Hyper-viscoelastic Constitutive Model Research Articles

Modeling the nonlinear dynamic behavior of filled elastomers: Application to the vibration of structures with large preloads

This study offers a global mechanical approach from filled rubber characterization and modeling to how this behavior affects vibratory structural simulations. This work focuses on the characterization and the modeling of the dynamic behavior of a filled rubber. Particularly the effects of frequency, static preload and amplitude of cyclic loading (i-e Payne effect) are studied. A new hyper-viscoelastic constitutive model is proposed and its linearization for a specific loading case in order to obtain a straight-forward stress–strain relationship in the frequency domain. After validation of the implementation, this model is used in vibratory cantilever beam simulations of CFRP (Carbon Fiber Reinforced Polymer) laminates containing constrained rubber layers. Damping capability is then linked to the non-linear behavior of the rubber material.

Novel hyper-viscoelastic approach to modelling elastomer mechanic behaviour with relaxation spectrum

Elastomers, such as polyurethane, exhibit hyperelastic behaviour and distinct rate dependence under a wide range of strain rates. Herein, a methodology for developing a hyper-viscoelastic constitutive model for succinctly characterising the mechanical behaviour of polyurethane under large deformations and a wide range of strain rates is proposed. The model is constructed using a long-term hyperelastic formulation combined with a rate-dependent viscoelastic model. This model is based on internal state variables and a finite strain formulation. A polyurethane elastomer was used as a sample to develop this model, by way of testing wide strain-rate mechanical behaviour (0.001–5000s−1) and viscoelastic behaviour. The viscoelastic behaviour was obtained using the equivalent time–temperature superposition relation. A parameter-fitting algorithm was adopted to separate the long-term behaviour from the viscoelastic behaviour. The long-term behaviour was modelled using a Mooney–Rivlin hyperelastic model, and its parameters were identified using the least-squares method. The time-dependent viscous effect calculated using the Prony series-based model was approximately determined based on the continuous relaxation spectrum. The characterisation capacity was confirmed through a thorough comparison with experimental curves. This model can be extended to other elastomers, even under tension, without any specific limitations of the internal components.

Brain Material Properties and Integration of Arachnoid Complex for Biofidelic Impact Response for Human Head Finite Element Model.

Finite element head models offer great potential to study brain-related injuries; however, at present may be limited by geometric and material property simplifications required for continuum-level human body models. Specifically, the mechanical properties of the brain tissues are often represented with simplified linear viscoelastic models, or the material properties have been optimized to specific impact cases. In addition, anatomical structures such as the arachnoid complex have been omitted or implemented in a simple lumped manner. Recent material test data for four brain regions at three strain rates in three modes of loading (tension, compression, and shear) was used to fit material parameters for a hyper-viscoelastic constitutive model. The material model was implemented in a contemporary detailed head finite element model. A detailed representation of the arachnoid trabeculae was implemented with mechanical properties based on experimental data. The enhanced head model was assessed by re-creating 11 ex vivo head impact scenarios and comparing the simulation results with experimental data. The hyper-viscoelastic model faithfully captured mechanical properties of the brain tissue in three modes of loading and multiple strain rates. The enhanced head model showed a high level of biofidelity in all re-created impacts in part due to the improved brain-skull interface associated with implementation of the arachnoid trabeculae. The enhanced head model provides an improved predictive capability with material properties based on tissue level data and is positioned to investigate head injury and tissue damage in the future.

Mechanical behaviour and constitutive modelling of an additively manufactured stereolithography polymer

Additive manufacturing enables the production of complex structures not possible with traditional methods. Such structures are attractive for use in various engineering applications. It follows that knowledge about the mechanical response of additive manufactured materials, and how to model it numerically, is required. In this work, a polymer manufactured with the stereolithography (SLA) method was studied through tensile and compression testing of smooth and notched specimens. The material exhibited an initial linear elastic behaviour followed by strain-rate- and pressure-dependent inelastic flow before failing at rather large strains in a brittle fracture mode. Motivated by the observed material behaviour, a hyper-viscoelastic constitutive model with a brittle fracture criterion was developed, implemented in a commercial finite element software, and calibrated to the material tests. Compression tests of lattice structures were performed and simulated to validate the model’s capabilities at complex stress states. The model captured the experimentally observed nonlinear stress–strain behaviour, and predicted the fracture initiation and a failure mode similar to the experimental results.

