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Contact mechanics theories are commonly developed using the half-space approximation, which may raise concerns when dealing with contact region sizes comparable to or even larger than the size of the contacting bodies. In this study, we examine the normal adhesive contact between a rigid, wavy indenter and a viscoelastic substrate with a finite thickness. To achieve this, we utilize a recently developed finite element model that incorporates adhesive interactions based on the Lennard–Jones potential law. The results demonstrate that adhesive behavior is influenced by a combination of rate and size effects. Additionally, when considering non-negligible viscous effects, an optimal thickness can be determined to maximize the pull-off stress. [ABSTRACT FROM AUTHOR]

Using the diaphragm-type air spring as the research object. The ratio of the vertical stiffness change caused by compressed air to the total vertical stiffness change was calculated, and it was determined that the nonlinearity of air spring vertical stiffness was mainly caused by the deformation stiffness of the rubber airbag. The variation law of vertical dynamic stiffness of air spring was predicted by theory: due to the material's viscoelasticity, the vertical dynamic stiffness rises as the excitation frequency rises, and the vertical dynamic stiffness decreases with the increase of excitation amplitude due to the damping of the material. An air spring finite element analysis (FEA) and experiment were conducted. The results show that the vertical dynamic stiffness obtained through simulation and experiment is consistent with the theoretical prediction, when various factors such as material nonlinearity, element coupling, and stiffness value sensitivity were considered. This proves that the predicted vertical dynamic stiffness variation law is reliable. The vertical dynamic stiffness obtained from both simulation and experiment showed a strong correlation in numerical values, which verified the accuracy of the FEA model of air spring established in this paper. [ABSTRACT FROM AUTHOR]

Background: Mechanical characterization of materials that solely relies on global responses may overlook important local behavior that significantly affects the characterization of material properties. Field displacements such as from digital image correlation (DIC) can provide high-fidelity experimental data, which combined with finite element method (FEM) can form DIC-FEM inverse method that can better account for complex mechanical properties of materials. Despite its capability, the DIC-FEM inverse method has been mainly applied to an elastic-dominant regime even though inelastic deformation is important in many engineering materials. Specifically, the DIC-FEM inverse method has not been fully extended to viscoelastic materials due to the complex representation of the time-dependent modulus. Objective: This study aimed at establishing a DIC-FEM inverse framework to identify constitutive properties of homogeneous elastic and viscoelastic materials. Methods: Two example materials (i.e., polyetheretherketone (PEEK) and a viscoelastic fine aggregate matrix (FAM) with a bituminous binder) were selected for the elastic and viscoelastic investigation, respectively. Both were experimentally tested using three-point bending incorporated with DIC. FEM simulated the experiment and the Nelder-Mead nonlinear optimization algorithm was implemented to solve the inverse problem. Results: The DIC-FEM inverse method successfully identified Young's modulus of an example linear elastic PEEK and the linear viscoelastic relaxation modulus of FAM. Conclusions: The resulting DIC-FEM inverse method is applicable to various materials with inelastic deformation and can be extended to localized behavior induced by microstructure heterogeneity and fracture. [ABSTRACT FROM AUTHOR]

The components of the stress-strain state of rubber shock absorbers under viscoelastic deformation are investigated. The contraction of rubber shock absorber under the action of a vertical force and a combination of vertical and shear forces is calculated. The dependence of the contraction of the structure on time was obtained. The specific mechanical properties inherent in rubber, such as the weak compressibility of the material and deformation viscoelasticity deformation, the mathematical modeling of which involves significant mathematical difficulties, were taken into account. In the numerical calculation, the weak compressibility of rubber was modeled using a finite element moment scheme for weakly compressible materials, the essence of which is the triple approximation of displacement fields, strain components and volume change function. For the mathematical modeling of the viscoelastic nature of strains, the hereditary Boltzmann–Volterra theory with exponential relaxation kernel is used. On the basis of the Lagrange variational principle, a system of resolving integral equations of viscoelasticity is obtained taking into account the weak compressibility of the material, and an iterative procedure for its solution is proposed. The modified Newton–Kantorovich method is used to solve a nonlinear boundary value problem. The numerical solution is obtained by the finite element method in the case of viscoelastic deformation of rubber material. The calculation is performed for the case when the rubber layer is vulcanized to metal plates. The influence of the viscoelastic properties of the rubber on the value of rubber shock absorber contraction for two cases of mechanical loading is investigated. Calculations were carried out for two rubber grades: 2959 and 1562. [ABSTRACT FROM AUTHOR]

Understanding tissue rheology is critical to accurately model the human heart. While the elastic properties of cardiac tissue have been extensively studied, its viscous properties remain an issue of ongoing debate. Here we adopt a viscoelastic version of the classical Holzapfel Ogden model to study the viscous timescales of human cardiac tissue. We perform a series of simulations and explore stress–relaxation curves, pressure–volume loops, strain profiles, and ventricular wall strains for varying viscosity parameters. We show that the time window for model calibration strongly influences the parameter identification. Using a four-chamber human heart model, we observe that, during the physiologically relevant time scales of the cardiac cycle, viscous relaxation has a negligible effect on the overall behavior of the heart. While viscosity could have important consequences in pathological conditions with compromised contraction or relaxation properties, we conclude that, for simulations within the physiological range of a human heart beat, we can reasonably approximate the human heart as hyperelastic. [ABSTRACT FROM AUTHOR]

