Behavior Of Viscoelastic Materials Research Articles

Adhesion, Friction and Lubrication of Viscoelastic Materials

The mechanical behavior of viscoelastic materials is a key factor of many physical phenomena occurring at the interface of contacting bodies [...]

Extrudate shape of three-dimensional viscoelastic, non-isothermal extrusion flows

A 3D transient non-isothermal finite element code is developed to predict the extrudate shape of viscoelastic fluids emerging from an asymmetric keyhole shaped die. The corner-line method is employed to model the movement of the free surfaces. The code is tested using two benchmark problems. First the corner-line method is tested employing a trumpet shaped object during a 3D uniaxial extensional flow. Secondly, the implementation of the energy balance and therefore the viscoelastic material behaviour is tested employing a non-isothermal pipeflow. For both benchmark problems convergence was obtained, giving confidence that the 3D non-isothermal swell problem is correctly implemented. The influence of shear-thinning, elasticity and temperature on the form of the extrudate is systematically studied. Results are shown for isothermal flows also as for non-isothermal flows, with isothermal and non-isothermal die walls. Results for isothermal die walls show increasing extrudate swelling with increasing elasticity which the swelling opposes extrudate bending. Shear-thinning on the opposite hand, opposes swelling, which initially promotes bending, but also flattens the asymmetric velocity profile, resulting in less extrudate bending for top amounts of shear-thinning. Furthermore, extrudate bending was observed even for purely viscous, isothermal extrudates, suggesting that bending is caused by asymmetry within the viscous stresses. Extrudate swelling are often influenced by the wall temperature of the die and non-isothermal die walls can cause a change in bending direction. Extrusion is widely utilized in the polymer processing industry. Common requirement on the extrudate is dimensional accuracy. However, the size of the extrudate are highly influenced by a phenomenon called extrudate swell. For Newtonian fluids, having a continuing viscosity, extruded from cylindrical dies, the swell ratio is about 13% when physical phenomenon, inertia and gravitational forces are often neglected. For viscoelastic fluids, the swelling is far larger and therefore the final diameter of the extrudate are often several times the diameter of the die. This effect is attributed to normal stresses within the material.

Nonexistence of global solutions for a class of viscoelastic wave equations

<p style='text-indent:20px;'>We consider a class of nonlinear evolution equations of second order in time, linearly damped and with a memory term. Particular cases are viscoelastic wave, Kirchhoff and Petrovsky equations. They appear in the description of the motion of deformable bodies with viscoelastic material behavior. Several articles have studied the nonexistence of global solutions of these equations due to blow-up. Most of them have considered non-positive and small positive values of the initial energy and recently some authors have analyzed these equations for any positive value of the initial energy. Within an abstract functional framework we analyze this problem and we improve the results in the literature. To this end, a new positive invariance set is introduced.</p>

Описание вязкоупругих свойств низко- и высоконаполненных эластомерных нанокомпозитов

In this work, an analytical solution is found for the change in the dissipative (inelastic) part of the stress tensor at a constant rate of uniaxial loading of the material within the framework of a new thermodynamic model of the behavior of viscoelastic materials. At the same time, a fairly accurate coincidence of the theoretical curve constructed on the basis of the obtained solution with the experimental results was demonstrated. For this, uniaxial tests with nested loading cycles were carried out for samples of low- and high-filled elastomeric nanocomposites with various fillers. At each section of loading and unloading, time holdings were set, which made it possible to neglect the temporal processes taking place in the material, this makes it possible to experimentally find the equilibrium deformation curve. The resulting equilibrium curve can be described using the elastic potential. Having determined the equilibrium (elastic) and finding the dissipative (inelastic) parts of the stress tensor, the viscoelastic response of the considered elastomeric materials was described with high accuracy.

A Combined Exponential-Power-Law Method for Interconversion between Viscoelastic Functions of Polymers and Polymer-Based Materials.

Understanding and modeling the viscoelastic behavior of polymers and polymer-based materials for a wide range of quasistatic and high strain rates is of great interest for applications in which they are subjected to mechanical loads over a long time of operation, such as the self-weight or other static loads. The creep compliance and relaxation functions used in the characterization of the mechanical response of linear viscoelastic solids are traditionally determined by conducting two separate experiments—creep tests and relaxation tests. This paper first reviews the steps involved in conducting the interconversion between creep compliance and relaxation modulus in the time domain, illustrating that the relaxation modulus can be obtained from the creep compliance. This enables the determination of the relaxation modulus from the results of creep tests, which can be easily performed in pneumatic equipment or simple compression devices and are less costly than direct relaxation tests. Some existing methods of interconversion between the creep compliance and the relaxation modulus for linear viscoelastic materials are also presented. Then, a new approximate interconversion scheme is introduced using a convenient Laplace transform and an approximated Gamma function to convert the measured creep compliance to the relaxation modulus. To demonstrate the accuracy of the fittings obtained with the method proposed, as well as its ease of implementation and general applicability, different experimental data from the literature are used.

