Viscoelastic Material Model Research Articles

Spring-in of composite L-shape specimens: An experimental and numerical investigation

The effect of stacking sequence, specimen thickness, tooling material and curing cycle on process induced distortions of L-shape composite structures is investigated experimentally and numerically. Sixty specimens were manufactured, and their spring-in angle was compared against simulation and analytical results. A thermo-chemo-mechanical simulation approach was developed to simulate the experiment by employing a modified Cure Hardening Instantaneously Linear Elastic (CHILE) and a linear viscoelastic material model. Freestanding, fixed and contact boundary conditions were investigated. The spring-in angle of the parts predicted by the modified CHILE material model, was found to be higher than that predicted by the viscoelastic model. The tool material significantly affects the distortion of the parts and contact boundary conditions should be employed for an accurate prediction of the part shape. Balanced, symmetric and thick laminates contribute to a reduction in part distortion, while elevated curing temperatures slightly affect the distortion level of the parts.

Dynamic mechanical analysis of PA 6 under hydrothermal influences and viscoelastic material modeling

Polyamides serve as matrix material for fiber reinforced composites and are widely applied in many different engineering applications. In this context, they are exposed to various environmental influences ranging from temperature to humidity. Thus, the influence of these environmental conditions on the mechanical behavior and the associated implications on the performance of the material is of utmost importance. In this work, the thermoviscoelastic behavior of polyamide 6 (PA 6) for two equilibrium moisture contents is investigated. To this end, dynamic mechanical analysis tests with and without humidity control of the environmental chamber were performed. In terms of relaxation tests, the experimental results reveal drying effects and increased diffusion activities when the sample’s equilibrium moisture content differs from the ambient humidity level within the testing chamber. Temperature-frequency tests quantify the humidity-induced shift of the glass transition temperature. The linear generalized Maxwell model (GMM) and time-temperature superposition are used to analyze the hydrothermal effects on the linear viscoelastic material properties and the onset of mechanical nonlinearity. Based on these investigations and findings, insight is gained on the humidity influence on the material properties and the limitations of linear thermoviscoelastic modeling. Furthermore, the computational construction of master curves and the parameter identification for a generalized Maxwell model are described in detail.

Mechanical investigations of the peltate leaf of Stephania japonica (Menispermaceae): Experiments and a continuum mechanical material model.

Stephania japonica is a slender climbing plant with peltate, triangular-ovate leaves. Not many research efforts have been devoted to investigate the anatomy and the mechanical properties of this type of leaf shape. In this study, displacement driven tensile tests with three cycles on different displacement levels are performed on petioles, venation and intercostal areas of the Stephania japonica leaves. Furthermore, compression tests in longitudinal direction are performed on petioles. The mechanical experiments are combined with light microscopy and X-ray tomography. The experiments show, that these plant organs and tissues behave in the finite strain range in a viscoelastic manner. Based on the results of the light microscopy and X-ray tomography, the plant tissue can be considered as a matrix material reinforced by fibers. Therefore, a continuum mechanical anisotropic viscoelastic material model at finite deformations is proposed to model such behavior. The anisotropy is specified as the so-called transverse isotropy, where the behavior in the plane perpendicular to the fibers is assumed to be isotropic. The model is obtained by postulating a Helmholtz free energy, which is split additively into an elastic and an inelastic part. Both parts of the energy depend on structural tensors to account for the transversely isotropic material behavior. The evolution equations for the internal variables, e.g. inelastic deformations, are chosen in a physically meaningful way that always fulfills the second law of thermodynamics. The proposed model is calibrated against experimental data, and the material parameters are identified. The model can be used for finite element simulations of this type of leaf shape, which is left open for the future work.

