Yeoh Model Research Articles

Flexible soft Pneumatic Bionic Hand Based on Multi-Jointed Structure

Compared with rigid robotic hands, soft hands can provide better safety and adaptability. In the process of gradual development, the multi-jointed structure that mimics the shape of the human hand has shown significant progress in realizing its personification. In this article, we propose a multi-jointed pneumatic soft hand, which is composed of multi-jointed soft fingers, thumb, thenar and 3D printed palm. It can express letters through sign language gestures and can grasp objects with different sizes, shapes, weights and surface textures. We tested the bending ability of the actuators under different air pressures to characterize the performance of actuators made of silicone rubber. Based on the strain energy density function of silicone rubber, the Yeoh model is used to calculate the relationship between the air pressure required and the bending angle. In addition, a dedicated pneumatic control system is designed and manufactured to enable the soft hand to automatically perform tasks set by the specific program. This new multi-jointed pneumatic soft hand has flexible bionic fingers, and has the advantages of fast response speed, low cost, easy manufacturing, assembly and replacement.

Hyper-Pseudo-Viscoelastic Model and Parameter Identification for Describing Tensile Recovery Stress–Strain Responses of Rubber Components in TBR

Tires are often in service under dynamic conditions. Realizing the high-precision prediction of the mechanical response of rubber materials under cyclic loading can provide guidance for the design of high-performance tires. In this work, the tensile recovery stress-strain responses of rubber materials in nine different components of a truck and bus radial (TBR) tire were obtained through experiments. Before fitting, an experimental data processing method was proposed to facilitate the parameter identification for a hyper-pseudo-viscoelastic model, that is, the raw experimental data were changed to the adjusted test data. The HyperFit software was used to fit the adjusted test data based on the Yeoh hyperelastic model and the Ogden-Roxburgh pseudoelastic model to obtain the initial material parameters for the two models. In order to describe the permanent set, the Prony series viscoelastic model was introduced. The Isight software was adopted to optimize the parameters. The results showed that the hyper-pseudo-viscoelastic model (i.e., the combination of Yeoh, Ogden-Roxburgh and Prony series models) can describe the tensile recovery mechanical responses (loading curve, unloading curve and permanent set) of nine different rubber components in TBRs. The fitting results are in good agreement with the adjusted data, and all the coefficients of determination (R2) exceed 0.975. Finally, the cyclic deformation simulation of a dumbbell rubber specimen was carried out based on the above constitutive model and fitted parameters. R2 was used to describe the simulation accuracy and its value reached 0.968.

Influence of Deformation on Sound-Absorbing Performance Under Hydrostatic Pressure

The sound-absorbing rubber coating is easy to deform under hydrostatic pressure, resulting in variation in acoustic properties. For improving the accuracy of the deformation of the sound-absorbing structure under hydrostatic pressure, four hyperelastic constitutive models of Mooney-Rivlin, Neo-Hookean, Yeoh and Arruda-Boyce were selected in fitting the tensile curve of the dumbbell specimen and the compressive curve of a cylindrical specimen. The comparison in their applicability and the accuracy showed that the Yeoh model can predict the compressive properties of carbon black filled styrene-butadiene rubber. Simulation in mechanics-sound coupling was further conducted by COMSOL software and verified by the acoustic experiments, which exhibit the non-negligible effects of pressure and tubes inserted in the cavities on the deformation and sound-absorption coefficient. Hydrostatic pressure exerts the deformation and thereafter the energy dissipation in sound transfer. Inserting a rigid tube is beneficial to improve the ability of the sound-absorbing tile to resist deformation and enhance sound absorption and dissipation. The sound absorption coefficient was above 0.4 in the frequency band above 1.5kHz even under the hydrostatic pressure of 2MPa. The numerical simulation provides one methodological reference in analyzing the influences of the structural change and the operational conditions on the sound-absorbing coating.

