Viscoelastic Material Parameters Research Articles

A pulse-echo measurement setup to determine viscoelastic material parameters

Abstract Due to their versatility, the application of polymers in research and industry continues to increase. Since the majority of design processes are simulation-aided, precise material parameters are required to obtain realistic results. The quasi-statically and destructively measured material parameters provided by manufacturers for this purpose are usually insufficient. An acoustic method is generally capable of measuring the frequency-dependent viscoelastic material parameters in a non-destructive manner. In particular, an ultrasonic transmission measurement setup for determining these parameters has already been presented in previous publications. However, this approach has several drawbacks, including a low sensitivity to shear parameters. To increase the sensitivity to shear parameters, a measurement setup using a pulse-echo method with a corresponding inverse approach is presented to obtain viscoelastic material parameters of polymers. A brief comparison is made between the transmission and pulse-echo methods.

Design of non-linear, viscoelastic architected foams

Flexible viscoelastic foams with relative density in the range of 5-50% are widely used to control interaction forces, notably in cushions for impact protection, shoes, mechanical grippers, etc. The design of new foams to improve performance is challenging, due to the lack of efficient models to connect cellular architecture, viscoelasticity of the base resin, and non-linear responses that stem from large deformation of open pores. This paper presents highly efficient solutions for the response of linearly viscoelastic, kinematically non-linear and shear-deformable struts that are loaded at an oblique angle to their axis. The models can be used to predict structure-property relationships for strut-based metamaterials, including non-linear stress-strain response and accompanying hysteresis. To illustrate this, the entire design space of a simple unit cell is mapped in terms of a broad range of strut angles and thicknesses; the unit cell is inspired by features in stochastic foams that dominate their response. An enormous range of stress-strain responses can be obtained from this single foam-like cell, including purely softening, purely stiffening, and non-monotonic stiffness with adjustable tangent moduli. The model is also used to illustrate connections between viscoelastic material parameters, loading rate, and hysteresis for two distinct classifications of non-linear stress-strain response.

Characterization on the mesostructural properties of asphalt mixtures based on meso-element equivalence method

The randomness and variation of material composition at the meso-scale lead to some limitations in the application of asphalt mixture. When all features are taken into account, the computational effort increases significantly. Therefore, the relationship can be established using the meso-element equivalence method (MEEM). In this paper, the effects of aggregate-asphalt interface, initial void defects and material damage were introduced and MEEM of asphalt mixture was established based on industrial computed tomography (ICT) and finite element method (FEM). The rationality of the model was verified by laboratory performance tests, and the effects of aggregate type, mixture gradation and mesostructural parameters on the mechanical response of MEEM were compared and analyzed. The results showed that the MEEM model captures the mechanical behavior of asphalt mixtures well, the input of visco-elastic material parameters is an important step of MEEM simulation accuracy. The aggregate type, the discrete degree of the skeleton structure and the distribution characteristics of mesostructural parameters are important factors affecting the mechanical properties of asphalt mixture in MEEM.

A comparison of brain retraction mechanisms using finite element analysis and the effects of regionally heterogeneous material properties

Finite element (FE) simulations of the brain undergoing neurosurgical procedures present us with the great opportunity to better investigate, understand, and optimize surgical techniques and equipment. FE models provide access to data such as the stress levels within the brain that would otherwise be inaccessible with the current medical technology. Brain retraction is often a dangerous but necessary part of neurosurgery, and current research focuses on minimizing trauma during the procedure. In this work, we present a simulation-based comparison of different types of retraction mechanisms. We focus on traditional spatulas and tubular retractors. Our results show that tubular retractors result in lower average predicted stresses, especially in the subcortical structures and corpus callosum. Additionally, we show that changing the location of retraction can greatly affect the predicted stress results. As the model predictions highly depend on the material model and parameters used for simulations, we also investigate the importance of using region-specific hyperelastic and viscoelastic material parameters when modelling a three-dimensional human brain during retraction. Our investigations demonstrate how FE simulations in neurosurgical techniques can provide insight to surgeons and medical device manufacturers. They emphasize how further work into this direction could greatly improve the management and prevention of injury during surgery. Additionally, we show the importance of modelling the human brain with region-dependent parameters in order to provide useful predictions for neurosurgical procedures.