Analysis of the effects of viscosity on the SH-wave band-gaps of 2D viscoelastic phononic crystals by Dirichlet-to-Neumann map method

The effects of viscosity on the band-baps of two-dimensional (2D) viscoelastic phononic crystals are studied by the Dirichlet-to-Neumann (DtN) map method. The viscoelastic phononic crystals are composed of square or triangular lattices of elastic circular solid cylinders in a viscoelastic solid matrix. Time-harmonic anti-plane transverse (SH) waves are considered and the standard linear solid model is used to describe the viscoelastic behavior of the matrix material, in which the shear modulus depends on the frequency. Based on the DtN map constructed by using the cylindrical wave expansions, a linear eigenvalue problem related to the Bloch wave vector is formulated, which involves relatively small matrices. By using real frequencies and complex-valued wave vectors, the complex band structures are computed for different viscosity parameters, and the wave propagation and attenuation characteristics in dependence of the viscosity are analyzed. Then based on the storage shear modulus, real band structures for the Pb/epoxy phononic crystals with viscosity in the square and triangular lattices are studied, and the effects of the different viscoelastic material parameters and other relevant influencing parameters on the band-gaps are discussed. The results show that the viscosity of the matrix material affects the location and the width of the band-gaps. This fact provides an alternative way to tune the band-gaps of phononic crystals by adjusting the viscoelastic parameters combined with other influencing parameters.

Impact and Bandgap Characteristics of Periodic Rods With Viscoelastic Inserts and Local Resonators

Abstract A comprehensive theoretical and experimental study is presented of the bandgap behavior of periodic viscoelastic material (VEM) composites subjected to impact loading. The composites under consideration consist of an assembly of aluminum sections integrated with periodic inserts which are arranged in one-dimensional configurations. The investigated inserts are manufactured either from VEM only or VEM with local resonators (LR). A finite element model (FEM) is developed to predict the dynamics of this class of VEM composites by integrating the dynamics of the solid aluminum sections with those of VEM using the Golla-Hughes-Mctavish (GHM) mini-oscillator approach. The integrated model enables, for the first time, the accurate predictions of the bandgap characteristics of periodic viscoelastic composites unlike previous studies where the viscoelastic damping is modeled using the complex modulus approach with storage modulus and loss factor are assumed constants and independent of the frequency or the unrealistic and physically inaccurate Kelvin–Voigt viscous-damping models. The predictions of the developed FEM are validated against the predictions of the commercial finite element package ansys. Furthermore, the FEM predictions are checked experimentally using prototypes of the VEM composites with VEM and VEM/LR inserts. Comparisons are also established against the behavior of plain aluminum rods in an attempt to demonstrate the effectiveness of the proposed class of composites in mitigation of the structural response under impact loading. Close agreements are demonstrated between the theoretical predictions and the obtained experimental results.

Modeling the Viscoelastoplastic Deformation of Flexible Reinforced Plates with Weak Resistance to Transverse Shear

Abstract—Based on the time step algorithm, we have developed a mathematical model of the viscoelastoplastic deformation of flexible plates cross-reinforced in planes parallel to the middle plane. The strains of the plate composite components are assumed to be small and are decomposed into elastic and plastic components. The viscoelastic behavior of the composite materials is described by the Maxwell–Boltzmann body relations. The inelastic deformation is represented by the equations of the theory of a plastic flow with isotropic hardening. The normal stresses in the transverse direction are approximated linearly over the plate thickness. For this reason, the linear strains in the transverse direction and their rates are excluded from the governing equations for the composite components. The weakened resistance of fibrous plates to transverse shear is taken into account within the nonclassical Reddy bending theory. The geometric nonlinearity of the problem is considered in the Karman approximation. The formulated initial-boundary value problems are solved numerically with the application of an explicit cross-type scheme. A workaround is used to obtain a stable numerical scheme: the stresses in the Maxwell–Boltzmann viscoelastic relations at the current discrete time are expressed via the stress rate by the trapezoid formula with a backward step. We have investigated the elastoplastic and viscoelastoplastic bending dynamic behavior of relatively thick, orthogonally reinforced fiberglass rectangular plates subjected to blast loads. A change in the reinforcement structure is shown to lead to a change in the residual deflection of the structure. We demonstrate that the amplitude of reinforced-plate oscillations in the vicinity of the initial time exceeds significantly the residual deflection.