Analysis of fractures in linear viscoelastic media using a generalized finite element method and the elastic–viscoelastic correspondence principle

A methodology for an efficient analysis of 3-D fracture mechanics problems in linear viscoelastic media is presented. It combines the Elastic–Viscoelastic Correspondence Principle (EVCP), a Generalized Finite Element Method (GFEM), and an inverse Laplace transform (ILT) method to compute Energy Release Rate (ERR) and Crack Mouth Opening Displacement (CMOD) for viscoelastic fracture problems in the time domain. The method is denoted EVCP-GFEM-ILT and consists of solving a reference elastic problem in the Laplace domain using a quadratic p-hierarchical GFEM, computing quantities of interest in this domain, and transforming them to the time domain with the aid of a numerical ILT method. One of the key features of the method is that a single elastic solution is required, regardless of the time interval of the target viscoelastic problem. A detailed verification of the methodology against analytical and reference numerical solutions is performed. Problems subjected to either non-homogeneous Neumann or Dirichlet boundary conditions of increasing complexity are considered. Two ILT methods are studied and the one based on Fourier series is shown to deliver accurate results for all tested boundary conditions, as well as non-trivial viscoelastic material models. The computational cost of the method applied to a 3-D problem is compared with the one for Abaqus which solves the problem directly in the time domain using a FEM mesh with quarter-point elements. A fully 3-D mixed-mode fracture problem with a non-trivial viscoelastic material model is solved to highlight the applicability of the proposed methodology. Finally, a problem of practical interest is analyzed in order to show how the methodology proposed in this work can be applied to efficiently handle large-scale simulations.

Mathematical modeling of viscoelastic foam material for design of filtering respirators

The work is devoted to the development of a mathematical model of the foam material of the filtering half mask. The analysis of the methods used to study the leveling of the negative effect of the compression pressure of the filtering half-mask on the soft tissues of the human face under conditions of long-term operation was carried out. In order to study the mutual influence in the medium "filter material - foam material - human soft tissues", it is proposed to conduct virtual tests using numerical methods. The development of mathematical models of linear viscoelastic materials is based on the study of the relationship between the input and output characteristics of viscoelastic materials: stress and strain. The paper is devoted to the development of the mathematical model of linear viscoelastic materials using a transfer function. The model is designed to investigate the relationship between stress and deformation in viscoelastic materials using numerical methods.

Mapping the role of oral cavity physiological factors into the viscoelastic model of denture adhesives for numerical implementation.

Physiological parameters of the oral cavity have a profound impact on any restorative solutions designed for edentulous patients including denture adhesives. This study aims to mathematically quantify the influence of three such variables, namely: the temperature, pH, and the swelling of such adhesives under the influence of saliva on its mechanical behavior. The mathematical quantification is further aimed to implement a material model for such adhesives which considers the impact of such physiological factors. The denture adhesive is experimentally investigated by means of rheological steady state frequency sweep tests to obtain the relaxation spectrum of the material. The relaxation behavior is measured for a wide range of oral cavity temperatures and pH. Also, the adhesive is hydrated and upon swelling to different levels again tested to understand the impact of swelling on the mechanical behavior. The experimentally measured continuous relaxation spectrum is modeled as a viscoelastic material using a discrete set of points based on the Prony series discretization technique. The relaxation spectrums for various temperatures are compared and the possibility of a time-temperature superposition is explored for the model. Similarly, the measured values of Storage and loss modulus are investigated to understand the role of pH and swelling. The results in this study clearly indicated a horizontal shift in the relaxation behavior with increase in temperature. And hence, the time-temperature shift factor was calculated for the adhesive. The relaxation spectrum also showed a strong correlation with swelling of the adhesive and the pH. The influence of these two parameters were captured into the model based on the relaxation time parameter in the Prony series approach. Based on this study the impact of these parameters could be appreciated on the performance and mechanical behavior of denture adhesives and implemented into a Prony series based viscoelastic material model which can be used with numerical simulations.