A hyper-viscoelastic constitutive model for elastomers: A case study of hydrogenated nitrile butadiene rubber and polychloroprene rubber

Elastomer materials are widely used as shock absorbers in a variety of practical applications including the automotive, aerospace, marine industries and structures. The straightforward Hooke’s law is insufficient to adequately describe the behavior of elastomeric materials due to their nonlinear elastic and viscous properties. This study proposes a hyper-viscoelastic model to describe the mechanical behavior of Hydrogenated Nitrile Butadiene Rubber (HNBR) 62 Duro shore A and Polychloroprene Rubber (PCR) 55 Duro shore A. Six distinct hyperelastic models—Yeoh, Rivlin, Arruda-Boyce, Mooney-Rivlin, Neo-Hookean, and Ogden— are compared herein to explain the nonlinear elastic behavior of elastomers. While the time-dependent characteristics of the considered materials have been described using the four parameters Generalised Maxwell (GM) model. The material parameters of models are determined using the least square fit (LSF) optimization algorithm from the uniaxial, planar, and stress relaxation test data. The stability and suitability of each hyperelastic model is assessed using the Drucker stability. The accuracy of each model is represented by Root Mean Square Error (RMSE) of curve fitting between theoretical and experimental data. On this basis, the Ogden order three ( N = 3) model and the four-parameter GM models are selected which well agreed with the experimental test data and they are integrated to generate the hyper-viscoelastic constitutive model. In addition, the hyper-viscoelastic model is used to simulate the HNBR and PCR dampers under shock load. The numerically generated response is finally compared with the experimental test result of natural rubber (NR) 60 IRH from the existing literature to confirm accuracy of the proposed model.

Modified hyper-viscoelastic damage evolution constitutive model for polyurethane materials – an experimental and numerical investigation

Elastomeric materials are widely used in different industries due to their excellent capability to withstand different loading types. There are significant challenges to the efficient design of elastomeric structures because of the rate-dependent and highly nonlinear behavior of this type of material. In this study, a damage zone model was employed to simulate the material behavior and damage evolution in polyurethane (PU) elastomers with different shore hardness. This model consists of three sections, hyper viscoelastic constitutive model, damage initiation, and damage evolution using a hyper viscoelastic traction-separation law. To simulate the nonlinear behavior of PU, a dynamic increase factor (DIF) implemented into the Mooney–Rivlin strain density function with 9 parameters. The material characteristics are specified by performing the experimental tests for three different shore hardness. In this study, a user-defined subroutine (VUMAT) was developed to predict the damage evolution in the pure shear tearing specimen of PU elastomers. The results verification proves a good agreement between the FEA simulation and experimental data. Therefore, the developed numerical analysis procedure can be used to investigate the damage initiation and evolution in elastomeric materials.

Friction Characteristics Analysis of Rubber Bushing with a Bionic Flexible Contact Surface Based on the Convex Hull Structure.

Inspired by the convex hull structure of the dung beetle head's surface, we extracted the non-smooth surface morphology of its head and designed a rubber bushing with a representative structure according to the bionics principle. According to the fitting results of the test data, Ogden N3-Prony N3 was selected as the hyper-viscoelastic constitutive model of the rubber material. Then, the two-direction (radial, axial) motion characteristics of the flexible friction pair in the rubber bushing were systematically analyzed from the aspects of stress, strain and thermal effect through the combination of numerical simulation and experimental research. Finally, the bionic design with the best drag reduction and wear resistance was determined.

Silicone rubber matrix composites with shear thickening fluid microcapsules realizing intelligent adaptation to impact loadings

In this paper, silicone rubber matrix composites with shear thickening fluid microcapsules (SR-STF) with intelligent adaptation to impact loadings are fabricated for advanced impact protective structure. The composites exhibit more flexibility at low strain rates but higher stiffness at high loading rates, indicating significant strain-rate sensitivity. In addition, the initial flexibility and the strain-rate sensitivity of the composite increase with increasing the mass fraction of the STF microcapsules, which should be ascribed to the shear thickening and compressive jamming of the STF microcapsules in the composite during impulse loadings. Based on experimental results, a hyper-viscoelastic constitutive model is developed, in which the influence of the mass fraction of STF microcapsules, the strain-rate sensitivity, and the strain-hardening effect are taken into account. The paper develops a practical strategy for applications of STF in soft protective structures and provides a reliable prediction of the dynamic mechanical behavior of the SR-STF composites.