Importance of experimental evaluation of structural parameters for constitutive modelling of aorta

The study compares stresses and strains in the aortic wall derived using different constitutive models for various stress-strain conditions. Structure-based constitutive models with two fibre families with (GOH) and without (HGO) dispersion of collagen fibres are compared. The constitutive models were fitted to data from equibiaxial tension tests of two separated layers of the porcine aortic wall. The initial fit was evaluated with unrestricted parameters and subsequently, the mean angles of the fibre families and the angular dispersion were fixed to the values obtained from histology. Surprisingly, none of the tested models was capable to provide a good quality fit with histologically obtained structural parameters. Fitting the HGO model to experimental data resulted in two fibre families under angles close to ±45°, while the GOH model resulted in a nearly isotropic fibre distribution. These results indicate that both of these models suffer from the absence of isotropic strain stiffening. After having modified both models with corresponding additional members based on the Yeoh model of matrix, we obtained a perfect fit to the measured data while keeping the structural histology-based parameters. Finally, significant differences in compliance and resulting stresses and strains between different models are shown by means of simulations of uniaxial tension test, equibiaxial tension tests and inflation of the aorta.

Влияние наполнителя на деформацию полидиметилсилоксановых композитов под действием электрического поля

The study considers some aspects of the development of new stimuliresponsive materials capable to reversible deformation under an electric field due to the Maxwell pressure. To increase the response of the material to an external stimulus, an approach of polymer composites formation was chosen. Particles of various nature and shape were considered as fillers: powders of iron, montmorillonite and cellulose. Composite elastomeric materials based on polydimethylsiloxane with a low filler content of 5 wt% have been obtained. The morphology of the filler particles was confirmed by electron microscopy. Mechanical properties of the materials in uniaxial tests were studied. The Young’s modulus and constants for the 3-parameter Yeoh model in the range of deformations up to 800 % were determined. The electrophysical properties of the materials, as well as their response to an electric field at different strengths of 0.84 and 2.5 kV/mm have been studied. The effect of the filler nature on the conductivity and permittivity of composite materials was revealed. The data of mechanical and dielectric studies indicate that the filler concentration is below the percolation threshold for all composites. The composite with cellulose exhibits the greatest response to an external stimulus over the considered materials, which is determined by the balance of two factors: the value of Young’s modulus and the values of electrophysical characteristics. Directions for further research were determined and the prospects for the dielectric elastomers creation with predetermined properties were briefly discussed

A new family of Constitutive Artificial Neural Networks towards automated model discovery

For more than 100 years, chemical, physical, and material scientists have proposed competing constitutive models to best characterize the behavior of natural and man-made materials in response to mechanical loading. Now, computer science offers a universal solution: Neural Networks. Neural Networks are powerful function approximators that can learn constitutive relations from large data without any knowledge of the underlying physics. However, classical Neural Networks entirely ignore a century of research in constitutive modeling, violate thermodynamic considerations, and fail to predict the behavior outside the training regime. Here we design a new family of Constitutive Artificial Neural Networks that inherently satisfy common kinematical, thermodynamical, and physical constraints and, at the same time, constrain the design space of admissible functions to create robust approximators, even in the presence of sparse data. Towards this goal we revisit the non-linear field theories of mechanics and reverse-engineer the network input to account for material objectivity, material symmetry and incompressibility; the network output to enforce thermodynamic consistency; the activation functions to implement physically reasonable restrictions; and the network architecture to ensure polyconvexity. We demonstrate that this new class of models is a generalization of the classical neo Hooke, Blatz Ko, Mooney Rivlin, Yeoh, and Demiray models and that the network weights have a clear physical interpretation in the form of shear moduli, stiffness-like parameters, and exponential coefficients. When trained with classical benchmark data for rubber under uniaxial tension, biaxial extension, and pure shear, our network autonomously selects the best constitutive model and learns its set of parameters. Our findings suggest that Constitutive Artificial Neural Networks have the potential to induce a paradigm shift in constitutive modeling, from user-defined model selection to automated model discovery. Our source code, data, and examples is available at https://github.com/LivingMatterLab/CANN.

Stretchable Conductive Tubular Composites Based on Braided Carbon Nanotube Yarns with an Elastomer Matrix.