Static reinforcement and vibration reduction of structures using topology optimization

This paper presents a topology optimization formulation based on the Solid Isotropic Material with Penalization (SIMP) method and solved by the Modified Optimality Criteria (MOC) algorithm. It addresses mechanical design problems such as structural reinforcement adding elastic material or vibration reduction using viscoelastic layers. The aim is thus to attach on a pre-existing given structure a design domain in order to improve the behavior of this elastic structure, according to an objective function. This can be useful when one wants to use, for example, additive manufacturing to reinforce a pre-existing structure or to maximize structural damping. Two objective functions are tested in both linear statics and dynamics: a compliance based objective function and a displacement based one. In the dynamic case, written in the frequency domain, the two proposed objective functions include the viscoelastic material model (a Zener fractional derivative one) used to fill the design domain. The displacement criteria is developed using a general formula able to take into account as many degree of freedom as necessary. Finally, some applications based on beams and CubeSat-like structures are shown in this article. The proposed examples show that in both statics and dynamics, the optimization of a restrained design domain attached to an existing structure can improve its behavior: stiffness improvement or vibration reduction.

Accounting for viscoelastic effects in a multiscale fatigue model for the degradation of the dynamic stiffness of short-fiber reinforced thermoplastics

Under fatigue loading, the stiffness decrease in short-fiber reinforced polymers reflects the gradual degradation of the material. Thus, both measuring and modeling this stiffness is critical to investigate and understand the entire fatigue process. Besides evolving damage, viscoelastic effects within the polymer influence the measured dynamic stiffness. In this paper, we study the influence of a linear viscoelastic material model for the matrix on the obtained dynamic stiffness and extend an elastic multiscale fatigue-damage model to viscoelasticity. Our contribution is two-fold. First, we revisit the complex-valued elastic models known in the literature to predict the asymptotic periodic orbit of a viscoelastic material. For small phase shifts in an isotropic linear viscoelastic material, we show through numerical experiments that a real-valued computation of an “elastic” material is sufficient to approximate the dynamic stiffness of a microstructure with a generalized Maxwell material and equal Poisson’s ratios in every element as matrix, reinforced by elastic inclusions. This makes standard solvers applicable to fiber-reinforced thermoplastics. Secondly, we propose a viscoelastic fatigue-damage model for the thermoplastic matrix based on decoupling of the time scales where viscoelastic and fatigue-damage effects manifest. We demonstrate the capability of the multiscale model to predict the dynamic stiffness evolution under fatigue loading of short-fiber reinforced polybutylene terephthalate (PBT) by a validation with experimental results.

The Effect of Intraocular Pressure Load Boundary on the Biomechanics of the Human Conventional Aqueous Outflow Pathway.

Aqueous humor outflow resistance in the trabecular meshwork (TM), juxtacanalicular connective tissue (JCT), and Schlemm's canal (SC) endothelium of the conventional outflow pathway actively contribute to intraocular pressure (IOP) regulation. Outflow resistance is actively affected by the dynamic outflow pressure gradient across the TM, JCT, and SC inner wall tissues. The resistance effect implies the presence of a fluid-structure interaction (FSI) coupling between the outflow tissues and the aqueous humor. However, the biomechanical interactions between viscoelastic outflow tissues and aqueous humor dynamics are largely unknown. A 3D microstructural finite element (FE) model of a healthy human eye TM/JCT/SC complex was constructed with elastic and viscoelastic material properties for the bulk extracellular matrix and embedded elastic cable elements. The FE models were subjected to both idealized and a physiologic IOP load boundary using the FSI method. The elastic material model for both the idealized and physiologic IOP load boundary at equal IOPs showed similar stresses and strains in the outflow tissues as well as pressure in the aqueous humor. However, outflow tissues with viscoelastic material properties were sensitive to the IOP load rate, resulting in different mechanical and hydrodynamic responses in the tissues and aqueous humor. Transient IOP fluctuations may cause a relatively large IOP difference of ~20 mmHg in a very short time frame of ~0.1 s, resulting in a rate stiffening in the outflow tissues. Rate stiffening reduces strains and causes a rate-dependent pressure gradient across the outflow tissues. Thus, the results suggest it is necessary to use a viscoelastic material model in outflow tissues that includes the important role of IOP load rate.