Background: The viscoelastic properties of aortic tissue dictate vessel behavior in certain disease states, injury modalities, and during some endovascular procedures. Objective: We characterized the viscoelastic response of porcine abdominal aortic tissue via test and simulation to demonstrate the utility of a viscoelastic anisotropic (VA) constitutive model. Methods: In this study, the measured stress relaxation response for five samples and uniaxial tensile testing for one sample measured with the digital image correlation (DIC) technique were used to identify material parameters for the VA model using an inverse method through finite element analysis (FEA). Results: Based on the stress relaxation test, the values of the stress-like parameter μ , relative stiffness of the fibers k 1 , dimensionless parameter k 2 , angle of fibers γ , dispersion parameter κ , relaxation times for the ground matrix T g 1 and collagen fibers T f 1 and the dimensionless parameters for the ground matrix β g 1 and collagen fibers β f 1 for 0 degree specimen orientation were 12.1 ± 8.96 kPa, 77.3 ± 46.4 kPa, 0.032 ± 0.043, 30.25 ± 6.81°, 0.19 ± 0.06, 0.028 ± 0.016 s, 92.76 ± 26.51 s, 3.46 ± 3.78, 0.24 ± 0.08 and for 90 degree specimen orientation were 13.7 ± 7.7 kPa, 72.6 ± 35.4 kPa, 2.18 ± 4.12, 55.35 ± 7.12°, 0.22 ± 0.06, 23.51 ± 38.90 s, 81.52 ± 29.16 s, 5.14 ± 8.72, 0.21 ± 0.05, respectively. The validation revealed an overall good agreement from cycles 2 and 3 based on uniaxial tensile tests and surface strains data from DIC measurements with the material parameters from inverse analysis using FEA for the response in cycle 1. Conclusions: The identified material model and numerical simulations provide a comprehensive description of the viscoelastic behavior of the aortic wall tissue and a quantitative understanding of the spatial and directional variability underlying aortic tissue mechanical behavior. [ABSTRACT FROM AUTHOR]

Constitutive models exhibiting viscoelastic and micro-inertia with vortex viscosity effects are used for modeling of transport of heat energy, (angular and linear) with conservation laws for dust phase flow. The governing models are solved via the finite element method. The convergence of numerical solutions is guaranteed and mesh-free results are computed in view of a variation of physical parameters. Micro-rotations have shown a remarkable impact on shear stress and wall heat flux. The momentum relaxation (memory effects) time has shown a remarkable decrease in velocity associated with macro-flow. An increase in vortex viscosity increases angular motion. The Deborah number has shown a decreasing trend on flow. This causes a significant decrease in convective transport of heat energy. The temperature of dust particles increases when the ratio of specific heat and fluid particle interaction parameter for temperature is increased. However, the opposite behavior is noted for the case of increasing the relaxation time of the particle phase. The hybrid nanofluid transports much momentum than the momentum transported by mono-nanofluid. [ABSTRACT FROM AUTHOR]

We propose new methods for the determination of the thermal stressed state of viscoelastic bodies made of functionally graded materials subjected to annealing. We develop a numerical algorithm for the solution of the corresponding problem and realize it for the problems of heat conduction and thermoviscoelasticity. The thermal stressed state of a hollow cylinder is determined according to the given conditions of annealing. The variations of its temperature and stressed state are illustrated. [ABSTRACT FROM AUTHOR]

This contribution aims at developing a formulation for the large viscoelastic deformation of hyperelastic beams and frames under various loading and boundary conditions. To do so, the kinematics of deformation in two-dimensional space is formulated and basic kinematics and kinetic quantities are introduced. The quasi-linear viscoelasticity theory is employed to capture the time-dependent behavior of the underlying material. The corresponding time integration scheme and the consistent tangent moduli are then presented. Because of the highly nonlinear nature of governing equations at the large regime of deformations including time dependency, a nonlinear finite element formulation in the total Lagrangian framework is developed. Several numerical examples are provided to investigate the applicability of derived formulations. It is observed that the formulation can successfully capture the relaxation and creep phenomena in visco-hyperelastic beams and frames. [ABSTRACT FROM AUTHOR]

Recurrent neural network (RNN)-based accelerated prediction was achieved for the long-term time-dependent behavior of viscoelastic composite laminated Mindlin plates subjected to arbitrary mechanical and hygrothermal loading. Time-integrated constitutive stress-strain relation was simplified via Laplace transform to a linear system to reduce the computational storage. A fast converging smooth finite element method named cell-based smoothed discrete shear gap was employed to enhance the data generation procedure for straining RNNs with a sparse mesh. This technique is applicable under varying hygrothermal conditions for real engineering structure problems with fluctuating temperature and moisture. Hence, accurate RNN-based long-term deformation prediction for laminated structures was realized using the history of environmental temperature and moisture condition. [ABSTRACT FROM AUTHOR]

Polyamide exhibits hygroscopic nature and can absorb up to 10% of moisture relative to its dry weight. The absorbed moisture increases the mobility of the molecular chains and causes a reduction in the glass transition temperature. Thus, depending on the moisture distribution, a polyamide component can show different stiffness and relaxation times. Moreover, the moisture distribution also depends on the mechanical loading of the material as the volumetric deformation results in a change of the available free volume for the moisture. Thus, a strongly coupled model is required to describe the material behaviour. In this work, a thermodynamically consistent coupled model within the framework of mixture theory is developed. The mechanical deformation of polyamide 6 (PA6) is based on a linear viscoelastic material model, and the moisture transport is based on a nonlinear diffusion model. The stiffness and the relaxation time of the viscoelastic model change with the moisture concentration. Furthermore, the moisture transport is affected by the pressure gradient generated by the mechanical loading of the material. This strongly coupled model has been implemented using the finite element method, and simulation results are presented for a three-point bending experiment. [ABSTRACT FROM AUTHOR]

