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The purpose of this paper is to establish a peridynamic method in predicting viscoelastic creep behaviour with recovery stage and to find the suitable numerical parameters of peridynamic method.

A rheological viscoelastic creep constitutive equation including recovery and an elastic peridynamic equation (with integral basis) are examined and used. The elasticity equation within the peridynamic equation is replaced by the viscoelastic equation. A new peridynamic method with two time parameters, i.e. numerical time and viscoelastic real time is designed. The two parameters of peridynamic method, horizon radius and number of nodes per unit volume are studied to get their optimal values. In validating this peridynamic method, comparisons are made between numerical and analytical result and between numerical and experimental data.

The new peridynamic method for viscoelastic creep behaviour is approved by the good matching in numerical-analytical data comparison with difference of < 0.1 per cent and in numerical-experimental data comparison with difference of 4-6 per cent. It can be used for further creep test which may include non-linear viscoelastic behaviour and creep rupture. From this paper, the variation of constants in Burger’s viscoelastic model is also studied and groups of constants values that can simulate solid, fluid and solid-fluid viscoelastic behaviours were obtained. In addition, the numerical peridynamic parameters were also manipulated and examined to achieve the optimal values of the parameters.

The peridynamic model of viscoelastic creep behaviour preferably should have only one time parameter. This can only be done by solving the unstable fluctuation of dynamic results, which is not discussed in this paper. Another limitation is the tertiary region and creep rupture are not included in this paper.

The viscoelastic peridynamic model in this paper can serve as an alternative for conventional numerical simulations in viscoelastic area. This model also is the initial step of developing peridynamic model of viscoelastic creep rupture properties (crack initiation, crack propagation, crack branching, etc.), where this future model has high potential in predicting failure behaviours of any components, tools or structures, and hence increase safety and reduce loss.

The application of viscoelastic creep constitutive model on peridynamic formulation, effect of peridynamic parameters manipulation on numerical result, and optimization of constants of viscoelastic model in simulating three types of viscoelastic creep behaviours.

In order to determine the range of medium temperature zone of road asphalt, it is hoped that the evolution of viscoelastic characteristics of road asphalt under medium temperature state can be deeply explored.

In this paper, the needle penetration test and temperature scanning test were designed for 90# and 70# bitumen as test materials, and the boundary of medium temperature zone of 90# and 70# bitumen was accurately determined by data analysis method. A mathematical model was established based on principal component analysis, and a comprehensive evaluation index was proposed to evaluate the evolution of temperature viscoelastic characteristics of road asphalt by means of standardization and rotational dimensionality reduction.

The test results show that the medium temperature zone of 90# asphalt is [−5 ± 1°C, 38 ± 1°C], and the medium temperature zone of 70# asphalt is [0 ± 1°C, 51 ± 1°C]. According to the viscoelastic response of road asphalt in the medium temperature zone, the medium temperature zone can be divided into three evolution stages: weak viscoelastic stage, viscoelastic equilibrium stage, strong viscoelastic weak stage. Analysis based on the intrinsic viscosity fillip target describing the various intrinsic viscoelastic index represents the viscoelastic properties of bitumen from different angles, and limitations inherent stick fillip for target put forward the integrated the inherent stick fillip mark information, as well as targeted and accurate evaluation of road asphalt temperature comprehensive evaluation indexes in the evolution of the viscoelastic properties of I_M-T. Finally, the temperature data of asphalt pavement in several representative regions of China are compared with the determined medium temperature region, and it is proved that the research on the evolution of viscoelastic characteristics of asphalt pavement under the medium temperature condition has important practical significance.

The boundary of medium temperature zone of 90# and 70# base asphalt was determined, and the viscoelastic characteristic evolution of road asphalt under medium temperature state was studied deeply. Aiming at the limitation of intrinsic viscoelastic index, a comprehensive evaluation index IM-T which not only integrates the information of intrinsic viscoelastic index but also can accurately evaluate the evolution of temperature viscoelastic characteristics in road asphalt is proposed.

The purpose of this paper is to present numerical studies on thermally induced vibrations of piezo‐thermo‐viscoelastic composite beam subjected to a transient thermal load using coupled finite element method.

The thermal relaxation and viscoelastic relaxations are taken into consideration to obtain the system response. The concept of “memory load” along with the thermal relaxation is accounted for viscoelastic core material. The influence of type of core material on the response of the system also analyzed.

The findings show viscoelastic behavior with relaxation times in composite sandwich structures.

