Yeoh Model Research Articles

Utilizing physics‐augmented neural networks to predict the material behavior according to Yeoh's law

AbstractThis article discusses physics‐augmented neural network approaches in the field of hyperelastic material modeling. Physical conditions such as objectivity, material symmetry, or a stress– and energy‐free reference configuration are considered in the construction of the neural networks. In addition, a new approach for stress normalization is proposed. The neural network is used to learn the behavior of Yeoh's constitutive model with sparse data. Finally, the trained networks are incorporated into a three‐dimensional finite element framework and compared with the classical material model in terms of accuracy. The paper demonstrates the ability of physics‐augmented neural networks to model hyperelastic materials using a small amount of data that could be generated by experiments. Compared to the classical constitutive laws of Yeoh's model, our trained material showed no material instabilities that could occur due to poorly chosen material parameters.

Influence of experimental conditions on some in-vitro biomechanical properties of the sow’s perineum

The aim of this work was to develop an experimental protocol that takes into account the influence of experimental conditions on these perineal tissues, before determining their mechanical properties. Samples of each perineal tissue layer were obtained from the skin, the vagina, the external anal sphincter (EAS), the internal anal sphincter (IAS) and anal mucosa of freshly dead sows. They were tested in quasi-static uniaxial tension using the Mach-1 testing machine. Stress-strain curves of each perineal tissue layer before the first damage for each sow were obtained and modeled by hyperelastic laws described by three coefficients: C1, C2, and C3 (Yeoh model). The influence of sample preparation conditions such as tissue freezing, hygrometry and sample orientation were evaluated, and the conditions under which the tests were performed such as the displacement velocity during testing were also evaluated by analysing C1-coefficient. This study suggested that sample preparation conditions such as tissue freezing for 24 h, storage in cellophane paper for two hours and the strain rate did not statistically affect the C1-hyperelastic coefficient for each perineal layer (p > 0.05). Samples should not be stored in saline for 2 h (p < 0.05). Sample orientation did not influence C1-hyperelastic coefficient (p > 0.05). This experimental protocol could be used to study in vitro biomechanical properties of perineal tissues in order to better understand perineal tears during delivery.

Bending/force switching control of pneumatic soft actuator based on multi-sensor fusion

Abstract The soft actuator has unlimited freedom, and can realize the grasping of irregular or fragile objects. A pneumatic soft actuator is designed in this paper, which consists of a series of symmetrically distributed pneumatic chambers. The soft actuator consists of a top expansion layer composed of 20 chambers and a bottom restraint layer. The Yeoh model and the finite element method (FEM) were employed to analyze the bending of the soft actuator. To improve the tracking performance, a PID strategy of the endocrine system (ES-PID) based on the neuroendocrine thyroid hormone regulation mechanism was constructed to tune the bending deformation. To achieve steady and precise force control, a bending/force switching control algorithm based on multi-sensor fusion is designed to realize high control accuracy. The bending/force switching control strategy mainly consists of two feedback loops for bending control, a force control, and a switching control. In the experimental process, the bending control is the primary control, and the force control is the primary control when the switching condition is satisfied. In order to prevent the occurrence of a false switching action, a switching factor is constructed using the method of successive comparison of neighboring values. Finally, several experiments are carried out to verify the effectiveness and feasibility of the control algorithm.

Nonlinear geometrically exact dynamics of hyperelastic pipes conveying fluid: Comparative study of different hyperelastic models

This work presents a comparative analysis of the nonlinear dynamic responses of fluid-conveying pipes modelled by four different phenomenological hyperelastic constitutive models, namely the Mooney-Rivlin model, the Neo-Hookean model, the Yeoh model, and the Ogden model. Based on the strain energy density functions and the exact geometric relation, the geometrically exact dynamic models corresponding to different hyperelastic contitutive models are established. Then the Galerkin's truncation is adopted to transfer the obtained nonlinear integral-partial differential equations into the nonlinear ordinary differential equations. Subsequently, linear dynamic study and finite difference method are taken to explore the natural frequencies and stabilities and nonlinear dynamic responses of the pipe, respectively. And the fitting coefficients for various models obtained from Treloar's experiment data are utilized in the numerical calculation. It is found the Hopf bifurcation and the limit cycle oscillations in the post-flutter status are influenced by the choice of the hyperelastic models, particularly under large flow velocity. However, hyperelastic constitutive models do not exert a significantly extreme influence on the results, which can be attributed to the relatively small strains even though large deformations occur in the pipe. Mathematically, it is proven that the symmetry observed in the pipe's displacement response stems from the symmetry of its cross-section and the inextensibility assumption of the centerline, with hyperelasticity having no effect on this symmetry.