Experimental and numerical study of buckling behavior of foam-filled honeycomb core sandwich panels considering viscoelastic effects

Honeycomb sandwich panels are widely used in marine, aerospace, automotive and shipbuilding industries. High strength to weight and excellent energy absorption are features that make these structures unique. Foam filling the honeycomb core enhances the mechanical properties of sandwich panels considerably. In the present study, the buckling behavior of Nomex honeycomb core/glass-epoxy face sheet sandwich panel for both bare and foam-filled honeycomb core is investigated numerically and experimentally, considering the viscoelastic properties of the sandwich panel. Indeed, the viscoelastic properties of the composite face sheet and foam are determined by relaxation test and are implemented in ABAQUS using VUmat code. The finite element method is also performed using ABAQUS to model the buckling behavior of the sandwich panel incorporating both elastic and viscoelastic material behaviour. The effects of composite face sheet lay-up, core thickness, core cell size, and foam filling are also evaluated. The experimental and numerical results show that the foam increases the critical buckling load and energy absorption.

Effect of wood and graphite fillers on the glass fiber reinforced composite

Glass fiber reinforced polymer is the most popular composite used in engineering applications. The objective of this study is twofold. First, to develop glass fiber reinforced composites with synthetic and natural fillers, namely graphite and various wood fillers. Second, to characterize the mechanical and thermomechanical properties of such filler composites. This study clearly demonstrated that graphite filled glass fiber composites exhibit more mechanical and thermomechanical strengths compared the composite without a filler. Thermomechanical properties were studied by using dynamic mechanical analysis (DMA) test to know the viscoelastic behaviour of the composite materials.

Adherence Kinetics of a PDMS Gripper with Inherent Surface Tackiness.

Damage and fiber misalignment of woven fabrics during discontinuous polymer processing remain challenging. To overcome these obstacles, a promising switchable elastomeric adherence gripper is introduced here. The inherent surface tackiness is utilized for picking and placing large sheets. Due to the elastomer’s viscoelastic material behavior, the surface properties depend on loading speed and temperature. Different peeling speeds result in different adherence strength of an interface between the gripper and the substrate. This feature was studied in a carefully designed experimental test set-up including dynamic thermomechanical, as well as dynamic mechanical compression analyses, and adherence tests. Special emphases were given to the analyses of the applicability as well as the limitation of the viscoelastic gripper and the empirically modeling of the gripper’s pulling speed-dependent adherence characteristic. Two formulations of poly(dimethylsiloxane) (PDMS) with different hardnesses were prepared and analyzed in terms of their applicability as gripper. The main insights of the analyses are that the frequency dependency of the loss factor tanδ is of particular importance for the application along with the inherent surface tackiness and the low sensitivity of the storage modulus to pulling speed variations. The PDMS-soft material formulation exhibits the ideal material behavior for an adhesive gripper. Its tanδ varies within the application relevant loading speeds between 0.1 and 0.55; while the PDMS-hard formulation reveals a narrower tanδ range between 0.09 and 0.19. Furthermore, an empirical model of the pulling speed-dependent strain energy release rate G(v) was derived based on the experimental data of the viscoelastic characterizations and the probe tack tests. The proposed model can be utilized to predict the maximum mass (weight-force) of an object that can be lifted by the gripper

Transient Effects of Applying and Removing Strain on the Mechanical Behavior of Rubber.

For viscoelastic materials, the relationship between stress and strain depends on time, where the applied strain (or stress) can be expressed as a step function of time. In the present work, we investigated two temporary effects in the response of viscoelastic materials when a given strain is applied and then removed. The application of strain causes a stress response over time, also known as relaxation. By contrast, recovery is the response that occurs following the removal of an applied stress or strain. Both stress and relaxation constitute transient stages of a viscoelastic material exposed to a permanent force. In the current work, we performed several experimental tests to record the recovery in response to the total or partial removal of the strain. By observing and analyzing the mechanical response of the material to strain, we deduced that recovery is a procedure not only related to creep but also to relaxation. Hence, we created a model that simulates the behavior of viscoelastic materials, contributing to the prediction of relevant results concerning different conditions.