Composite materials consisting of negative-stiffness inclusions in positive-stiffness matrix may exhibit anomalous effective coupled-field properties through the interactions of the positive and negative phases, giving rise to extremely large or small effective properties. In this work, effective viscoelastic properties of a continuum composite system under the effects of negative inclusion Young's modulus ratio λ E = E inc / E matrix are studied with the finite element method. Furthermore, effective coupled-field properties, such as thermal expansion coefficient, dielectric constants and piezeoelectric constants, are numerically calculated under the effects of negative inclusion bulk modulus ratio λ K = K inc / K matrix . Stability boundaries are determined by applying small dynamic perturbation to the systems through boundary surfaces, and the system is unstable if its field variables become divergent in time. For viscoelastic composite systems containing small volume fractions, less than V i = 1.5 % , the systems can be stable up to λ E ≈ - 0.3 in 0.3 s under 10 Hz driving frequency. For V i = 5.1 % case, its stability boundary is around λ E ≈ 0 . Larger inclusion volume fraction reduces allowable negative stiffness in the viscoelastic system. All anomalous peaks found in the coupled-field properties are in the unstable regime, except for the piezoelectric and thermal-expansion anomalies in the composite system with electrically insulated inclusions and large inclusion volume fraction V i = 26.81 % . Insulated inclusions may cause charge accumulation at the inclusion–matrix interface and boundary surface effects may serve as stabilizing agents to the composite system. Since it is known that negative-stiffness composite is unstable in the purely elastic system in statics, stability enhancement found here in the negative-stiffness systems with viscoelastic and coupled-field effects may be considered as multiphysics-induced stabilization. [ABSTRACT FROM AUTHOR]

We consider a fractional order viscoelasticity problem modelled by a power-law type stress relaxation function. This viscoelastic problem is a Volterra integral equation of the second kind with a weakly singular kernel where the convolution integral corresponds to fractional order differentiation/integration. We use a spatial finite element method and a finite difference scheme in time. Due to the weak singularity, fractional order integration in time is managed approximately by linear interpolation so that we can formulate a fully discrete problem. In this paper, we present a stability bound as well as a priori error estimates. Furthermore, we carry out numerical experiments with varying regularity of exact solutions at the end. [ABSTRACT FROM AUTHOR]

A technique is developed for identifying the hereditary properties of technical rubber in short-term shear creep from the experimental shift the center of damped flexural vibrations of a vertically fixed three-layer test specimens of symmetrical structure with a technical rubber midlayer after their preliminary holding in a static bent state. This technique is based on the finite element method and integral equations of the hereditary viscoelasticity theory with the Koltunov–Rzhanitsyn heredity kernel. For identifying the rheological parameters of this kernel an objective function is constructed. To minimize the function, the direct zero-order search is used, which does not require the calculation of its gradient. The rheological parameters found are compared with experimental data of the long-term shear creep of the rubber. Noted is the unfoundedness of the direction, developed by some researchers, where only equations of the theory of hereditary viscoelasticity is used to model the vibration processes and the energy dissipation. The parameters of rubber creep kernel were identified in a long-term regime at a constant shear stress, and results showed that this type of testing is inapplicable to studying the short-term creep of rubber in shear. [ABSTRACT FROM AUTHOR]

An investigation is carried out on natural cellulosic fibers which have gained interest in the composite field due to their superior specific properties as well as their eco-friendly environment character and biodegradability. A multi-scale finite element (FE) model of natural fiber composite materials is developed. The study is performed for multiple fibers in hexagonal packings with 10, 20, and 30% of fiber mass fractions. The mechanical behavior of the composite, processed by means of hand lay-up method and examined thanks to scanning electron microscopy (SEM), is simulated at macro-scale as well as mesoscopic scale. In particular, the response to tensile and three-point bending test is studied. Linear material properties are obtained by using pure strain assumptions in the implicit analysis of the composite, while the non-linear behavior and viscoelastic parameters require the explicit dynamic analysis. Simulation is performed thanks to ABAQUS finite element software. Comparison of experimental and FEM tensile and three-point bending strength shows very good agreement. From the results, it has been found that the prepared natural fiber composite materials can be used for structural engineering applications. [ABSTRACT FROM AUTHOR]

Deformation of soft polymeric materials often involves complex nonlinear or transient mechanical behaviors. This is due to the dynamic behaviors of polymer chains at the molecular level within the polymer network. In this paper, we present a computational formulation to describe the transient behavior (e.g., viscoelasticity) of soft polymer networks with dynamic bonds undergoing large to extreme deformation. This formulation is based on an Eulerian description of kinematics and a theoretical framework that directly connects the molecular-level kinetics of dynamic bonds to the macroscopic mechanical behavior of the material. An extended finite element method is used to discretize the field variables and the governing equations in an axisymmetric domain. In addition to validating the framework, this model is used to study how the chain dynamics affect the macroscopic response of material as they undergo a combination of flow and elasticity. The problems of cavitation rheology and polymer indentation under extreme deformation are investigated in this context. [ABSTRACT FROM AUTHOR]

Highlights • A new hybrid damper composed of elastomeric layers and metallic links is presented. • The proposed hybrid damper is effective for multi-level vibration control. • The operational mechanism of hybrid damper resolves the limitations of VED and MD. • The behavior of hybrid damper is evaluated by experimental and numerical analysis. Abstract In this study, a new hybrid damper (HD) is introduced that consists of elastomeric layers, which act as a viscoelastic damper (VED), and metallic dampers (MDs). Metallic part is composed of flexural yielding strips. This HD not only removes the limitations of each of these two types of dampers, but also facilitates its application for multi-level vibration control. Based on operational mechanism and design objectives of the proposed HD, three specimens have been manufactured and tested under quasi-static cyclic loading to evaluate the functional objectives. Two types of elastomers and two types of metallic dampers are used in these specimens. Experimental results show stable hysteretic behavior and high energy dissipation capacity. Also, the multi-phase behavior of the proposed HD confirms the proper function that is intended. However, the HD that is made of natural rubber (NR) and comb-teeth damper (CTD) can tolerate more cycles and possesses more ductility in comparison with the HD made of butyl rubber (IIR) and steel slit damper (SSD). A finite element model (FEM) is also used to simulate the behavior of the proposed HD. A good correlation between numerical outputs, analytical equations and experimental results indicates the accuracy of the proposed FEM. [ABSTRACT FROM AUTHOR]