The Change of Sealing Property in the Aging Process of NBR Sealing Equipment Based on Finite Element Analysis

Sealing rings are the core components of flange sealing structures and play a crucial role in the storage and operation of gas generators. The aging and deformation of seals affect the safe operation of the device. This paper aims to investigate the effect of rubber aging on the sealing performance of the components, which is realized by nonlinear finite element analysis. Firstly, an accelerated degradation test method was used to obtain the compression permanent deformation and stress–strain curve of rubber during the aging process. A two-dimensional finite element model of the sealing structure was constructed and the Yeoh model was utilized to describe the mechanical response of rubber. During the simulation, the contact area was modified based on the compression permanent deformation, and the Yeoh model was updated based on the stress–strain curve changes obtained by the test. The impact of key parameters such as material property changes, rubber physical section deformation, and fluid pressure on sealing performance during the seal ring aging process was systematically studied. The numerical results indicate that due to the aging deformation of rubber seals, there is a significant decrease in contact stress and contact width, as well as a shift in maximum equivalent stress area. Taking into account these findings, this study proposes a new design concept for sealing structures. This provides a relatively simple research method for studying flange sealing structure performance.

Prediction Accuracy of Hyperelastic Material Models for Rubber Bumper under Compressive Load.

Different hyperelastic material models (Mooney-Rivlin, Yeoh, Gent, Arruda-Boyce and Ogden) are able to estimate Treloar's test data series containing uniaxial and biaxial tension and pure shear stress-strain characteristics of rubber. If the rubber behaviour is only determined for the specific load of the product, which, in the case of rubber bumpers, is the compression, the time needed for the laboratory test can be significantly decreased. The stress-strain characteristics of the uniaxial compression test of rubber samples were used to fit hyperelastic material models. Laboratory and numerical tests of a rubber bumper with a given compound and complex geometry were used to determine the accuracy of the material models. Designing rubber products requires special consideration of the numerical discretization process due to the nonlinear behaviours (material nonlinearity, large deformation, connections, etc.). Modelling considerations were presented for the finite element analysis of the rubber bumper. The results showed that if only uniaxial compression test data are available for the curve fitting of the material model, the Yeoh model performs the best in predicting the rubber product material response under compressive load and complex strain state.

Analysis of Inherent Frequencies to Mitigate Liquid Sloshing in Overhead Double-Baffle Damper

A disco-rectangular volume-fraction-of-fluid (VOF) model tank of a prismatic size is considered here for investigating the severe effect of overhead baffles made of three different materials, nylon, polyamide, and polylactic acid. In this work, the overdamped, undamped, and nominal damped motion of baffles and their effect are studied. In this research, the behaviour of different material baffles based on the sloshing effect and natural frequency of each baffle excited in damped, undamped, and overdamped cases is studied. VOF modelling is carried out in moving Yeoh model mesh with fluid–structure interaction between the water models for various baffle plates. The results of the water volume distribution and baffle displacement operating between a sloshing time of 0 and 1 s are recorded. Also, a strong investigation is carried out for the water volume suspended on overhead baffles by three different material selections.

KAJI NUMERIK GROUND PAD SHOE KENDARAAN TEMPUR DENGAN MODEL MATERIAL HYPERELASTIC

One of the important components on a combat vehicle is the ground pad shoe (GPS) or track pad. GPS that has been developed at this time mostly uses rubber material. Rubber raw materials themselves are found in Indonesia in large amount. Indonesia left 3 million tonnes of natural rubber unprocessed in 2018. On the other hand, natural rubber research is quite expensive and takes a long time to become a product. To make rubber products is needed special molds and tests. To solve the high costs and long time involved in rubber research, it is necessary to carry out numerical research. In this study, a numerical study of GPS rubber for combat vehicles was carried out with a hyperelastic material model. The research was conducted experimentally and numerically. Tensile testing is carried out on imported GPS samples which are then used as comparison data for numerical studies. The Mooney-Rivlin, Neo-Hookean, Yeoh, and Ogden hyperelastic models were varied to get the stress and strain values ​​closest to the experimental test. The results of the numerical study show that the best hyperelastic model for the imported GPS rubber model is the Neo-Hookean model. The tensile strength of GPS according to the experimental tensile test results is 16.93 MPa, while the result of the finite element method (FEM) is 16.75 MPa. The GPS modulus 200% according to the experimental tensile test results is 14.7 mm/mm, while the FEM result is 15.3 mm/mm. The difference between the FEM and experimental test values ​​for tensile strength and modulus 200% are below 5%. Maximum stress on GPS is 4,4 MPa and safety factor 3,8.