We report an innovative approach to creating stretchable conductive materials composed of a tubular shell made from braided carbon nanotube yarns (CNTYs) embedded in an elastomeric matrix. For stretchable electronics, both mechanical properties and electrical conductivities are of interest. Consequently, both the mechanical behavior and electrical conductivities under large deformations were investigated. A new hyperelastic composite model was developed to predict the large deformation response to applied stress for a braid in a tubular elastomer composite. The composite demonstrated a hyperelastic response due to the architecture of the braid, and the behavior was affected by the braiding angle, braid modulus, and volume fraction of fibers. The elastomer matrix was considered a neo-Hookean material and represented by the Yeoh model. An interaction parameter was proposed to account for the effect of the elastomer/braid cooperative restriction as observed in experimental and calculated results. This novel approach enabled the determination of the constitutive behavior of the composite in large deformations (>150%), taking into account the elastomer and yarn properties and braid configurations. The model exhibited good agreement with the experimental results. As the CNTYs are conductive, a stretchable conductive composite was obtained having a resistivity of 5.01 × 10-4 and 5.67 × 10-5 Ω·cm for the 1-ply and 4-ply composites, respectively. The resistivity remained constant through cyclic loading under large deformations in tension until mechanical failure. The material has potential for use in stretchable electronics applications.

Frequency domain analysis of pre-stressed elastomeric vibration isolators

Two types of elastomeric vibration isolators used for equipment vibration isolation in aerospace vehicles are considered for the present study. These isolators are constructed using elastomers mounted in steel encasings. These isolators are initially deformed statically and dynamic loads are applied on the deformed configuration. To capture the static deformation, equivalent static load corresponding to its load rating and specified displacements are created. Static deformation is computed using Finite Element methods with four node axi-symmetric element which include the geometric non-linear effect for steel and with standard Yeoh hyper-elastic material model for elastomers (Muhammed and Zu, 2012) [1]. Yeoh material constants are derived from uni-axial tension test data of the elastomer specimen. These isolators are subjected to harmonic and random excitations in the pre-deformed state. For numerical analysis, elastomeric constants at dynamic conditions are obtained as complex function of frequency using Dynamic Mechanical Analyzer (DMA) for a range of frequencies. The standard material model of Yeoh is modified incorporating frequency dependant material characteristics and damping in the range of frequencies of interest. A multiplicative non-separable variables law is derived for Yeoh material model to include the effect of static pre-stress, based on the methodology given in literature (Nashif et al., 1985; Beda et al., 2014) [2,3]. The modifications of Yeoh model suitable for frequency domain analysis is the novelty in the present study. In the analysis, while dynamic loads are applied, the configuration is updated considering initial static loading. The frequency response of the isolators is computed using material properties evaluated at progressive dynamic strains until a match in natural frequency is observed. Appropriate damping corrections are then incorporated to match the test observed transmissibility. Then updated material properties are used to compute the random response which showed good agreement with results of experiments, validating the approach taken for the development of this model.

A comparative study of invariant-based hyperelastic models for silicone elastomers under biaxial deformation with the virtual fields method

Silicone elastomers have been widely used for biomedical applications. A variety of hyperelastic models have been proposed to describe this type of materials in the past few decades. The assessment of the quality of the proposed models is mostly based on stress–strain data obtained from uniform deformation, but very little work has been done to investigate model performances with heterogeneous deformation fields and full-field characterization methods. In this study, thirteen hyperelastic models are evaluated using the virtual fields method combined with full-field deformation data obtained from biaxial tests. The quality of these models is assessed by their capabilities to predict the mechanical responses of silicone elastomers, and the influences of the first and second invariants on modeling of elastomers are investigated through comparative studies between models. The results indicate that for elastomers under finite biaxial deformation, Yeoh model performs the best among selected models; the first invariant plays an important role in constitutive modeling; the second invariant does not have obvious influence on improving the fitting performance. This study provides a full-field method to calibrate and compare hyperelastic models of silicone elastomers under biaxial loading conditions.

Numerical investigation of load-induced fatigue cracking in curved ramp bridge deck pavement considering tire-bridge interaction

Load-induced fatigue cracking is one of the main distresses of bridge deck pavement; however, due to the complexity of curved ramp bridge structures, it is difficult to effectively consider this damage behavior in the deck pavement design procedure. To deal with this problem, a three-dimensional (3D) tire-bridge interaction finite element (FE) model was developed in the present study to investigate the load-induced fatigue damage behavior within the curved ramp bridge deck pavement. In this FE model, an inflated tire model was developed to simulate the rolling tire load, and the Yeoh model was used to define the constitutive relationship of the hyperelastic material. In addition, the extended finite element method (XFEM) was utilized to describe the crack initiation and evolution, and a direct cycle algorithm was used to calculate the fatigue crack propagation law of deck pavement under different structural design parameters. The results indicated that the developed tire-bridge interaction FE model furnishes an in-depth insight into the fatigue crack propagation within curved ramp bridge deck pavement. The consideration of the tire-bridge interaction and structural design parameters has a significant influence on the accurate prediction of the fatigue crack evolution law within different deck pavement locations. Because the developed full-scale FE model is capable of simultaneously considering multiple factors, including the curvature radius, transverse and longitudinal slope, traffic speeds and tire-bridge interaction loads, it can be expected to be a mechanistic tool to facilitate and enhance fatigue damage analysis of curved ramp bridge deck pavement.