Simulation of four-point bending tests for the viscoelastic fracture properties of concrete

Understanding the fracture properties of concrete, such as crack propagation behavior and fracture energy, is crucial for designing and evaluating concrete structures. Experimental results are insufficient and cannot be directly employed for a comprehensive analysis of the fracture behavior of concrete structures under load, particularly when considering concrete as viscoelastic with the presence of cracks. Recognizing the time and cost constraints of traditional experimental testing, this research leverages numerical simulations as a cost-effective alternative to determine viscoelastic material parameters. Thus, the critical evaluation of concrete fracture properties, fundamental for the design and assessment of concrete structures, is addressed. Employing a finite element method for four-point bending tests, the study systematically investigates parameters such as initial crack depth, displacement acceleration, and time step. The material properties of concrete are described using viscoelastic models. The findings provide valuable insights into crack propagation behavior and deformation characteristics, emphasizing the significant influence of the modulus of elasticity on both maximum load values and displacement. These findings contribute to a deeper understanding of the structure's response and underscore the importance of considering these parameters in similar simulations. The study highlights the importance of considering these parameters in simulations to enhance the understanding of concrete fracture behavior. The paper's contributions can extend to optimizing concrete mixtures, formulating repair strategies, and improving structural assessments. Further research is suggested to improve the accuracy of simulations and investigate material properties under various conditions.

Modeling viscoelasticity and cyclic creep of PEEK by parallel rheological framework (PRF)

Although creep is usually regarded as a quasistatic phenomenon, in multiple engineering applications the load is not constant, hence creep under cyclic loading conditions should be considered. The current work presents the theoretical and experimental study on the viscoelasticity and cyclic creep of PEEK (Polyether ether ketone) – the polymer with good chemical and thermal stability. Among other demanding applications, PEEK is used in bearings industry for the fabrication of cages, which main function is to isolate and to guide rolling elements. In this application the polymer cage is subjected to the long-term load alternating in time, meaning that classical creep (under constant load) cannot be presumed. In the current study, the non-linear viscosity is included into the generalized Maxwell model, employing the Eyring equations which postulate that the viscosity coefficient is not constant but is dependent on stress. The model is implemented with the Parallel Rheological Framework (PRF) (the numerical technique recently implemented in the commercial software ABAQUS), used to construct the generalized Maxwell model with hyper-elastic springs and dashpots of non-linear viscosity. Initially, the viscoelastic material parameters are identified from the uniaxial test, and later these parameters are used to simulate the PEEK response under cyclic loading, to predict the time to creep/fatigue failure. Eventually, the numerical predictions are compared to the test results. The comparison indicates that the developed method and its numerical implementation by PRF can be successfully used to model the non-linear viscoelastic behavior of PEEK under uniaxial load. It is also found, that the simulation of cyclic creep can be reasonably performed by using the current material model and PRF.

Research on simplified tire finite element modeling and simulation method

A simplified tire finite element model modeling and simulation method with high efficiency and accuracy is proposed to address the issues of poor efficiency and low accuracy in tire finite element simulation. Firstly, the detailed finite element model of the tire is established, and the viscoelastic material parameters are determined through theoretical analysis and simulation verification. Then, the Hyperelastic material parameters are obtained through cyclic Tensile testing, and finally, the static tire condition test verification is completed. Based on the established detailed finite element model of the tire, the influence of different rubber materials on the dynamic characteristics of the tire is studied. On this basis, simplified friction and structure models are proposed to complete the establishment of a simplified tire finite element model. The simulation results of lateral and longitudinal slip conditions are compared with experimental data by implanting a finite element friction model that considers slip velocity and contact pressure. Through simulation analysis, it was found that the tread compound has a significant impact on the dynamic characteristics of the tire, while other compounds have a relatively small impact. Simplifying the tire finite element model can significantly improve the efficiency of finite element simulation and reduce convergence issues. The comparison accuracy between the finite element model simulation results and experimental data is relatively high, with the average accuracy of longitudinal force, lateral force, and correction moment reaching 89%, 95%, and 81%, respectively. This verifies the correctness and effectiveness of the simplified tire finite element model modeling and simulation method. This method provides certain reference significance for improving the efficiency of tire finite element simulation and providing virtual matching between tires and the entire vehicle.