Design of a robotic gripper for casting sorting robots with rigid–flexible coupling structures

AbstractIn order to solve the problem of the insufficient adaptability of the current small- and medium-sized casting sorting robot gripper, we have designed a casting sorting robot bionic gripper with rigid–flexible coupling structures based on the robot topology theory. The second-order Yeoh model was used to statically model the clamping belt in the gripper to derive the relationship between the external input air pressure and the bending angle of the driving layer, and the feasibility of multiangle bending of the driving layer was verified by finite element analysis. The maximum gripping diameter of the gripper is 140 mm, and in order to test the adaptive gripping ability of the gripper, a prototype of the casting sorting robot gripper is prepared, and the pneumatic control system and human–machine interface of the gripper are designed. After several experimental analyses, the designed casting sorting robot gripper is characterized by strong adaptability and high robustness, with a maximum load capacity of 930 g and a maximum wrap angle of 296°, which can complete the gripping operation within 1 s, and the comprehensive gripping success rate reaches 96.4%. The casting sorting robot gripper designed in the paper can provide a reference for the design and optimization of various types of shaped workpiece gripping manipulators.

Towards the biomechanical modelling of the behaviour of ex-vivo porcine perineal tissues

The perineum is a layered soft tissue structure with mechanical properties that maintain the integrity of the pelvic floor. During childbirth, the perineum undergoes significant deformation that often results in tears of various degrees of severity. To better understand the mechanisms underlying perineal tears, it is crucial to consider the mechanical properties of the different tissues that make up the perineum. Unfortunately, there is a lack of data on the mechanical properties of the perineum in the literature. The objective of this study is to partly fill these gaps. Hence sow perineums were dissected and the five perineal tissues involved in tears were characterized by uniaxial tension tests: Skin, Vagina, External Anal Sphincter, Internal Anal Sphincter and Anal Mucosa. From our knowledge, this study is the first to investigate all these tissues and to design a testing protocol to characterize their material properties. Six material models were used to fit the experimental data and the correlation between experimental and predicted data was evaluated for comparison. As a result, even if the tissues are of different nature, the best correlation was obtained with the Yeoh and Martins material models for all tissues. Moreover, these preliminary results show the difference in stiffness between the tissues which indicates that they might have different roles in the structure. These obtained results will serve as a basis to design an improved experimental protocol for a more robust structural model of the porcine perineum that can be used for the human perineum to predict perineal tears.

Mathematical modeling of biomechanical elastic and hyperelastic properties of the myocardium

BACKGROUND: The study of mechanical properties of biological tissues is extremely informative and is one of the most important areas of biomechanics. Knowledge of these aspects of biological objects based on experimental data can become a source of new medical and technical solutions for the reconstruction of organs and the development of replacement materials. AIM: Passive mechanical properties of isolated myocardium are compared with linear, bilinear, exponential and the most common hyperelastic models (neohookean, Mooney–Rivlin, Ogden, Yeoh, polynomial and Veronda–Westmann). MATERIALS AND METHODS: Literature data on mechanical tests of autopsy material obtained from mongrel dogs were used as initial data. To search for the most advanced calculation algorithms the computer algebra system was used, the Mathcad 15.0 software package and the multifunctional finite element analysis application ANSYS 2022 R2 were used. Direct comparison of models was made based on mathematical statistics. RESULTS: Among the first group of models, the results closest to the experimental data were demonstrated by the exponential model R = 0.9958/0.9984 (in the longitudinal/transverse direction with respect to the myocardial fibers), the lowest accuracy was demonstrated by the linear model R = 0.9813/0.9803. Young’s moduli of linear, bilinear and exponential models and material constants of hyperelastic models are determined. The coefficient of elastic anisotropy of the myocardium, defined as the ratio of the elastic moduli of the linear model measured along and across the direction of the fibers, is equal to 2.18, which is very different from the literature data for the myocardium of the human heart. Deformation along the fibers of the heart muscle is more energy-consuming in the direction along the fibers than in the transverse direction (3.81 and 2.52 mJ/cm3). The most accurate hyperelastic models turned out to be the 2nd order polynomial model R = 0.9971 and the 3rd order Yeoh model R = 0.997. The largest deviations and the lowest correlation coefficient between the experimental and model data were demonstrated by the simple neohookean model R = 0.974 with a single parameter μ. The numerical values of the parameters of hyperelastic models obtained by calculation methods used practically did not differ from each other (≤2.16%). CONCLUSIONS: The study demonstrated the importance of selecting the correct mechanical model for isolated myocardium. The data obtained can be useful in virtual interventions (simulations) for predicting outcomes and supporting clinical decisions, developing replacement materials and structures made of them for reconstructive operations on heart structures.