Temperature Dependence of Rubber Hyper-Elasticity Based on Different Constitutive Models and Their Prediction Ability.

Based on the electronic universal testing machine with a temperature chamber, this paper investigated the temperature and filler effects on the hyper-elastic behavior of reinforced rubbers and revealed the regulation of the stress and strain of the natural rubber and filled rubber with temperature. The experimental results showed that the hyper-elastic behavior of the filled rubber was temperature-dependent in a wide range. Comparing the adaptability of different models to the stress–strain variation with temperature, the Yeoh model was proven to reasonably characterize the experimental data at different temperatures. Based on the Yeoh model, an explicit temperature-dependent constitutive model was developed to describe the stress–strain response of the filled rubber in a relatively large temperature range. The prediction data of this proposed constitutive model fit well with the test data of the mechanical experiments, indicating that the model is suitable to characterize the large deformation behavior of filled rubbers at different temperatures to a certain degree. The proposed model can be used to obtain the material parameters and has been successfully applied to finite element analysis (FEA), suggesting a high application value. Notably, the model has a simple form and can be conveniently applied in related performance tests of actual production or finite element analysis.

The Sealing Effect Improvement Prediction of Flat Rubber Ring in Roller Bit Based on Yeoh_Revised Model.

In a roller bit, the flat rubber ring (FRR) often needs to apply a certain amount of compression to ensure that its rotation and static sealing surfaces can be stably sealed. For the predicted Mises stress, values smaller than the actual Mises stress due to soft single-axis compression (SAC) stress are predicted by the Yeoh (N = 3) model. To more reasonably predict stress under the static compression of the FRR in the roller bit, the sealing effect of the FRR based on the SAC contact stress and the calculated Mises stress was evaluated by the Yeoh_revised model. Based on the assumption that hydrogenated nitrile-butadiene rubber (HNBR) is isotropic and incompressible, first, we derived the fitting formulas for three types of constitutive models and the Jacobi matrix of the Yeoh_revised model and developed hyperelastic constitutive subroutines. Simultaneously, the accuracy of three models (Yeoh, Yeoh_revised and Ogden) was evaluated by the goodness of fit (R2) to data from three kinds of tensile experiment tests. The highest R2 is 0.9771 with the Yeoh_revised model, which merges the advantages of the other two fitting models and effectively improves the Yeoh model’s soft property of SAC contact stress. Additionally, by measuring on-site FRR wear, the maximum Mises stress on the sealing surface calculated based on the Yeoh_revised model is about twice that of the Yeoh model, and the maximum Mises stress on the rotation contact sealing surface is higher than that on the outside (static sealing) surface, which makes the aging of the rotation surface more severe. Thus, it was demonstrated that, on the premise of ensuring FRR sealing contact stress, the Yeoh_revised model can more reasonably predict the sealing effect of the FRR to more precisely calculate Mises stress than the Yeoh model. This also contributes to FRR structure optimization to prolong the service life of the FRR in the roller bit.

Fabrication, characterization and modelling of the fabric electrode-based highly stretchable capacitive strain sensor

Highly stretchable and capacitance-based strain sensors were fabricated utilizing highly stretchable silicone elastomer as dielectric film sandwiched between the conducting and stretchable cloth-based top and bottom electrodes. Electromechanical characterizations for the proposed sensor after multiple and reversible loading and unloading cycles up to 150% applied strain were conducted followed by the modelling of the sensing performance. It has been shown that the sensor exhibits reproducible electromechanical performance under multiple reversible stretching and relaxation cycles. There was a very small deviation (< 10%) in the observed values of the capacitance upon the applied strain of 150% up to the 1000 loading and unloading cycles. Tensile measurement for the sensor under various applied strains, not only exhibits almost constant force indicating negligible Mullins effect and negligible time-dependent changes at a fixed strain up to 100% suggesting that viscoelastic losses can also be neglected. From uniaxial tensile experiments, constitutive model of the dielectric elastomer sensor was validated. For the fitting of the experimental data obtained from the uniaxial tensile measurement, a variety of strain energy formulations have been compared for predicting the constitutive behaviour of sensor using the Mooney– Rivlin, Neo-Hookean, Yeoh and Ogden models, where 2nd term of the Ogden model was found to explain the experimental tensile data most accurately. To explain some observed losses at 150% of applied strain, the Prony series-based time dependent model was used for predicting stress at any value of time and it was found that experimental data was well fit with 4th order of Prony series.