Experimental hyperviscoelastic constitutive model for numerical study of elastomer materials

Experimental hyperviscoelastic constitutive model for numerical study of elastomer materials

A hyper-viscoelastic model for battery separators based on inverse-stress-solution parametrical calibration method

As the most important component in a rechargeable battery, the mechanical behaviors of separator play a crucial role in the overall safety of the battery. However, there is still a lack of effective calibration procedure for the parameters in the finite-strain viscoelasticity model of separators. To address this issue, a comprehensive analytical-experimental-numerical study is performed to characterize the time-dependent mechanical behavior in large deformation for the wet-processed isotropic separator within the framework of a hyper-viscoelastic (HVE) constitutive model. Based on ASTM E328-13, a tension-relaxation test is designed under various loading strain-rates (from 10−4 –10−1 s−1), and it is found that the difference in stress response under various loading strain-rates is mainly caused by viscoelastic effect instead of strain-rate effect. Then an inverse-stress-solution (ISS) parametrical calibration method is proposed to determine the parameters in the HVE model. By comparing the experimental results with the numerical results based on HVE models determined by three different parametrical calibration methods, it is found that the proposed ISS method can give the most robust and accurate predictive results for the isotropic separator within a finite-strain of 0.10 under loading strain-rates from 10−4 to 10−1 s−1 in this study.

A nonlinear hyper-viscoelastic model for predicting recoverable behavior of largely-deformed asphalt mortar

For predicting the recoverable behavior of largely-deformed asphalt mortar with geometrical-material nonlinearity and viscoelastic-viscoplastic coupling, a nonlinear hyper-viscoelastic constitutive model is established in the local intermediate configuration based upon the Clausius-Duhem inequality. Although with a stress-dependent parameter to represent the viscoelastic nonlinearity, the proposed model follows the linear superposition principle in a creep-recovery (C-R) process. Based on this feature, recovery curves in C-R tests can be transformed to creep curves for model calibration. It is applied to two types of asphalt mortar labeled AM-1 and AM-2. AM-1 comes from dense-graded asphalt concrete and contains filler, while AM-2 has an idealized gradation and a lower bitumen content. The increasing-stress repeated C-R tests under uniaxial compression are performed for determining model parameters, and the other C-R tests for model validation. A numerical algorithm of the constitutive model is presented and implemented in the ABAQUS finite element (FE) software, in order to validate the constitutive model and the obtained model parameters by comparing the measurements with the FE predictions. Reasonable agreements are found in the comparisons, and the R-squared values are more than 0.7. The determined model parameters show that AM-2 has higher initial moduli and better deformation resistance, but its long-term relative moduli are lower than those of AM-1.

Tensile creep mechanical behavior of periodontal ligament: A hyper-viscoelastic constitutive model

ObjectiveIn orthodontic treatment, the biomechanical response of periodontal ligament (PDL) induces tooth movement. Coupling modeling of PDL can effectively reflect its biomechanical response. The nonlinear creep mechanical behavior of PDL was studied by uniaxial tensile creep test and a new hyper-viscoelastic constitutive model. Two coupling modeling methods with limitations were excluded. MethodsPDL specimens were prepared from the central incisors of pig mandible. The theoretical step function was replaced by static loading with a total loading time of 1 s. The creep loading with the constant stresses of 0.05, 0.1, and 0.15 MPa was selected and kept unchanged for 1000 s. The instantaneous hyperelastic mechanical behavior and time-dependent nonlinear viscoelastic mechanical behavior of PDL were characterized by coupled instantaneous third-order Ogden hyperelastic and time-dependent nonlinear creep models. ResultsThe results showed that the instantaneous elastic curve of PDL increases in the form of hyperelastic index. The creep strain and creep compliance curves increase rapidly before 200s, and then increase slowly in steady state. The creep strain increased with an increase in the constant stress; conversely, the creep compliance decreased with an increase in the constant stress. The results showed that the experimental data were highly consistent with the hyper-viscoelastic constitutive model (R2>0.97). SignificanceWe normalize the framework of hyper-viscoelastic coupling modeling (Instantaneous hyperelastic model + time-dependent nonlinear viscoelastic model). Which can be extended to other nonlinear viscoelastic biomaterials.