Measurement of Relaxation Modulus of Viscoelastic Materials and Design of Testing Device

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

Optimization of precision molding process parameters of viscoelastic materials based on BP neural network improved by genetic algorithm

Micro-structured optical components (MOC) are popular due to their unique optical and mechanical properties. Glass molding processing (GMP) is currently the main method of MOC manufacturing. In GMP, the process parameters determine the efficiency and quality of the glass processing. However, the optimization of their multi-objective molding process parameters has not been studied comprehensively enough. In this paper, a thermocompression model of a viscoelastic material and a mold is developed using coupled thermal-structural analysis in Abaqus. In addition, the data was analyzed to investigate the influence of process parameters on GMP performance. Then, a BP neural network model was built, and the model was trained and tested. A prediction model that can reasonably reveal the relationship between the process parameters and the molding effect was obtained. A multi-objective optimization algorithm GA was used to optimize the design of the hot-pressing process parameters. At last, a set of process parameters with the best forming effect was obtained. This study provides valuable insights into optimizing glass molding process parameters for practical production.

Experimental Verification of the Neural Network Optimization Algorithm for Identifying Frequency-Dependent Constitutive Parameters of Viscoelastic Materials

Experimental Verification of the Neural Network Optimization Algorithm for Identifying Frequency-Dependent Constitutive Parameters of Viscoelastic Materials

Homogenization modeling and numerical simulation of piezolaminated lattice sandwich structures with viscoelastic material

Lattice sandwich structures have the advantage of high strength-to-weight and stiffness-to-weight ratios. The laminated structures filled with viscoelastic materials have active and passive damping properties and have great potential for applications in aerospace engineering. To overcome numerical modeling challenges, the paper first proposes a homogenization approach for periodic lattice core filled with viscoelastic materials using periodic boundary conditions. Based on the homogenized elastic and viscoelastic material parameters, a two-dimensional finite element modeling method based on the zig-zag hypothesis is proposed for piezolaminated lattice sandwich structures, where continuous interlayer shear stresses are satisfied due to independent shear strains in each layer. The homogenization approach is applied to corrugated and honeycomb core structures for obtaining orthotropic elastic and viscoelastic material parameters. Additionally, the two-dimensional finite element modeling method is implemented to the simulation of piezolaminated sandwich structures filled with viscoelastic materials.

粘弾性体落下衝撃における材料係数の同定

This paper deals with the material modulus estimation for the impact of dropped viscoelastic material bodies. A bar model was investigated firstly as it is easy to understand the impact phenomena. Besides the fundamental material modulus of impact, Young's modulus and density, two dimensionless viscoelastic material parameters, the ratio of the long-term elastic modulus to the short-term one and the relaxation modulus to the wave propagation time along a bar, were found to be the other key parameters. The dropped viscoelastic spheres were investigated secondly and shown to have similar impact characteristics to bars regarding these two key parameters. We can estimate the material modulus very quickly in the computation analysis by tuning these parameters. And this approach is very useful to design the impact source of dropped sphere from the point of view of the viscoelastic materials.

Design optimization of door sealing for the sound transmission performance

Noise isolation properties of the closure systems are important factors for the acoustic performance of vehicles. This study explains sound transmission through a door sealing system, and numerical methods analyze all acoustic responses’ parameters. A specific design of experiments (DoE) analysis is carried out to reveal the effects of each material along with the predefined geometric entities and their dimensions. Viscoelastic material parameters are included with full factorial designs for a particular geometry. Material optimization is implemented with the Taguchi method by incorporating noise factors. Optimization of the geometric entities is studied, and the best section shapes for acoustic performance are obtained. A robust optimization study is conducted by considering the uncontrollable noise factors. Consequently, the door closing efforts compromise the acoustic design to present an overall method with design constraints.