Micromechanical models can be used to calculate the mechanical properties of short glass fiber reinforced thermoplastics. In the present work, a three-step framework is used to validate a three-phases micromechanical model (RDI model) in the time domain, since the analysis of technical components by the finite element method is usually carried out in the time domain. The framework includes mechanical characterization, the implementation of the RDI model and a finite element analysis. The characterization delivers necessary information about the material phases of the composite. A dynamic mechanical analysis is performed to characterize the matrix material in order to obtain the linear viscoelastic properties. The mechanical properties of the matrix-fiber interphase are determined with an inverse calculation. In the second step, the RDI model is used to calculate the frequency depended effective stiffness of the composite. A new developed approach transforms the effective stiffness from the frequency domain into the time domain thus avoiding an explicit inverse Laplace-Carson transformation. In the third step, the RDI model is experimentally validated. [ABSTRACT FROM AUTHOR]

Detailed finite element (FE) models are used as promising tools to investigate traumatic brain injuries, although their accuracy is strongly dependent on the characterization of the mechanical behaviors of the different anatomic structures in the brain. In some cases, when the FE models require finer spatial resolution, the heterogeneous and anisotropic corona radiata cannot be taken as a homogeneous whole body. In this work, indentation experiments were conducted on the anterior, superior, and posterior regions of the corona radiata in the sagittal plane. To determine the parameters available for computational modeling purposes, a linear viscoelastic model using the Boltzmann hereditary integral was fitted to the force-time data of the three regions. In the indentation tests, the superior region appeared to be the stiffest, while no significant differences were observed between the anterior and posterior regions until the viscoelastic tissue reached equilibrium. During the period of relaxation, statistical comparisons among the different regions indicated significant differences between the superior and anterior regions, and between the superior and posterior regions. This work complements existing investigations into the anatomic heterogeneity of the brain, and contributes toward improving the spatial resolution of future computational models. Graphical abstract Relaxation functions of different regions based on the Prony series parameters and the multiregional Kolmogorov-Smirnov comparisons (*p < 0.017). The anisotropy and interregional differences of the corona radiata observed in this study are supplementary to the previous explorations of the mechanical properties of different brain anatomic structures. [ABSTRACT FROM AUTHOR]

Surface roughness is one of the critical parameters that affect the component performance during its working life. To develop any process to its full potential, it is necessary to understand the physics of that process. Abrasive flow finishing (AFF) is one of the advanced finishing processes. In the current research work, an effort is made to understand physics and mechanism of surface roughness improvement during the AFF process. This research paper is divided into two sections. Firstly, the amount of finishing stresses and forces generated during the finishing of microholes fabricated on surgical stainless steel (316L) workpieces are computed by using the finite element method. Finishing stresses are generated in the viscoelastic medium. So, to compute finishing stresses, finite element analysis of the viscoelastic medium is carried out by incorporating its experimentally measured rheological properties. Finishing stresses are calculated along the circumferential direction of the microhole. Later, at the same workpiece surface location, simulated and experimentally measured surface roughness value are compared. Secondly, a new simulation model is proposed to predict the surface roughness on the microhole wall surface for various AFF input parameters. Maximum percentage change in surface roughness error of 8% is observed between simulated and experimental results after AFF process. [ABSTRACT FROM AUTHOR]

Viscosity effects on the mechanical behaviour of functionally graded (FG) Timoshenko microbeams are investigated; the model possesses both linear nonlinear viscous terms. The Mori-Tanaka homogenisation method is used for the continuous variations of the material properties of the microsystem along the thickness; the Kelvin-Voigt scheme is employed for the internal damping; the shear deformation and rotary inertia are modelled for the viscoelastic microbeam via the Timoshenko theory; the modified couple stress theory is used for size influences. An energy loss/balance via Hamilton's principle is used for obtaining the equations of motion. Galerkin's approach together with a continuation method is employed for the mechanical responses. The simultaneous effects of viscosity, being small, and FG materials on the mechanical behaviour are investigated. [ABSTRACT FROM AUTHOR]

There has recently been a rising interest in the nonlinear wave transmission behavior of phononic crystals. However, experimental studies focusing on the nonlinear wave transmission behavior of phononic crystals have been predominantly performed on 1-D granular crystals using customized impact apparatus. In this study, we explore split Hopkinson pressure bar (SHPB) apparatus as a tool to study the nonlinear wave characteristics of a 1-D continuum viscoelastic phononic crystal. In order to resolve experimental challenges relating to signal-to-noise ratios and input impulse magnitudes, we propose a hybrid SHPB system composed of an aluminum input bar and a nylon output bar. For a considered viscoelastic phononic crystal, the application of the hybrid SHPB apparatus enabled us to observe some low transmission frequency zones, which were not identified from the linearly perturbed settings such as the analytical solution and the electrodynamic shaker tests. We further conducted a series of additional FE simulations to ensure the appearance of impulse-dependent low transmission frequency zones of the considered viscoelastic phononic crystal specimen. The additional sets of simulations evidently illustrate the impulse-dependent evolution of wave transmission coefficients, and demonstrate that the impulse-dependent wave transmission behavior can be experimentally investigated by adopting the hybrid SHPB apparatus. Thus, this study shows that the conventional SHPB apparatus can be employed effectively to study the emerging research field of nonlinear wave characteristics of phononic crystals. [ABSTRACT FROM AUTHOR]