Characterizing the hyper-viscoelastic behavior of adhesive films

Abstract In this study, the hyper-viscoelastic behavior of adhesive films was characterized. A constitutive model was developed by combining the Mooney–Rivlin hyperelastic model and a viscoelastic model expressed in terms of the Prony series to describe the constitutive behavior of the adhesive films. The material parameters of the developed constitutive model were determined through single-step stress relaxation tests conducted for 30 min at four strain levels: 100%, 200%, 300% and 400%. Based on the reduced gradient method, the optimized material parameters were then evaluated by curve fitting the experimental data. To validate the proposed constitutive model, we performed the tensile tests at different strain rates from 5 × 10−4 to 5 × 10−1 s−1 and the multistep stress relaxation tests on the adhesive films. The model predictions and experimental data were in good agreement. Thus, the proposed hyper-viscoelastic constitutive model with parameters determined through single-step stress relaxation tests is effective in characterizing the mechanical behavior of adhesive films.

Mechanical response of kerogen at high strain rates

As the main organic component of shale, the kerogen has a direct impact on the shale reservoirs. A molecular aggregate is used to study mechanical behaviour of kerogen, of which the molecular weight distribution is rational conforming to the Gaussian distribution. The mechanical response of kerogen is obtained with different strain rates by using molecular dynamics simulations. The results show that kerogen shows material hardening and fracture strain decrease with the strain rate. In the plastic range, we analyse the causes of stress oscillation at the microscopic level, and obtain the relationship between the stress oscillation and hydrogen bond. A compressible hyper-viscoelastic constitutive model of kerogen is established, which describes the mechanical behaviour of kerogen with different strain rates. Our research provides a valuable insight in the kerogen properties, and helps to understand the mechanical behaviour of shale reservoirs from a micro-perspective.

A Hyper-viscoelastic model for filled-rubber materials: experiments and simulations

Rubber has been widely addressed as anti-vibration components in long time service structure, time-dependent behavior is an undesirable problem contributing to the low acceptance by applications. In this paper, a hyper-viscoelastic model is established so that the tension behavior of rubber is simulated and analyzed. This model is constructed by a hyperelastic element in parallel with a viscoelastic model and Polynomial model, which was examined by uniaxial tension test, was proved validly to be hyperelastic. A fairly good agreement between the tension creep test and analytical results claimed that the Generalized Maxwell model with six variables is suitable for expression of hyper-viscoelastic method. In this paper, by combining the results of uniaxial tensile and tensile creep experiments, a hyper-viscoelastic constitutive model is established, and the experiment is simulated compared with the experimental results.

Mechanical characterization and viscoelastic model of the ovine temporomandibular joint Disc in indentation, uniaxial tension, and biaxial tension

There have been recent investigations into developing disc replacements and regenerative medicine to treat internal derangements of the temporomandibular joint (TMJ) disc. Previous attempts at disc replacements have faced challenges related in part to a limited understanding of the TMJ's complex mechanical environment. The purpose of this study was to characterize the mechanical behavior of the ovine TMJ disc and to derive viscoelastic constitutive models from the experimental data. Fresh ovine TMJ discs were tested in indentation stress-relaxation tests on the inferior surface, uniaxial tension tests to failure, and dynamic biaxial tensile tests. Results showed an order of magnitude stiffer behavior in tension in the anteroposterior (primary fiber) direction compared to the mediolateral direction. The stiffness in tension was much greater than in compression. Regional comparisons showed greater elastic moduli in indentation in the posterior and anterior bands compared to the central region. A hyper-viscoelastic constitutive model captured the dynamic stress-stretch behavior in both indentation and biaxial tension with good agreement. These data will support ongoing and future computational modeling of local TMJ mechanics, aid in biomaterials identification, and ultimately enhance development of implant designs for TMJ disc replacement.

Investigating the Mechanical Behavior of Clot Analogues Through Experimental and Computational Analysis.