Isogeometric FE-BE method with non-conforming coupling interface for solving elasto-thermoviscoelastic problems

The isogeometric finite element (FE) and boundary element (BE) coupling method with non-conforming interface is applied to solve 3D elasto-thermoviscoelastic problems. The thermoviscoelastic constitutive relation is expressed by Stieltjes integral, and the equivalent integral weak form of the problem is derived according to the principle of virtual work, in which the time integral is discretized by the trapezoidal difference approximation formula. The parameters of viscoelastic material are described by Prony series, and the discrete formula can be simplified by recursive relationship to avoid storing all solutions in time steps. The equilibrium and compatibility conditions of FE and BE subdomains on the coupling interface are used to couple two different system matrices, and the coupling of non-conforming non-uniform rational B-splines (NURBS) surfaces in different subdomains is achieved by using virtual knot insertion technique. In addition, the time-temperature equivalent principle is applied to observe the mechanical behavior of viscoelastic materials over a wide temperature range in a short time. Through several numerical examples, the effects of different working conditions and geometrical parameters of combustion chamber on the structure of the solid rocket motor (SRM) are studied, and the correctness and robustness of this method are verified.

Lamb wave based approach to the determination of acoustic material parameters

Abstract In this paper a measurement procedure to identify viscoelastic material parameters of plate-like samples using broadband ultrasonic waves is presented. Ultrasonic Lamb waves are excited via the thermoelastic effect using laser radiation and detected by a piezoelectric transducer. The resulting measurement data is transformed to yield information about multiple propagating Lamb waves as well as their attenuation. These results are compared to simulation results in an inverse procedure to identify the parameters of an elastic and a viscoelastic material model.

Thermal fluctuation spectrum of flexoelectric viscoelastic semiflexible filaments and polymers: A line liquid crystal model

AbstractIn this paper, we generalize the internal viscosity model developed by Professor Williams to semiflexible polymers, biofilaments, and worm‐like micelles, where molecular dissipation is generated by bending. Current models for viscoelasticity with internal viscosity in semiflexible polymers and filaments are based on generalizations of the worm‐like model, but they neglect potential electromechanical couplings such as flexoelectricity. In this paper, inspired by the early work of Professor Williams, we develop a model for worm‐like viscoelastic flexoelectric filaments based on the “line liquid crystal model”. The electroelastic free energy and entropy production are formulated and used to derive the shape equation for these filaments undergoing thermal fluctuations. The resulting time relaxation spectrum is a useful tool to characterize experimentally viscoelastic material parameters. We show that flexoelectricity or polarization‐induced bending softens the filaments. The predicted time relaxation spectrum shows that at longer wavelength modes, the filament behaves like a rigid rod in a viscous solvent, but at shorter wavelengths, it reaches a plateau defined by the bending time scale. The key effect of flexoelectricity is to shift the entire spectrum to higher values, slowing down the response. The model itself is validated using the worm‐like chain and the viscoelasticity of liquid crystals, and the predictions are shown to be in qualitative consistency with the data. Since filament flexoelectricity is associated with 1D sensor‐actuator functionalities, the presented model has many potential novel applications in reduced geometries.

Advanced Characterisation of Soft Polymers under Cyclic Loading in Context of Engine Mounts.

The experimental investigation of viscoelastic behavior of cyclically loaded elastomeric components with respect to the time and the frequency domain is critical for industrial applications. Moreover, the validation of this behavior through numerical simulations as part of the concept of virtual prototypes is equally important. Experiments, combined measurements and test setups for samples as well as for rubber-metal components are presented and evaluated with regard to their industrial application. For application in electric vehicles with relevant excitation frequencies substantially higher than by conventional drive trains, high-frequency dynamic stiffness measurements are performed up to 3000 Hz on a newly developed test bench for elastomeric samples and components. The new test bench is compared with the standard dynamic measurement method for characterization of soft polymers. A significant difference between the measured dynamic stiffness values, caused by internal resonance of the bushing, is presented. This effect has a direct impact on the acoustic behavior of the vehicle and goes undetected by conventional measurement methods due to their lower frequency range. Furthermore, for application in vehicles with internal combustion engine, where the mechanical excitation amplitudes are significantly larger than by vehicles with electric engines, a new concept for the identification of viscoelastic material parameters that is suitable for the representation of large periodic deformations under consideration of energy dissipation is described. This dissipated energy causes self-heating of the polymer and leads to the precocious aging and failure of the elastomeric component. The validation of this concept is carried out thermally and mechanically on specimen and component level. Using the approaches developed in this work, the behavior of cyclically loaded elastomeric engine mounts in different applications can be simulated to reduce the time spent and save on the costs necessary for the production of prototypes.