Working mechanisms of the cardiac defibrillation are still in debate due to the limited experimental facilities and one-third of patients even do not respond to cardiac resynchronization therapy. With an aim to develop a milestone towards reaching the unrevealed mechanisms of the defibrillation phenomenon, we propose a bidomain based finite element formulation of cardiac electromechanics by taking into account the viscous effects that are disregarded by many researchers. To do so, the material is deemed as an electro-visco-active material and described by the modified Hill model (Cansız et al. in Comput Methods Appl Mech Eng 315:434-466, 2017). On the numerical side, we utilize a staggered solution method, where the elliptic and parabolic part of the bidomain equations and the mechanical field are solved sequentially. The comparative simulations designate that the viscoelastic and elastic formulations lead to remarkably different outcomes upon an externally applied electric field to the myocardial tissue. Besides, the achieved framework requires significantly less computational time and memory compared to monolithic schemes without loss of stability for the presented examples. [ABSTRACT FROM AUTHOR]

This paper presents a numerical simulation of the laser shock peening (LSP) process using the finite element method. The majority of controlling parameters of the LSP process have been taken into account. The LSP loading has been characterized by the use of a repetitive time Gaussian increment pressure applied uniformly at a circular impacted zone. The utilized model of the treated material behaviour law is the Johnson-Cook’s visco-elastic-plastic coupled with damage. The proposed model leads to determine the LSP surface modifications: (i) the in-depth residual stresses, (ii) the induced plastic strains and (iii) the superficial damage. These modifications can be significantly induced in few cases, particularly when the operating conditions are not well optimized. An application is carried out on the laser peened titanium aero-engine super alloy Ti-6Al-4V. A satisfactory correlation between the computed and experimental results is observed. Also, it is noted that the computed superficial damage values increase with the growth of the maximal peak pressure of the laser spot, which are physically consistent. Otherwise, in order to optimize the laser peening operating conditions, a design of experiments is established. It allows having surface-response relationships between the operating parameters and the three announced induced effects. [ABSTRACT FROM AUTHOR]

The problem of structural design of polymeric and composite viscoelastic materials is currently of great interest. The development of new methods of calculation of the stress-strain state of viscoelastic solids is also a current mathematical problem, because when solving boundary value problems one needs to consider the full history of exposure to loads and temperature on the structure. The article seeks to build an iterative algorithm for calculating the stress-strain state of viscoelastic structures, enabling a complete separation of time and space variables, thereby making it possible to determine the stresses and displacements at any time without regard to the loading history. It presents a modified theoretical basis of the iterative algorithm and provides analytical solutions of variational problems based on which the measure of the rate of convergence of the iterative process is determined. It also presents the conditions for the separation of space and time variables. The formulation of the iterative algorithm, convergence rate estimates, numerical computation results, and comparisons with exact solutions are provided in the tension plate problem example. [ABSTRACT FROM AUTHOR]

To evaluate and analyze the pedestrian injury risk of automobiles, the finite element models of headform impactors are used. In this study, a modeling method that can accurately estimate the peak of the headform impactor impact pulse and head injury criterion (HIC) was developed. The headform impactor skin has the characteristics of both hyperelasticity and viscoelasticity. Therefore, compression tests, stress relaxation tests, and rheometer tests were conducted, and the hyperelastic and viscoelastic models were developed. The models were combined and used in the finite element analysis. The new headform impactor model was verified to accurately estimate the peak of impact pulse and HIC at the certification test of the headform impactor. [ABSTRACT FROM AUTHOR]

Discrete models such as the lumped parameter model and the finite element model are widely used in the solution of soil amplification of earthquakes. However, neither of the models will accurately estimate the natural frequencies of soil deposit, nor simulate a damping of frequency independence. This research develops a new discrete model for one-dimensional viscoelastic response analysis of layered soil deposit based on the mode equivalence method. The new discrete model is a one-dimensional equivalent multi-degree-of-freedom (MDOF) system characterized by a series of concentrated masses, springs and dashpots with a special configuration. The dynamic response of the equivalent MDOF system is analytically derived and the physical parameters are formulated in terms of modal properties. The equivalent MDOF system is verified through a comparison of amplification functions with the available theoretical solutions. The appropriate number of degrees of freedom (DOFs) in the equivalent MDOF system is estimated. A comparative study of the equivalent MDOF system with the existing discrete models is performed. It is shown that the proposed equivalent MDOF system can exactly present the natural frequencies and the hysteretic damping of soil deposits and provide more accurate results with fewer DOFs. [ABSTRACT FROM AUTHOR]

While predicting the impact force histories from the Zener impact model with different material properties of impactors, several discrepancies were observed and reported in this article. To overcome these discrepancies, a modified Zener model is proposed to accurately calculate impact force histories. In the original Zener theory, nonlinear Hertzian contact law was used, and it was assumed that impact forces are transmitted through natural intensity factors depending on coupled physical properties of the plate and the impactor. However, when the force histories were predicted, a diverging trend appeared for softer materials with elastic moduli below 20 GPa. It is hypothesized that the primary reasons for this divergence are due to the contact time delay and the viscoelastic dissipation of energy, which are not considered in current Zener models. Several modifications of the model have been proposed since its inception, but it has been found that they are not independently sufficient to accurately predict impact force histories. In this article, a modified Zener theory is proposed introducing two new parameters in the governing differential equation derived from the sensor phase lag index and the dominant frequency band through a set of experiments employing a spiral sensing mechanism followed by an optimization process. The spiral lag index shows an unexpected peculiar trend with soft impactors (< 20 GPa), which are distinctly different from hard impactors and are judicially incorporated in the model. Furthermore, the force histories are accurately reconstructed with the proposed modifications. [ABSTRACT FROM AUTHOR]

The mechanical properties of Composite solid propellant (CSP) are the critical material parameters to analyze the structural integrity of propellant grains, and have a significant influence on the life and reliability of solid rocket motors. A Voronoi cell finite element method using an adaptive algorithm in the time domain is proposed for investigating the linear viscoelasticity of CSP in the present paper. A process is brought forward to produce a Representative volume element (RVE) model, which reflects the microstructural features of CSP. Numerical viscoelastic examples are used for varying the accuracy of this method. In addition, finite element simulations are conducted to understand the effect of microstructural morphology and material properties of inclusion on the effective mechanical properties of CSP using the new method. When this method is applied to the design process of CSP, it can reduce the design cost and shorten the design cycle effectively. The current microscopic numerical analysis method can be used to provide guidance for designing and analyzing the mechanical properties of composite viscoelastic materials. [ABSTRACT FROM AUTHOR]