The paper shows accounting relaxation times as a memory load in composite sandwich structures.

The purpose of this paper is to equip damping performance of frame structure with viscoelastic dampers connected to supports is studied, the influence of the damper supports and the damping parameters on the damping performance of the structure is analyzed, the practical economical arrangement of viscoelastic dampers on each floor is researched and the calculation method of the seismic effect of the damping structure is presented.

In this paper, Fourier transform is applied to the vibration equation of the structure equipped with viscoelastic dampers, the frequency domain solution of the vibration equation is solved and the time-domain solution of the equation is obtained by Fourier inverse transform, from which effects of the support coefficient and the relaxing time coefficient on the seismic response of the structure are analyzed.

The seismic effect of each floor and the bottom shear force of each vibration mode of a structure are analyzed, which indicates that the relaxing time coefficient of the damper should be controlled reasonably.

In this paper, the vibration equation is solved in the frequency domain for frame structure equipped with viscoelastic dampers. The time-domain solution of the equation is obtained by Fourier inverse transform, from which the seismic response of frame structure equipped with viscoelastic damper connected to supports is studied.

This study aims to propose a novel viscoelastic–viscoplastic combined constitutive model for glassy amorphous polymers within the framework of thermodynamics at finite strain that is capable of capturing their rate-dependent inelastic mechanical behavior in wide ranges of deformation rate and amount.

The rheology model whose viscoelastic and viscoplastic elements are connected in series is set in accordance with the multi-mechanism theory. Then, the constitutive functions are formulated on the basis of the multiplicative decomposition of the deformation gradient implicated by the rheology model within the framework of thermodynamics. Dynamic mechanical analysis (DMA) and loading/unloading/no-load tests for polycarbonate (PC) are conducted to identify the material parameters and demonstrate the capability of the proposed model.

The performance was validated in comparison with the series of the test results with different rates and amounts of deformation before unloading together. It has been confirmed that the proposed model can accommodate various material behaviors empirically observed, such as rate-dependent elasticity, elastic hysteresis, strain softening, orientation hardening and strain recovery.

This paper presents a novel rheological constitutive model in which the viscoelastic element connected in series with the viscoplastic one exclusively represents the elastic behavior, and each material response is formulated according to the multiplicatively decomposed deformation gradients. In particular, the yield strength followed by the isotropic hardening reflects the relaxation characteristics in the viscoelastic constitutive functions so that the glass transition temperature could be variant within the wide range of deformation rate. Consequently, the model enables us to properly represent the loading process up to large deformation regime followed by unloading and no-load processes.

When explicit integral analysis is performed on a numerical model with viscoelastic artificial boundary elements, an instability phenomenon is likely to occur in the boundary area, reducing the computational efficiency of the numerical calculation and limiting the use of viscoelastic artificial boundary elements in the explicit dynamic analysis of large-scale engineering sites. The main purpose of this study is to improve the stability condition of viscoelastic artificial boundary elements.

A stability analysis method based on local subsystems was adopted to analyze and improve the stability conditions of three-dimensional (3D) viscoelastic artificial boundary elements. Typical boundary subsystems that can represent the localized characteristics of the overall model were established, and their analytical stability conditions were derived with an analysis based on the spectral radius of the transfer matrix. Then, after analyzing the influence of each physical parameter on the analytical-stability conditions, a method for improving the stability condition of the explicit algorithm by increasing the mass density of the artificial boundary elements was proposed.

Numerical wave propagation simulations in uniform and layered half-space models show that, on the premise of ensuring the accuracy of the viscoelastic artificial boundary, the proposed method can effectively improve the numerical stability and the efficiency of the explicit dynamic calculations for the overall system.

The stability improvement method proposed in this study are significant for improving the applicability of viscoelastic artificial boundary elements in explicit dynamic calculations and the calculation efficiency of wave analysis at large-scale engineering sites.

The purpose of this paper is to cover an experimental investigation of the impulse response of the foam-mass system (FMS) to unveil some of the foam dynamic behavior features needed to optimize the impact comfort of seat-occupant system. The equation of motion of the studied system is modeled as a sum of a linear elastic, pneumatic damping and viscoelastic residual forces. An identification methodology based on two separated calibration processes of the viscoelastic parameters was developed.

The viscoelastic damping force representing the foam short memory effects was modeled through the hereditary formulation. Its parameters were predicted from the free vibrational response of the FMS using iterative Prony method for autoregressive–moving–average model. However, the viscoelastic residual force resulting in the long memory effects of the material was modeled with fractional derivative term and its derivative order was predicted from previous cyclic compression standards.