Modeling deformation and failure of viscoelastic composites at finite strains

A micromechanical analysis is proposed for the establishment of the macroscopic constitutive relations for viscoelastic composite materials undergoing large deformations. The composites are assumed to possess a triply periodic microstructure and their viscoelastic constituents are modeled by the incorporation of the viscoelastic effects with an arbitrary chosen hyperelastic strain energy function. Furthermore, an energy limiter is introduced which enforces the saturation of the viscoelastic strain energy function. The value of the strain energy at the saturation corresponds to the failure energy of the viscoelastic constituent. In conjunction with the derived micromechanical analysis, the occurrence of the energy saturation of the viscoelastic constituent predicts the composite failure. Applications are given for the determination of the macroscopic (overall) response and creep of a viscoelastic unidirectional composite, and the behavior of viscoelastic porous materials. In all cases, failure occurrences of the unidirectional composite and porous materials are predicted.

Nonlinear vibrations and damping of fractional viscoelastic rectangular plates

Damping is largely increasing with the vibration amplitude during nonlinear vibrations of rectangular plates. At the same time, soft materials present an increase in their stiffness with the vibration frequency. These two phenomena appear together and are both explained in the framework of the viscoelasticity. While the literature on nonlinear vibrations of plates is very large, these aspects are rarely touched. The present study applies the fractional linear solid model to describe the viscoelastic material behavior. This allows to capture at the same time (i) the increase in the storage modulus with the vibration frequency and (ii) the frequency-dependent nonlinear damping in nonlinear vibrations of rectangular plates. The solution to the nonlinear vibration problems is obtained through Lagrange equations by deriving the potential energy of the plate and the dissipated energy, both geometrically nonlinear and frequency dependent. The model is then applied to a silicone rubber rectangular plate tested experimentally. The plate was glued to a metal frame and harmonically excited by stepped sine testing at different force levels, and the vibration response was measured by a laser Doppler vibrometer. The comparison of numerical and experimental results was very satisfactorily carried out for: (i) nonlinear vibration responses in the frequency and time domain at different excitation levels, (ii) dissipated energy versus excitation frequency and excitation force, (iii) storage energy and (iv) loss factor, which is particularly interesting to evaluate the plate dissipation versus frequency at different excitation levels. Finally, the linear and nonlinear damping terms are compared.

Force reversal and energy dissipation in composite tubes through nonlinear viscoelasticity of component materials.

Fibre-reinforced, fluid-filled structures are commonly found in nature and emulated in devices. Researchers in the field of soft robotics have used such structures to build lightweight, impact-resistant and safe robots. The polymers and biological materials in many soft actuators have these advantageous characteristics because of viscoelastic energy dissipation. Yet, the gross effects of these underlying viscoelastic properties have not been studied. We explore nonlinear viscoelasticity in soft, pressurized fibre-reinforced tubes, which are a popular type of soft actuation and a common biological architecture. Relative properties of the reinforcement and matrix materials lead to a rich parameter space connecting actuator inputs, loading response and energy dissipation. We solve a mechanical problem in which both the fibre and the matrix are nonlinearly viscoelastic, and the tube deforms into component materials' nonlinear response regimes. We show that stress relaxation of an actuator can cause the relationship between the working fluid input and the output force to reverse over time compared to the equivalent, non-dissipative case. We further show that differences in design parameter and viscoelastic material properties can affect energy dissipation throughout the use cycle. This approach bridges the gap between viscoelastic behaviour of fibre-reinforced materials and time-dependent soft robot actuation.

Viscoelastic properties and self‐healing behavior in a family of supramolecular ionic blends from silicone functional oligomers

Supramolecular solid‐like polymer gels were obtained, through acid‐base interactions, starting from highly viscous amino‐terminated and carboxylic‐terminated telechelic PDMS oligomers, with different molecular weights, ranging approximately from 900 to 27 000 g/mol. The obtained blends were studied and characterized in terms of viscoelastic behavior, tensile properties, and self‐healing abilities, with the aim of gaining a better understanding of structure‐property relationships in these supramolecular ionic blends. IR spectroscopy confirmed the formation of supramolecular ionic interactions thanks to the presence of ammonium carboxylate group absorbance. Thermal analysis showed the formation of a crystalline phase at room temperature in some of the supramolecular blends when the molecular weight was lower than 27 000 g/mol. An increase in crystallinity by decreasing the chain length and therefore their molecular weights was also observed. These supramolecular PDMS materials showed self‐healing abilities with a value of healing efficiency ranging from 25% up to 52%. Samples tested with creep recovery analyses showed a viscoelastic behavior. Interpolation of the creep curves according to the four‐parameter Voigt model provides a relationship between the viscoelastic behavior of these PDMS materials and their self‐healing abilities. Our results show how the control of the thermal, viscoelastic, and mechanical properties of these materials allows the design of supramolecular blends based on acid‐base interactions with improved self‐healing properties.