The stability and convergence of a linearly extrapolated second order backward difference (BDF2-LE) time-stepping scheme for solving viscoelastic fluid flow in $\mathbb{R}^{d}$ , $d=2,3$ , are presented in this paper. The time discretization is based on the implicit scheme for the linear term and the two-step linearly extrapolated scheme for the nonlinear term. Mixed finite element (MFE) method is applied for the spatial discretization. The approximations of stress tensor σ, velocity vector u and pressure p are $P_{m}$ -discontinuous, $P_{k}$ -continuous and $P_{q}$ -continuous elements, respectively. Upwinding needed for convection of σ is made by a discontinuous Galerkin (DG) FE method. For the time step △ t small enough, the existence of an approximate solution is proven. If $m, k \geqslant \frac{d}{2}$ , $q+1\geqslant\frac{d}{2}$ , and $\triangle t \leqslant C_{0} h^{\frac{d}{4}}$ , then the discrete $H^{1}$ and $L^{2}$ errors for the velocity and stress, and $L^{2}$ error for the pressure, are bounded by $C(\triangle t^{2}+h^{\min\{m,k,q+1\}})$ , where h denotes the mesh size. The derived theoretical results are supported by numerical tests. [ABSTRACT FROM AUTHOR]

In this study, we first present a classical finite element (FE) method for a two-dimensional (2D) viscoelastic wave equation and analyze the existence, stability, and convergence of the FE solutions. Then we establish an optimized FE extrapolating (OFEE) method based on a proper orthogonal decomposition (POD) method for the 2D viscoelastic wave equation and analyze the existence, stability, and convergence of the OFEE solutions and furnish the implement procedure of the OFEE method. Finally, we furnish a numerical example to verify that the numerical computing results correspond with the theoretical ones. This signifies that the OFEE method is feasible and efficient for solving the 2D viscoelastic wave equation. [ABSTRACT FROM AUTHOR]

The paper is devoted to non-linear vibrations of plates, made of the Zener viscoelastic material modelled with the Caputo fractional derivative, and in particular to their response to harmonic excitation. The plate geometric non-linearity is of the von Kármán type. In the formulation shear effects and rotary inertia are considered, too. The problem is solved in the frequency domain. A one-harmonic form of the solution for plate displacements corresponding to the plate formulation is assumed. The amplitude equation is obtained from the time averaged principle of virtual work. The time averaging precedes the use of the harmonic balance method. In the space discretization the finite element method is used involving 8-noded rectangular plate elements with selective-reduced integration. Several numerical examples are analyzed and the response curves are found using a path-following method. The purpose of these analyses is to identify material features of the adopted model of viscoelasticity with the fractional derivative. [ABSTRACT FROM AUTHOR]

We propose mixed finite element methods for the standard linear solid model in viscoelasticity and prove a priori error estimates. In our mixed formulation the governing equations of the problem become a symmetric hyperbolic system, so we can use standard techniques for a priori error estimates and time discretization. Numerical results illustrating our theoretical analysis are included. [ABSTRACT FROM AUTHOR]

In this study, we first establish a stabilized mixed finite element (SMFE) model based on parameter-free and two local Gauss integrals for the two-dimensional (2D) nonlinear incompressible viscoelastic fluid system. And then, we prove the existence, uniqueness, and convergence of the SMFE solutions. Finally, we use a numerical example to verify the correctness of the previous theoretical results. [ABSTRACT FROM AUTHOR]

An optimized splitting positive definite mixed finite element (SPDMFE) extrapolation approach based on proper orthogonal decomposition (POD) technique is developed for the two-dimension viscoelastic wave equation (2DVWE). The errors of the optimized SPDMFE extrapolation solutions are analyzed. The implement procedure for the optimized SPDMFE extrapolation approach is offered. Some numerical simulations have verified that the numerical conclusions are accordant with theoretical ones. This implies that the optimized SPDMFE extrapolation approach is viable and valid for solving 2DVWE. [ABSTRACT FROM AUTHOR]

Trabecular bone has been previously recognized as time-dependent (viscoelastic) material, but the relationships of its viscoelastic behaviour with bone volume fraction (BV/TV) have not been investigated so far. Therefore, the aim of the present study was to quantify the time-dependent viscoelastic behaviour of trabecular bone and relate it to BV/TV. Uniaxial compressive creep experiments were performed on cylindrical bovine trabecular bone samples ( $$\textit{n}\,{=}\,13$$ ) at loads corresponding to physiological strain level of 2000 $${\upmu }{\upvarepsilon }$$ . We assumed that the bone behaves in a linear viscoelastic manner at this low strain level and the corresponding linear viscoelastic parameters were estimated by fitting a generalized Kelvin-Voigt rheological model to the experimental creep strain response. Strong and significant power law relationships ( $$r^2\,{=}\,0.73,\ p\,{<}\,0.001$$ ) were found between time-dependent creep compliance function and BV/TV of the bone. These BV/TV-based material properties can be used in finite element models involving trabecular bone to predict time-dependent response. For users' convenience, the creep compliance functions were also converted to relaxation functions by using numerical interconversion methods and similar power law relationships were reported between time-dependent relaxation modulus function and BV/TV. [ABSTRACT FROM AUTHOR]