Impact simulation of composite panels for aerospace applications

The aerospace research community has been working towards the development of a comprehensive framework for the design of composite structures at the component, subassembly, assembly, and system levels. Such a framework requires accurate, efficient and easy-to-use mathematical and computational models that are in sync with physical reality. The research work in this paper is designed to help an aerospace structural engineer move towards this goal by simulating dynamic impact to composite panels. First, the existing orthotropic visco-elastic visco-plastic material model in LS-DYNA commercial finite element program, MAT_COMPOSITE_TABULATED_PLASTICITY_DAMAGE (MAT_213) is enhanced with the development and use of rate-dependent damage data. Using state-of-the-art experimental procedures, impact validation test data are created. Second, the versatility of the constitutive model is examined by its ability to simulate a low velocity (27 ft/s, 8 m/s) impact test, and two high velocity impact tests (385–417 ft/s, 117–127 m/s) that straddle the ballistic limit of the projectile and the composite panels. Third, these impact events are modeled using three different finite element types – under-integrated and fully-integrated solid elements, and fully-integrated thin shell elements. Insight into accuracy versus numerical efficiency is gained by comparing the performance of solid versus thin shell elements. The numerical results show that accurate predictions of these impact events can be obtained with reasonable effort and care.

Influence of tooth asymmetry and mating gear material on the tooth deflection characteristics of polymer gears

Transmission error (TE) in polymer gears is significantly affected by the elastic deflection of meshing teeth. The present work describes the deflection characteristics of the asymmetric Nylon 66 spur gears under similar and dissimilar engagements. The load sharing and deflection behavior were estimated numerically using a linear viscoelastic material model. Experimental determination of mesh deflection was carried out through static load tests. The peak mesh deflection in a cycle for the 20°/34° configuration was found to be 8% and 12% smaller as compared to 34°/20° and 20°/20° configurations, respectively. The peak tooth deflection was found to be highest for the 34°/20° configuration and lowest for the 20°/34° configuration, with the deviation between their peak deflections being 15% in metal-polymer pairs and 17% in polymer-polymer pairs. In the 34°/20° configuration, the higher drive side pressure angle increased the single tooth contact period, causing greater peak-to-valley amplitude in a cycle. The negligible tooth compliance of steel gear caused unsymmetrical load sharing in the double tooth contact zones of metal-polymer engagements. The greater compliance of driver gear in polymer-polymer engagements increased the mesh deflections of 20°/20° and 20°/34° configurations by 45% and that of 34°/20° configuration by 37%. Also, gear pairs with similar material stiffness balanced the load sharing in the addendum and dedendum double tooth contact zones. The large tooth deflection extended the contact duration of all configurations for both the similar as well as for the dissimilar engagements, respectively. This was signified by the contact path extension at the peripheries of the mesh cycle.

Determination of dynamic deformation behavior of Golden Delicious apple using finite element method and its validation by scanning electron microscopy

Apple fruit is affected by operations such as harvesting, packing, grading, storage, and transportation on the way from the garden to the sales centers. During these stages, the products are subjected to several static and dynamic loads applied to each product, damaging them. The aim of this study was to determine the dynamic deformation behavior using finite element simulation and to investigate the surface temperature changes of Golden Delicious apple cultivar due to impact loads. For this purpose, the physical, mechanical and rheological properties of the internal components of apples were determined in three parts: skin, flesh and core. A viscoelastic material model was defined for more accurate simulation. Scanning electron microscope is used to measure the volume of damage and a thermal camera is used to measure the surface temperature of the product. To collect valid data in the dynamic loading section, the pendulum impact test was performed in the form of a factorial design. In this test, the independent variables included impact levels at 3 levels, product temperature at 2 levels and product radius of curvature at 2 levels, and dependent variables included bruising volume and surface temperature difference. The simulation results showed that the difference in bruise volume in the force-time and velocity-time methods with the bruise volume in the experimental test was 14.12% and 18.53%, respectively, and the maximum difference in reaction force was 9.36% and 15.97%. Therefore, in dynamic simulation based on pendulum impact test results, the use of force-time data offers better results than velocity-time data. The results of surface temperature measurements showed that with a gradual increase in apple temperature, the surface temperature of the bruised area is lower than the temperature of the healthy area. The highest surface temperature difference was observed in 30 minutes after impact and in the third impact level (33 N) equivalent (0.4 °C). Also, the results of the experimental pendulum impact test showed that all three factors of impact level, product temperature and radius of curvature had significant differences in bruising volume. Thus, the volume of bruising is directly related to the impact surface and the radius of curvature and inversely related to the apple temperature.