Comparative study on the sealing performance of packer rubber based on elastic and hyperelastic analyses using various constitutive models

Evaluation of the sealing performance of the packer rubber varies according to specific simulation models. This paper aims at revealing the difference between elastic and hyperelastic analyses using the finite element mothed (FEM). The study extracts the hyperelastic parameters of the neo-Hookean, the Mooney-Rivlin, and the Yeoh models from a uniaxial tensile test. Then, the setting process of a mechanical packer is simulated by elastic and hyperelastic calculations. We compare the deformed configuration and the contact stress given by these models. Our results show that the Yeoh model produces the minimum residual sum of squares (RSS) among the hyperelastic models for hydrogenated nitrile butadiene rubber (HNBR). The mooney-Rivlin model has a negative parameter, making the calculation unstable. The linear elastic model fails to simulate the setting process, while the neo-Hookean model overestimates the contact stress. Despite the similar stress distribution, the nonlinear elastic model provides a 17.8% higher contact stress on average than the Yeoh model. A parametric study based on the Yeoh model points out that the sub-thickness of the packer rubber needs an elaborate design. Reducing the sub-thickness could increase the contact stress but decrease the seal length in the force control mode. From an engineering perspective, this study demonstrates that it needs to pay more attention when selecting an appropriate material model and a sound analysis method to evaluate the sealing performance of an oil packer.

Mechanical Deformation Analysis of a Flexible Finger in Terms of an Improved ANCF Plate Element

In recent years, flexible continuum robots have been substantially developed. Absolute nodal coordinates formulation (ANCF) gives a feasible path for simulating the behavior of flexible robots. However, the model of finger-shaped robots is often regarded as a cylinder and characterized by a beam element. Obviously, this is short of characterizing the geometrical feature of fingers in detail, especially under bending conditions. Additionally, for the lower-order plate element, it is hard to characterize the bending behavior of the flexible finger due to fewer nodes; a higher-order plate element often requires an extremely long computing time. In this work, an improved ANCF lower-order plate element is used to increase the accuracy of the Yeoh model and characterize the geometrical structure of silicone rubber fingers, taking into particular consideration the effect of volume locks and multi-body system constraints. Since it is a kind of lower-order plate element, essentially, the computing time is nearly the same as that of conventional lower-order plate elements. The validity of this model was verified by comparing it with the results of the published reference. The flexible finger, manufactured using silicone rubber, is characterized by the novel ANCF lower-order plate element, whereby its mechanical deformation and bending behavior are simulated both efficiently and accurately. Compared to the ANCF beam element, conventional lower-order plate element, and higher-order plate element, the novel plate element in this paper characterizes the external contour of the finger better, reflects bending behavior more realistically, and converges in less computing time.

Response of binder-filler systems into and beyond linear viscoelastic domain: Modeling and healing efficiency

This study is devoted to present insights into linear and nonlinear viscoelastic responses as well as the healing efficiency (HE) of binder-filler systems. To this aim, linear viscoelastic (LV) rheometric results were collected via implementing temperature and frequency sweep measurements, while for probing the nonlinear viscoelastic (NLV) response, large-amplitude oscillatory shear test was executed for various strain maxima. A parallel rheological framework assembled from 2 Yeoh models and hyperbolic-sine flow law, hereinafter abbreviated as 2Y-HS model, was explored to emulate the stress response for LV and NLV behavior of the binder-filler systems. In addition, a strain-dependent healing protocol was developed to test the HE of materials for varying strain-amplitudes. The tested binder-filler systems were blends of a plain binder and two mineral fillers, hydrated lime (HL) and silica fume (SF), added one at a time at different rates based on the best-practice limits. The binder-filler mastics undergone different behaviors into and beyond linear viscoelastic domain (LVD). The 2Y-HS model has efficiently constituted the rheometric results in a manner that elucidates the link between the stresses and strains for both LV and NLV behaviors. The proposed HE protocol showed its efficacy to evaluate the healability of materials at varying rest periods and stretch magnitudes. The damage-mending process at small-amplitude strains tended to improve better, and worst HE was attained as the strain level increases. The richer the asphalt binder with mineral filler, the less the HE is registered; however the binder-HL system is predisposed to heal much more than SF mastics.