In this paper, the phenomena of resorption and growth of bone tissue and resorption of the biomaterial inside a bicomponent system are studied by means of a numerical method based on finite elements. The material behavior is described by a poro-viscoelastic model with infiltrated voids. The mechanical stimulus that drives these processes is a linear combination of density of strain energy and viscous dissipation. The external excitation is represented by a bending load slowly variable with sinusoidal law characterized by different frequencies. Investigated aspects are the influence of the load frequency, of type of the stimulus and of the effective porosity on the time evolution of the mass densities of considered system. [ABSTRACT FROM AUTHOR]

The propagation characteristics of laser-generated Lamb waves in multilayered fiber-reinforced composite plates with different fiber orientations and number of layers have been investigated quantitatively. Considering the viscoelasticity of the composite materials, we have set up finite element models for simulating the laser-generated Lamb waves in two types of the multilayered composite plates. In the first type, different fiber orientations are adopted. In the second one, different number of layers are considered. The results illustrate the occurrence of attenuation and dispersion, which is induced by the viscoelasticity and multilayer structure, respectively. [ABSTRACT FROM AUTHOR]

In order to gain a deeper knowledge of the interactions in the coupled tire-pavement-system, e.g. for the future design of durable pavement structures, the paper presents recent results of research in the field of theoretical-numerical asphalt pavement modeling at material and structural level, whereby the focus is on a realistic and numerically efficient computation of pavements under rolling tire load by using the finite element method based on an Arbitrary Lagrangian Eulerian (ALE) formulation. Inelastic material descriptions are included into the ALE frame efficiently by a recently developed unsplit history update procedure. New is also the implementation of a viscoelastic cohesive zone model into the ALE pavement formulation to describe the interaction of the single pavement layers. The viscoelastic cohesive zone model is further extended to account for the normal pressure dependent shear behavior of the bonding layer. Another novelty is that thermo-mechanical effects are taken into account by a coupling of the mechanical ALE pavement computation to a transient thermal computation of the pavement cross-section to obtain the varying temperature distributions of the pavement due to climatic impact. Then, each ALE pavement simulation considers the temperature dependent asphalt material model that includes elastic, viscous and plastic behavior at finite strains and the temperature dependent viscoelastic cohesive zone formulation. The temperature dependent material parameters of the asphalt layers and the interfacial layers are fitted to experimental data. Results of coupled tire-pavement computations are presented to demonstrate potential fields of application. [ABSTRACT FROM AUTHOR]

In this article, we establish a space-time continuous finite element (STCFE) method for viscoelastic wave equation. The existence, uniqueness, and stability of the STCFE solutions are proved, and the optimal rates of convergence of STCFE solutions are obtained without any time and space mesh size restrictions. Two numerical examples on unstructured meshes are employed to verify the efficiency and feasibility of the STCFE method and to check the correctness of theoretical conclusions. [ABSTRACT FROM AUTHOR]

Rubbers are commonly used in industry to reduce vibration transfer and, consequently, reduce structural noise. The vibration transfer through rubber can be modelled with finite elements; however, to achieve satisfactory results it is necessary to know the viscoelastic properties of the rubber. This paper describes the commonly used theory of vibration transmission through rubber modelled as a single-degree-of-freedom (SDOF) system. Three simplified rubber models are used to identify the constant Young's modulus and damping factor from the measurements of two different rubber specimens, and with the obtained results the theoretical transmissibilities are calculated. The frequency-dependent Young's modulus and damping factor are also calculated from measurements. The practical use of previous measurements of dynamic material properties is presented in a finite-element analysis, where three different definitions of the dynamic material properties are carried out for four different rubber specimens, which corresponds to 12 analyses. The finite-element analyses are then compared with the measurements, and general guidelines for using dynamic material properties in ANSYS Workbench v.14 are given. [ABSTRACT FROM AUTHOR]

The correspondence principle is an important mathematical technique to compute the non-ageing linear viscoelastic problem as it allows to take advantage of the computational methods originally developed for the elastic case. However, the correspondence principle becomes invalid when the materials exhibit ageing. To deal with this problem, a second-order two-scale (SOTS) computational method in the time domain is presented to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. First, in the time domain, the SOTS formulation for calculating the effective relaxation modulus and displacement approximate solutions of the ageing viscoelastic problem is formally derived. Error estimates of the displacement approximate solutions for SOTS method are then given. Numerical results obtained by the SOTS method are shown and compared with those by the finite element method in a very fine mesh. Both the analytical and numerical results show that the SOTS computational method is feasible and efficient to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. [ABSTRACT FROM AUTHOR]

The remarkable mechanical properties of cartilage derive from an interplay of isotropically distributed, densely packed and negatively charged proteoglycans; a highly anisotropic and inhomogeneously oriented fiber network of collagens; and an interstitial electrolytic fluid. We propose a new 3D finite strain constitutive model capable of simultaneously addressing both solid (reinforcement) and fluid (permeability) dependence of the tissue's mechanical response on the patient-specific collagen fiber network. To represent fiber reinforcement, we integrate the strain energies of single collagen fibers-weighted by an orientation distribution function (ODF) defined over a unit sphere-over the distributed fiber orientations in 3D. We define the anisotropic intrinsic permeability of the tissue with a structure tensor based again on the integration of the local ODF over all spatial fiber orientations. By design, our modeling formulation accepts structural data on patient-specific collagen fiber networks as determined via diffusion tensor MRI. We implement our new model in 3D large strain finite elements and study the distributions of interstitial fluid pressure, fluid pressure load support and shear stress within a cartilage sample under indentation. Results show that the fiber network dramatically increases interstitial fluid pressure and focuses it near the surface. Inhomogeneity in the tissue's composition also increases fluid pressure and reduces shear stress in the solid. Finally, a biphasic neo-Hookean material model, as is available in commercial finite element codes, does not capture important features of the intra-tissue response, e.g., distributions of interstitial fluid pressure and principal shear stress. [ABSTRACT FROM AUTHOR]