A highly efficient explicit constitutive model for linear viscoelastic closed-cell porous materials

In this paper, a highly efficient explicit constitutive model for linear viscoelastic closed-cell porous materials is proposed based on micromechanics and homogenization method in the time domain. The deformation first is additively divided into volumetric and deviatoric parts and then the viscoelastic behaviors are decomposed into the time-dependent and time-independent parts. Finite element simulations based on representative volume element models are utilized to numerically verify the constitutive model. The effects of the void-shape, porosity, elastic and viscous parameters of the matrix, strain rate, and angular frequency on the effective linear viscoelastic responses are studied. The results demonstrate that the constitutive model can provide accurate estimation of the effective linear viscoelastic properties for the closed-cell porous materials in both time and frequency domains. The 3D printed nylon porous materials with various porosities are employed to experimentally validate the constitutive model through simple uniaxial compression tests, stress relaxation uniaxial compression tests, and uniaxial compression tests with different strain rates. The results reveal that the constitutive model can also predict well the behaviors of linear viscoelastic closed-cell porous materials with different porosities in the time domain under various loading conditions.

Data-driven analytical mechanics of aging viscoelastic shotcrete tunnel shells

Based on the principle of virtual power, equilibrium conditions are established for the forces within a cross section of a tunnel top heading driven according the New Austrian Tunneling Method (NATM). External forces, namely impost actions and ground pressure distributions following a third-order polynomial, are analytically linked with internal forces, such as axial forces and bending moments, arising as integrals over the shell thickness, of circumferential normal stresses. The latter are related, via an aging viscoelastic shotcrete material model, to circumferential normal strains, as well as to radial and circumferential displacement components. This allows for analytical transformation of displacement measurement data collected at the crown and the footings of the shell segment, into ground pressure and impost action evolutions, together with all the associated force and stress quantities. For the Sieberg tunnel, driven in Miocene clay marl, our data-driven analytical mechanics model evidences virtually uniform ground pressure distributions, leading to a first rapidly increasing, and then mildly decreasing utilization degree of the shotcrete shell.

Numerical simulation of axially impacted elastic bar

This numerical analysis considers a model of an elastic cylindrical bar impacted by rigid mass, where the accuracy of the model is benchmarked by a closed-form solution developed for this impact process. The analytical solution provides theoretical background and understanding, however, practical problem is not always restricted to a simple one-dimensional geometry and boundary conditions of a purely elastic material behaviour. Hence, the current work numerically simulates the impacted elastic bar, then explores parameters which are not considered in its theoretical model. A two-dimensional (2D) solid axisymmetric system is considered, in which rigid impactor is assigned with initial velocity corresponding to certain drop height and a 2D contact type is defined between interacting bodies. Both elastic and time-dependent viscoelastic material models are considered in this study. The simulation results reveal time intervals gradually increase in every sequential intervals, while relatively small discrepancies are recorded for peak load and pulse width outputs. The parameters of impactor’s mass, drop height and structural stiffness are varied; showing how these parameters individually affect the resulting force response at end struck. The models then evaluate time-dependent viscoelastic material model; showing stiffer response of the resulting force in comparison to models assigned with long-term elastic moduli. Derived elastic modulus-output variable relations show comparable mathematical forms to corresponding equations formulated analytically.

