results quantitatively assessed contribution of interaction: hydrogen bonds interaction > calcium ions (calcium bridge) >electrostatic interaction. [ABSTRACT FROM AUTHOR]

Experimental determination of relaxation modulus of linear viscoelastic materials, in principle, requires the application of an ideal step strain to the specimen. This could not be achieved in practice, however, and is replaced by a ramp-constant strain history. The material response to the ramp-constant strain deviates from its ideal step response and should be corrected. Different correction methods have been proposed for the full-range modulus extraction from ramp-constant strain experiments, and among them the three methods of Zapas–Phillips, Lee–Knauss, and Sorvari–Malinen are distinguishable. Few comparative studies have been performed on these methods, all of which have been based on the simulated response of a hypothetic material rather than on the real experimental data. Furthermore, the simulations have been performed assuming specific material models not essentially appropriate for the material parameter extraction purposes, leading to undesirable errors in the simulation results. In this paper, the above-mentioned methods are compared based on both simulation and experimental approaches. The simulation results show that all methods effectively improve the range of modulus extraction compared to the well-known "ten-times rule", and the Lee–Knauss method provides the best predictions, in contrast to some of the previously published results. Considering the experimental results, however, it is observed that all the modulus extraction methods lose their performance if a sufficiently small sampling rate is not provided by the experimental data acquisition system. It has been discussed that the conclusion of some authors regarding the invalidity of ten-times-rule stems from a misinterpretation of their simulation results and is faultful. [ABSTRACT FROM AUTHOR]