Visco-elastic material models with fractional characteristics have been used for several decades. This paper provides a simple methodology for Finite-Element-based dynamic analysis of structural systems with viscosity characterized by fractional derivatives of the strains. In particular, a re-formulation of the well-known Newmark method taking into account fractional derivatives discretized via the Grünwald-Letnikov summation allows the analysis of structural systems using standard Finite Element technology. [ABSTRACT FROM AUTHOR]

Hood stiffness scanning tests were conducted and numerical modeling of hoods was implemented to simulate hoods having the same stiffness as the test results in order to predict the hood surface deflections occurring during the dipping process among automobile manufacturing processes through the finite element analysis (FEA). The flow stress of the mastic sealer and the hemming sealer was measured through viscosity tests to express the material properties of the adhesive and decreases in the thickness of inner panels were reflected in order to accurately calculate surface deflections. The yield stress of the hemming part and the width of the master sealer were selected as virtual joining properties so that joint complexity and singularity could be compensated for. The virtual joining properties were applied to a total of six hood models and tendencies that correspond to individual hood models were analyzed to define tendency functions thereby presenting a method of predicting virtual properties without undergoing stiffness scanning test and analysis processes. When the results of analyses that predicted surface deflections after dipping processes were compared to 3D-scanning results, the results of analyses were found to have accuracy not lower than 85%. In addition, analyses to predict surface deflections after the dipping process were conducted using numerical models that reflected inner panels with reinforced stiffness and decreases in surface deflections were identified according to the results. Therefore, the fact that designs for reducing surface deflections after the dipping process could be made utilizing the technique implemented in the present study to predict permanent deformation of hoods was proved. [ABSTRACT FROM AUTHOR]

Finite element modeling (FEM) of machining has recently become the most attractive computational tool to predict and optimize metal cutting processes. High-speed computers and advanced finite element code have offered the possibility of simulating complex machining processes such as turning, milling, and drilling. The use of an accurate constitutive law is very important in any metal cutting simulation. It is desirable that a constitutive law could completely characterize the thermo-visco-plastic behavior of the machined materials at high strain rate. The most commonly used law is that of Johnson and Cook (JC) which combines the effect of strains, strain rates, and temperatures. Unfortunately, the different coefficients provided in the literature for a given material are not reliable since they affect significantly the predicted results (cutting forces, temperatures, residual stresses, etc.). In the present work, five different sets of JC are determined based on orthogonal machining tests. These five sets are then used in finite element modeling to simulate the machining behavior of Al2024-T3 alloy. The effects of these five different sets of JC constants on the numerically predicted cutting forces, chip morphology, and tool-chip contact length are the subject of a comparative investigation. It is concluded that these predicted cutting parameters are sensitive to the material constants. [ABSTRACT FROM AUTHOR]

In the present study, nanoindentation and macroindentation tests are performed on a soft polymer: polyurethane (PU). Strong viscoelasticity is represented by the force-displacement data on both scales. A finite element method based on an inverse procedure is employed to identify the nonlinear viscoelasticity of PU. An appropriate viscoelastic model is chosen, and the corresponding parameters are identified by matching the experimental responses with the predictions of the computational model. At the very beginning, the uniaxial tensile test, which has a homogeneous deformation, is used to prove the isotropic properties and incompressibility of PU and to identify the viscoelasticity as a reference and verification source. The comparison between the identified results from nanoindentation and macroindentation allows to quantifying the adhesion effects in nanoindentation. The quantification is treated with a traction-separation relationship incorporated into the numerical adhesive contact model. Comparable strain rates in the macro-, nanoindentation and uniaxial tensile tests are considered to identify the viscoelasticity. [ABSTRACT FROM AUTHOR]

In this paper a purely phenomenological formulation and finite element numerical implementation for quasi-incompressible transversely isotropic and orthotropic materials is presented. The stored energy is composed of distinct anisotropic equilibrated and non-equilibrated parts. The nonequilibrated strains are obtained from the multiplicative decomposition of the deformation gradient. The procedure can be considered as an extension of the Reese and Govindjee framework to anisotropic materials and reduces to such formulation for isotropic materials. The stress-point algorithmic implementation is based on an elastic-predictor viscous-corrector algorithm similar to that employed in plasticity. The consistent tangent moduli for the general anisotropic case are also derived. Numerical examples explain the procedure to obtain the material parameters, show the quadratic convergence of the algorithm and usefulness in multiaxial loading. One example also highlights the importance of prescribing a complete set of stress-strain curves in orthotropic materials. [ABSTRACT FROM AUTHOR]

Simulations of blood flows in arteries require numerical solutions of fluidstructure interactions involving Navier-Stokes equations coupled with large displacement visco-elasticity for the vessels. Among the various simplifications which have been proposed, the surface pressure model leads to a hierarchy of simpler models including one that involves only the pressure. The model exhibits fundamental frequencies which can be computed and compared with the pulse. Yet unconditionally stable time discretizations can be constructed by combining implicit time schemes with Galerkin-characteristic discretization of the convection terms in the Navier-Stokes equations. Such problems with prescribed pressure on the walls will be shown to be efficient and accurate as an approximation of the full fluid structure interaction problem. [ABSTRACT FROM AUTHOR]

Employing a finite element computing scheme implemented onto the Leonov viscoelastic model, we newly describe various kinds of melt fracture for the extrudate exiting from the Poiseuille flow in the contraction channel with wall slip ignored. Four types such as sharkskin, gross melt fracture, slow surface undulation, and ripples are found depending on the flow conditions like the flow rate and liquid property, and they are expressed as 2D elastic instability in this inertialess flow regime. Even though not considered, the effect of die wall slip has to be included in the realistic modeling of melt fracture. However, here, we make the first attempt to analyzing extrudate instability in terms of purely fluid mechanical factors. As a result, each type of melt fracture is verified to result from the different origin, and thus, geometric singularities and streamline vortices at contraction corner and die exit determine this type of extrudate distortion. [ABSTRACT FROM AUTHOR]