The coefficients of the motion law were determined using closed form solution approach. The predictions obtained from the simulations of the impulse and cyclic tests are reasonably accurate. The physical interpretations as well as the mathematical correlations between the system parameters were discussed in details.

The prediction model combines hereditary and fractional derivative formulations resulting in short and long physical memory effects, respectively. Simulation of impulse and cyclic behavior yields good correlation with experimental findings.

The purpose of this paper is to develop a numerical (finite-difference) model exploring phase and group velocities of SH-wave propagation in initially stressed transversely isotropic poroelastic multi-layered composite structures and initially stressed viscoelastic-dry-sandy multi-layered composite structures in two distinct cases.

With the aid of relevant constitutive relations, the non-vanishing equations of motions for the propagation SH-wave in the considered composite structures have been derived. Haskell matrix method and finite-difference scheme are adopted to deduce velocity equation for both the cases. Stability analysis for the adopted finite-difference scheme has been carried out and the expressions for phase as well as group velocity in terms of dispersion-parameter and stability-ratio have been deduced.

Velocity equations are derived for the propagation of SH-wave in both the composite structures. The obtained results are matched with the classical results for the case of double and triple-layered composite structure along with comparative analysis. Stability analysis have been carried out to develop expressions of phase as well as group velocity in terms of dispersion-parameter and stability-ratio. The effect of wavenumber, dispersion parameter along with initial-stress, porosity, sandiness, viscoelasticity, stability ratio, associated with the said composite structures on phase, damped and group velocities of SH-wave has been unveiled.

To the best of authors’ knowledge, numerical modelling and analysis of propagation characteristics of SH-wave in multi-layered initially stressed composite structures composed of transversely isotropic poroelastic materials and viscoelastic-dry-sandy materials remain unattempted inspite of its importance and relevance in many branches of science and engineering.

The efficiency of fractional derivative and hereditary combined approach in modeling viscoelastic behavior of soft foams was successfully addressed in Elfarhani et al. (2016a). Since predictions obtained on flexible polyurethane foam (FPF) type A (density 28 kg m⁻³) were found very promoting, the purpose of this paper is to apply the approach basing on two other types of foams. Both soft polyurethane foams type B of density 42 kg m⁻³ and type C of density 50 kg m⁻³ were subjected to multi-cycles compressive tests.

The total foam response is assumed to be the sum of a non-linear elastic component and viscoelastic component. The elastic force is modeled by a seven-order polynomial function of displacement. The hereditary approach was applied during the loading half-cycles to simulate the short memory effects while the fractional derivative approach was applied during unloading cycles to simulate the long memory effects. An identification methodology based on the separation of the measurements of each component force was developed to avoid parameter admixture problems.

The proposed model reveals good reliability in predicting the responses of the two considered flexible foams. Predictions as measurements establish that residual responses were negligible compared to elastic and viscoelastic damping responses.

The development of a new combined model reveals good reliability in predicting the responses of the two polyurethane foams type A and B.

In this paper, the formulation and analytic solutions for fractional continuously variable order dynamic models, namely, fractional continuously mass-spring damper (continuously variable fractional order) systems, have been presented. The authors will demonstrate via two cases where the frictional damping given by fractional derivative, the order of which varies continuously – while the mass moves in a guide. Here, the continuously changing nature of the fractional-order derivative for dynamic systems has been studied for the first time. The solutions of the fractional continuously variable order mass-spring damper systems have been presented here by using a successive recursive method, and the closed form of the solutions has been obtained. By using graphical plots, the nature of the solutions has been discussed for the different cases of continuously variable fractional order of damping force for oscillator. The purpose of the paper is to formulate the continuously variable order mass-spring damper systems and find their analytical solutions by successive recursion method.

The authors have used the viscoelastic and viscous – viscoelastic dampers for describing the damping nature of the oscillating systems, where the order of the fractional derivative varies continuously.

By using the successive recursive method, here, the authors find the solution of the fractional continuously variable order mass-spring damper systems, and then obtain close-form solutions. The authors then present and discuss the solutions obtained in the cases with the continuously variable order of damping for an oscillator through graphical plots.

Formulation of fractional continuously variable order dynamic models has been described. Fractional continuous variable order mass-spring damper systems have been analysed. A new approach to find solutions of the aforementioned dynamic models has been established. Viscoelastic and viscous – viscoelastic dampers are described. The discussed damping nature of the oscillating systems has not been studied yet.