FINITE ELEMENT EVALUATION OF THE EFFECT OF ADHESIVE CREAMS ON THE STRESS STATE OF DENTURES AND ABUTMENT TEETH

The appropriate fit of removable partial dentures (RPDs) is hypothesized to lead to lower tooth mobility. An adhesive layer between the denture and oral mucosa can facilitate better denture retention and therefore increased stability. Study objectives were to model and compare the response of abutment structures with and without the application of a denture adhesive and to observe the stress response of abutment periodontal ligaments (PDLs) during the application of occlusal force on the RPD. A 3D finite element (FE) model was developed from computer tomography datasets of the mandibular region and the RPD. An adhesive layer was developed by extending the denture surface and using the Prony series approximation of rheological data to implement a viscoelastic material model. FE simulations were performed by applying a bite force on one of the denture segments, with the resulting deformation in PDL compared between the model with the adhesive layer and the base model without. The maximum deformation of 15[Formula: see text][Formula: see text]m was observed in the 2nd molar abutment PDL with the implementation of the adhesive, as compared to 42[Formula: see text][Formula: see text]m for the model without. The lower impact of RPDs on the supporting abutment teeth could potentially reduce the discomfort of denture wearers.

Direct measurement of storage and loss behavior in AFM force–distance experiments using the modified Fourier transformation

Force–distance curve experiments are commonly performed in atomic force microscopy (AFM) to obtain the viscoelastic characteristics of materials, such as the storage and loss moduli or compliances. The classic methods used to obtain these characteristics consist of fitting a viscoelastic material model to the experimentally obtained AFM data. Here, we demonstrate a new method that utilizes the modified discrete Fourier transform to approximate the storage and loss behavior of a material directly from the data, without the need for a fit. Additionally, one may still fit a model to the resulting storage and loss behavior if a parameterized description of the material is desired. In contrast to fitting the data to a model chosen a priori, departing from a model-free description of the material's frequency behavior guides the selection of the model, such that the user may choose the one that is most appropriate for the particular material under study. To this end, we also include modified Fourier domain descriptions of commonly used viscoelastic models.

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.

Shrinkage simulation of blow molded parts using viscoelastic material models

AbstractThe utilization of simulation procedures is gaining increasing attention in the product development of extrusion blow molded parts. However, some simulation steps, like the simulation of shrinkage and warpage, are still associated with uncertainties. The reason for this is on the one hand a lack of standardized interfaces for the transfer of simulation data between different simulation tools, and on the other hand the complex time‐, temperature‐ and process‐dependent material behavior of the used semi crystalline polymers. Using a new vendor neutral interface standard for the data transfer, the shrinkage analysis of a simple blow molded part is investigated and compared to experimental data. A linear viscoelastic material model in combination with an orthotropic process‐ and temperature‐dependent thermal expansion coefficient is used for the shrinkage prediction. A good agreement is observed. Finally, critical parameters in the simulation models that strongly influence the shrinkage analysis are identified by a sensitivity study.

Research Progress on Analytical and Numerical Prediction of Curing Deformation in Thermoset for Large Composite Parts

Solidification deformation will produce certain drawbacks, so that a composite material part may not meet the requirements of a stress-free assembly for a modern aircraft. This issue holds particularly in the composite material part of large aircrafts. To predict and control this deformation, a novel method is applied for shifting the relaxation times of the composite based on its temperature and degree of cure. The choice of a suitable material model to simulate induced distortions is important to achieve the right-first-time approach. This work investigates the ability of the multi-physics model within a linear viscoelastic material model to predict induced distortions into an aerospace composite wing. It is shown that a L-shaped stiffened wall was less dominated by all deformations, but two stiffened wall panels were more dominated. Yet, wing box panels with four stiffened wall panels reduced the contribution to deformation. Their effects were included in the theory reported for the curing, and found to account for approximately 6.25% of the part deformation. The deformation effect could be analyzed by the proposed analytical solution, which was coupled with a cure kinetics model and a chemical shrinkage model to capture the multi-physics that take place during the curing.