Viscoelastic Behavior of Glass-Fiber-Reinforced Silicone Composites Exposed to Cyclic Loading.

The aim of this work was to analyze the influence of fibers on the mechanical behavior of fiber-reinforced elastomers under cyclic loading. Thus, the focus was on the characterization of structure–property interactions, in particular the dynamic mechanical and viscoelastic behavior. Endless twill-woven glass fibers were chosen as the reinforcement, along with silicone as the matrix material. For the characterization of the flexible composites, a novel testing device was developed. Apart from the conventional dynamic mechanical analysis, in which the effect of the fiber orientation was also considered, modified step cycle tests were conducted under tensile loading. The material viscoelastic behavior was studied, evaluating both the stress relaxation response and the capability of the material to dissipate energy under straining. The effects of the displacement rate of the strain level, the amplitude of the strain applied in the loading–unloading step cycle test, and the number of the applied cycles were evaluated. The results revealed that an optimized fiber orientation leads to 30-fold enhanced stiffness, along with 10 times higher bearable stress. The findings demonstrated that tailored reinforced elastomers with endless fibers have a strong influence on the mechanical performance, affecting the structural properties significantly.

A novel evaluation of shock absorption and adhesive strength under shear impact loading

ABSTRACT The authors study shock absorption characteristics and their measurement methods because test standards and specifications for shock absorbing adhesives are not clearly established. Especially, microscale shock absorbing adhesive characteristics are important for mechanical properties of small-sized mobile electronics with slim, bezel-less design. For this purpose, a piezoelectric force sensor is utilized to evaluate impact response of various adhesives under ball drop impact due to high-frequency data acquisition. Next, the evaluated impact responses are compared with dynamic mechanical analysis results to confirm the viscoelastic material behavior of adhesives. In addition, the impact response is proportionally correlated with the damping factor. In order to characterize both shock absorption and adhesive strength simultaneously, a novel test apparatus for shear impact is devised based on the previous test. The correlation between two mechanical properties is determined by analyzing the change of the impact force transmitted through the adhesive. The degradation of the adhesion strength is described by the damage model, which estimates its change before detachment. The proposed experimental mechanics not only enables a concurrent evaluation of adhesion strength and shock absorption but also assesses required adhesive materials for delicate electronic components.

Performance Evaluation of Dynamic Modulus Predictive Models for Asphalt Mixtures

Dynamic modulus characterizes the viscoelastic behavior of asphalt materials and is the most important input parameter for design and rehabilitation of flexible pavements using Mechanistic–Empirical Pavement Design Guide (MEPDG). Laboratory determination of dynamic modulus is very expensive and time consuming. To overcome this challenge, several predictive models were developed to determine dynamic modulus of asphalt mixtures instead of laboratory testing. Present study utilizes a large database of 1320 dynamic modulus test results developed at the University of Maryland to evaluate the performance and accuracy of different dynamic modulus predictive models. For this purpose, six conventional dynamic modulus predictive models including Witczak, Modified Witczak, Hirsch, Al-Khateeb, Global and Simplified Global models were considered and dynamic moduli of asphalt mixtures were determined. These moduli were then compared with those determined from laboratory test results. Performance evaluation of the models showed high prediction accuracy and low prediction bias with good correlation between predicted moduli and measured values for Witczak and Global models.

A new approach to describe the elastic behavior of filled rubber-like materials under complex uniaxial loading

The construction of a model capable of describing viscoelastic behavior of rubber-like materials is a challenging problem. Although this task can be simplified, if we restrict our consideration only to elastic behavior of the material, excluding all temporary (rate-dependent) effects. In practice, it can be achieved by testing polymer samples at very low loading rates. However, our research is devoted to the performance of complex experiments on uniaxial cyclic loading with different degrees of deformation of the samples, in which the arising stresses are considered as the sum of equilibrium (elastic) and dissipative (inelastic) terms. A series of experiments have been carried out on the samples of materials, which have identical matrices (styrene-butadiene rubber) but different degrees of filling with carbon black. The result of our research is the construction of a constitutive model, which can describe the elastic behavior of rubber-like materials taking account of the Mullins softening effect.