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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]

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]

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]

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]

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]

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]

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]

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 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]

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]

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]

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]

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]

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]

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 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]

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 study, two different thermoforming molds, i.e., male and female, were prepared and used to conduct different tests at various heating times and evacuation powers. High impact polystyrene sheets of 0.5 mm thick were used to produce the cups with two vacuum and drape forming process. The experimental results showed that a more uniform thickness distribution could be obtained by increasing the heating time for the female mold. However, for the male mold, the heating time must be decreased in order to achieve a more uniform thickness distribution. Our findings showed that biaxial stretching was dominant in the vacuum forming, while uniaxial stretching was dominant in the drape forming. A finite element simulation of the vacuum forming process was also conducted to present a simple and accurate study of the forming process. In this work, a hyperviscoelastic constitutive model was used for modeling the high impact polystyrene behavior at forming temperature. The thickness distribution obtained by the finite element analysis is in a good agreement with the experimental results. In addition, the effect of friction coefficient was investigated by finite element analysis on the thickness distribution of the cup. [ABSTRACT FROM AUTHOR]

Polyimide is widely used as the dielectric material in wafer level packaging. One potential problem with its application is the warpage and stress generated in the curing process. This paper investigated the material properties of polyimide and its influence on the wafer warpage. The viscoelastic properties of polyimide film were measured and a mathematical model of the properties was developed. Finite element analysis of the wafer warpage was performed and this indicates that the viscoelastic material model gave the best prediction. To better understand the causation of the warpage, curvature evolution of the polyimide-coated silicon wafer during its curing process was measured by a multi-beam optical sensor system. It was found that the warpage was mainly induced by the coefficient of thermal expansion mismatch and that the cure shrinkage of polyimide had little effect. Additionally, the effect of the cooling rate on the wafer warpage was also studied. Both simulation and experiment results showed that a slower cooling rate in the temperature range around the glass transition temperature ( T) of polyimide will help to reduce the final wafer warpage. [ABSTRACT FROM AUTHOR]

In this paper, we present a stabilized lowest equal-order mixed finite element (FE) method for the Oseen viscoelastic fluid flow obeying an Oldroyd-B type constitutive law. To approximate the velocity, pressure, and stress tensor, we choose lowest equal-order FE triples p1−p1−p1dg respectively. It is well known that these elements don't satisfy the inf-sup (or LBB) condition. Owing to the violation of the essential stability condition, the system became unstable. To overcome this difficulty, a standard pressure stabilization term is added to the discrete variational formulation, which ensures the well-posedness of the FE scheme. The existences and uniqueness of the FE scheme are derived. The desired optimal error bound is obtained. Three numerical experiments are executed to illustrate the validity and efficiency of the numerical method. The stabilized method provides attractive computational advantages, such as simpler data structures, parameter-free, no calculations of higher-order derivatives, and fast solver in simulations. [ABSTRACT FROM AUTHOR]