Design and Simulation Experiment of Rigid-Flexible Soft Humanoid Finger

This paper is based on the “Fast Pneumatic Mesh Driver” (FPN) used to couple a silicone rubber soft body with a rigid skeleton. A rigid-flexible coupling soft-body human-like finger design scheme is proposed to solve the problem of low load on the soft-body gripping hand. The second-order Yeoh model is used to establish the statics model of the soft humanoid finger, and the ABAQUS simulation analysis software is used for correction and comparison to verify the feasibility of the soft humanoid finger bending. The thickness of the driver cavity and the confining strain layer were determined by finite element simulation. The mold casting process is used to complete the preparation of human-like fingers and design a pneumatic control system for experiments combined with 3D printing technology. The experimental results show that the proposed rigid-flexible coupling soft body imitating the human finger structure can realize the corresponding actions, such as the multi-joint bending and side swinging, of human fingers. Compared with the traditional pure soft-body finger, the fingertip output force is significantly improved. The optimal design and simulation analysis of the human gripper and the feasibility of the application have practical guiding significance.

Computational Data of Gelatin for Hybrid Biomaterials

Gelatine is a soluble protein derived from animal skin, white connective tissue, or bones via collagen hydrolysis. This project began with CATIA modelling adaptation and progressed through ANSYS Workbench computational analysis processes. The two hyperelastic models (Mooney-Rivlin and Yeoh) were contrasted computationally with assess the distinction in chart execution and other mechanical properties that ought to be corresponding to the exploratory information. The material went through three stages: pre-processing, static structural, and post-processing. Through this computational analysis, the best data execution was presented with the optimum stress and stretch according to hyperelastic constitutive models. The nodes distance expanded was determined by the total deformation plot in addition to the simulation. In comparison to the experimental approach, the Yeoh model yields the lowest percentage error. As a result, when the skin patch can stretch and maintain the condition when force is applied to it, this product has potential to contribute in medical needs. Keywords—Artificial skin, computational analysis, gelatine skin, hyperelastic models, Mooney-Rivlin, tissue engineering.

An improved dynamic formulation for nonlinear response analysis of thin soft silicone plates with large deflection

This present paper develops an absolute nodal coordinate formulation (ANCF) improved lower-order plate element (ILOPE) for nonlinear dynamic response analysis of thin soft silicone plates with large deflection. Different from a common linear metallic plate which is modeled by combining linear constitutive model with original lower-order plate element (OLOPE), both material nonlinearity and geometric nonlinearity should be taken into account for this type of silicone plate. An improved dynamic formulation is developed for modeling and analyzing the soft deformable silicone plate based on Yeoh nonlinear constitutive model combined with ILOPE, meanwhile the stiffening effect problem is circumvented smoothly. By bringing in penalty function, and the elastic force and its derivative matrices of Yeoh model are deduced, and then a dynamic equations of motion for the silicone plate is founded in the frame of ANCF. The second order differential dynamic equation is solved by uniting Newton–Raphson iterative approach with Newmark numerical integral method. Dynamic free-falling motion process of a half-cantilevered silicone plate and a spherical hinge silicone plate only under the influence of gravitational force are simulated by adopting OLOPE and ILOPE, respectively. The comparison of the simulation results calculated by ILOPE with those obtained by the previously proposed reduced-order plate element and commercial software ANSYS demonstrates that the improved dynamic formulation is feasible and effective. Finally, the displacement nephograms of middle surface of two types of silicone plates are elaborated in terms of displacements and configuration variations, and the law of conservation of energy is elucidated from perspective of different energy variations.

A time-dependent Yeoh model to predict the corrosion effect of supercritical CO2 on the HNBR sealing rubber

A time-dependent Yeoh model to predict the corrosion effect of supercritical CO2 on the HNBR sealing rubber