With mechanical thrombectomy emerging as the new standard of care for stroke treatment, clot analogues provide an extremely useful tool in the testing and design of these treatment devices. The aim of this study is to characterise the mechanical behavior of thrombus analogues as a function of composition. Platelet-contracted clot analogues were prepared from blood mixtures of various hematocrits. Mechanical testing was performed whereby clots were subjected to unconfined compression between two rigid plates. Two loading protocols were imposed: cyclic compression for 10 cycles at a constant strain-rate magnitude; stress-relaxation at a constant applied compressive strain. A hyper-viscoelastic constitutive law was identified and calibrated based on the experimental mechanical test data. Scanning electron microscopy (SEM) investigated the clot microstructure at various time-points. Clot analogue composition was found to strongly affect the observed mechanical behavior. The SEM found that the microstructure of the clot analogues was affected by the storage solution and age of the clot. The proposed hyper-viscoelastic constitutive model was found to successfully capture the material test data. The results presented in this study are of key importance to the evaluation and future development mechanical thrombectomy devices and procedures.

Effect of meso-scale structures and hyper-viscoelastic mechanics on the nonlinear tensile stability and hysteresis of woven materials

Woven textiles are not only a craft and industrial product but also a thousand-year-old crystallization of human technology. However, the highly sought after mechanical behavior of fabric, generally undergoing large structural distortion along with material deformation even under small stress, is still not clearly understood despite a growing interest in emerging applications, such as flexible electron devices, biomedicine and other engineering fields. Herein, a numerical methodology was introduced to strengthen the comprehensive understanding of the synergy effect of material mechanics and mesostructures of woven materials. A hyper-viscoelastic constitutive model for yarn materials was proposed, and a meso-scale geometry model captured from a resin-cured woven fabric was used, down to micron-sized weaving structures, to investigate the uniaxial loading and unloading process based on finite element (FE) method. The tensile and hysteresis mechanics was identified based on the validated FE model and parameter study of friction effect and fabric structures. The nonlinear tensile and recovery behaviors were reasonably represented by the developed models and the synergistic effect of inner yarn friction and viscoelasticity on the hysteresis was proved. This study can provide an effective method to analyze and predict the nonlinear tensile and hysteresis behavior of woven fabric, laying down the way to textile-based strain sensing materials by enhancing our design and tuning capabilities of the dimension stability of woven materials under tension.

A Bayesian model calibration framework to evaluate brain tissue characterization experiments

A Bayesian model calibration framework is implemented to determine the posterior parameter distributions of a hyper-viscoelastic constitutive model using mechanical testing data of brain tissue. Despite the fact that brain tissue exhibits large property variability and uncertainty, least squares model calibration remains common practice. It is shown that through Bayesian calibration, the capability of an experimental design to identify parameter values can be quantitatively evaluated. A large range of experimental designs (i.e., loading modes) are considered, including rate dependent, cyclic loading through compression, shear, and tension, as well as shear and compression relaxation loading. An implementation of the nested sampling algorithm is utilized to compute the joint posterior probability distributions of the constitutive parameters based on the data considered. The joint probability distribution of the parameters enables assessment of parameter sensitivity, uncertainty, correlation, and model calibration error as a function of experimental design. By calibrating simultaneously to numerous combinations of loading modes, redundancy in loading mode as well as parameter convergence can be evaluated based on model calibration error and parameter variability. The results of this study verify that the inclusion of more loading modes in the calibration increases the accuracy of parameter identification, while only one or two loading modes may provide almost no information for identifying certain parameters.

Investigation on failure properties and constitutive modeling of EPDM used for pulse separation device

In order to characterize the rate-dependent deformation-failure behavior of pulse separation device (PSD) of ethylene propylene diene monomer (EPDM), uniaxial constant rate tension, variable rate tension, and stress relaxation experiments were conducted for EPDM in a universal testing machine. It was found that the deformation-failure behavior of EPDM was dependent on the applied strain rates. An improved hyper-viscoelastic constitutive model with an energy limiter (in which the constant energy limiter was replaced by a rate-dependent energy limiter) was proposed to predict the rate-dependent deformation-failure behavior of EPDM under quasi-static loading. The proposed model was first calibrated by fitting it (based on the least squares method) to the data obtained from uniaxial constant rate tension experiments and then further examined by the data obtained from variable rate tension and stress relaxation experiments. The comparative results revealed that the constitutive model with a rate-dependent energy limiter predicted the rate-dependent deformation-failure behavior of EPDM under finite deformation and quasi-static loadings very well.