A unified numerical approach for soft to hard magneto-viscoelastically coupled polymers

The last decade has witnessed the emergence of magneto-active polymers (MAPs) as one of the most advanced multi-functional soft composites. Depending on the magnetisation mechanisms and responsive behaviour, MAPs are mainly classified as hard magnetic MAPs and soft magnetic MAPs. Polymeric materials are widely treated as fully incompressible solids that require special numerical treatment to solve the associated boundary value problem. Furthermore, both soft and hard magnetic particles-filled soft polymers are inherently viscoelastic. In this paper, we propose a unified simulation framework for magneto-mechanically coupled problems that can model hard and soft MAPs made of compressible and fully incompressible polymers, including the effects of the time-dependent viscoelastic behaviour of the underlying matrix. First, variational formulations for the uncoupled and coupled problems are derived. Later, the weak forms are discretised with higher-order Bézier elements while the evolution equation for internal variables is solved using the generalised-alpha scheme. Finally, using a series of experimentally-driven examples consisting of beam and robotic gripper models under magneto-mechanically coupled loading, the versatility and benefits of the proposed framework are demonstrated. The effect of viscoelastic material parameters on the response characteristics of MAPs under coupled magneto-mechanical loading is also studied.

A High-Efficiency Inversion Method for the Material Parameters of an Alberich-Type Sound Absorption Coating Based on a Deep Learning Model

Research on the acoustic performance of an anechoic coating composed of cavities in a viscoelastic material has recently become an area of great interest. Traditional forward research methods are unable to manipulate sound waves accurately and effectively, are difficult to analyse, have time-consuming solution processes, and have large optimization search spaces. To address these issues, this paper proposes a deep learning-based inverse research method to efficiently invert the material parameters of Alberich-type sound absorption coatings and rapidly predict their acoustic performance. First, an autoencoder (AE) model is pretrained to reconstruct the viscoelastic material parameters of an Alberich-type sound absorption coating, the material parameters are extracted into the latent feature space by the encoder, and the decoder model is saved. The internal relationship between the reflection coefficient and latent feature space is trained to establish a multilayer perceptron (MLP). Then, the reflection coefficients in the test set are input to the trained MLP and decoder models to automatically invert the material parameters. The accuracy of the inversion result is 95.08%. Finally, a predictive model is trained to rapidly predict the acoustic performance of the inverted material parameters. The speed of a single test target is 80 times faster than that of the finite element method (FEM). Furthermore, sound absorber material parameters with the best sound absorption performance and a three-band sound absorber are inverted, and their actual sound absorption performance is predicted by the proposed method. The proposed deep learning-based inversion research method provides a solution for low-frequency, wide-band, strong attenuation, and precisely controlled sound waves. It achieves an efficient inversion of material parameters and the rapid forecasting of acoustic performance. The training model can be used for a sound absorbing coating composed of irregular cavities in a viscoelastic material and predict its acoustic performance by only modifying the dataset.

Identification of Fractional Damping Parameters in Structural Dynamics Using Polynomial Chaos Expansion

In order to analyze the dynamics of a structural problem accurately, a precise model of the structure, including an appropriate material description, is required. An important step within the modeling process is the correct determination of the model input parameters, e.g., loading conditions or material parameters. An accurate description of the damping characteristics is a complicated task, since many different effects have to be considered. An efficient approach to model the material damping is the introduction of fractional derivatives in the constitutive relations of the material, since only a small number of parameters is required to represent the real damping behavior. In this paper, a novel method to determine the damping parameters of viscoelastic materials described by the so-called fractional Zener material model is proposed. The damping parameters are estimated by matching the Frequency Response Functions (FRF) of a virtual model, describing a beam-like structure, with experimental vibration data. Since this process is generally time-consuming, a surrogate modeling technique, named Polynomial Chaos Expansion (PCE), is combined with a semi-analytical computational technique, called the Numerical Assembly Technique (NAT), to reduce the computational cost. The presented approach is applied to an artificial material with well defined parameters to show the accuracy and efficiency of the method. Additionally, vibration measurements are used to estimate the damping parameters of an aluminium rotor with low material damping, which can also be described by the fractional damping model.