Mechanical Behaviour, Contact Pose Estimation, and Finite Element Analysis of Vision Based Tactile Sensors Fabricated by Molding and Direct Ink Writing: A Comparative Study

This work pioneers the application of direct ink writing (DIW) to fabricate elastomeric additively manufactured vision based tactile sensor (VBTS). DIW cuts down the fabrication time by 76%, allowing design precise control and reducing the complexities of the process compared to the state‐of‐the‐art (SOTA) molding techniques. Successful fabrication of DIW sensor is verified in three stages. Firstly, the mechanical characteristics of the DIW sensor are at par with those of SOTA molded Ecoflex in terms of depth of compression, compression rate, and the number of cycles. Secondly, using robotic pose estimation as a demonstration, the force enables deformation in the DIW sensor shows comparable normality estimation performance to that of the SOTA Ecoflex with a mean absolute error of less than 0.6°. Thirdly, finite element analysis (FEA) of DIW and SOTA Ecoflex sensors using Yeoh model shows similar stress and strain distributions as another evidence of DIW deformability and durability signaling sensor's successful fabrication.

Experimental and computational analysis of elastomer membranes used in oscillating water column WECs

The study investigates the structural characterisation of flexible membranes used in oscillating water column (OWC) wave energy converters (WECs). Four commonly utilised elastomers – natural rubber, nitrile rubber, silicone, and latex – were subjected to a novel hyperelastic model selection process. A custom bulge test setup enabled the selection of second-order Mooney-Rivlin (SOMR) and Yeoh models for relevant accuracy (RMSE<0.018 MPa), stability and numerical validation. A 1:20 scale OWC model with latex was tested in a water tank to examine the effects of waves with a frequency range of 0.25–1.4 Hz and up to 0.24m amplitude. Water tank experiments demonstrated smooth frequency responses for OWC with membrane, beneficial for consistent power generation. A dry test rig was designed and built to replicate OWC inflation conditions and apply cyclic loadings up to 1.5 Hz, overcoming pressure limitations of the water tank, exploring wider material options, and validating numerical simulation. An optical motion capture system, Qualisys, supported the validation process by providing precise data on membrane deformation during experiments. Furthermore, finite element analysis (FEA) was utilised to conduct stress analysis and parametric studies, assessing the suitability of these materials for flexible OWC application.

In vitro biomechanical properties of porcine perineal tissues to better understand human perineal tears during delivery.

Data concerning the mechanical properties of the perineum during delivery are very limited. Invivo experiments raise ethical issues. The aim of the study was to describe some of the biomechanical properties of each perineal tissue layer collected from sows in order to better understand perineal tears during childbirth. Samples of each perineal tissue layer were obtained from the skin, the vagina, the external anal sphincter (EAS), the internal anal sphincter (IAS), and the anal mucosa of fresh dead sows. They were tested in quasi-static uniaxial tension using the testing machine Mach-1®. Tests were performed at a displacement velocity of 0.1 mm·s-1. Stress-strain curves of each perineal tissue layer before the first damage for each sow were obtained and modeled using a hyperelastic Yeoh model described by three coefficients: C1, C2, and C3. Pearson correlation coefficients were calculated to measure the correlation between the C1 hyperelastic coefficient and the duration between the first microfailure and the complete rupture for each perineal tissue layer. Pearson correlation was computed between C1 and the number of microfailures before complete rupture for each tissue. Ten samples of each perineal tissue layer were analyzed. Mean values of C1 and corresponding standard deviations were 46 ± 15, 165 ± 60, 27 ± 10, 19 ± 13, 145 ± 28 kPa for the perineal skin, the vagina, the EAS, the IAS, and the anal mucosa, respectively. According to this same sample order, the first microfailure in the population of 10 sows appeared at an average of 54%, 27%, 70%, 131%, and 22% of strain. A correlation was found between C1 hyperelastic coefficient and the duration between the first microfailure and the complete rupture (r = 0.7, p = 0.02) or the number of microfailures before complete rupture only for the vagina (r = 0.7, p = 0.02). In this population of fresh dead sow's perineum, the vagina and the anal mucosa were the stiffest tissues. The IAS and EAS were more extensible and less stiff. A significantly positive correlation was found between C1 and the duration between the first microfailure and the complete rupture of the vagina, and the duration between the first microfailure and the complete rupture of the vagina.

Comparative analysis of nonlinear dynamic behaviors of hyperelastic curved structure modelled by different constitutive laws

This work focuses on conducting numerical studies and comparisons on the nonlinear dynamic behaviors of hyperelastic curved structures subjected to external dynamic loadings. A numerical model of the hyperelastic structure is developed using the nonlinear finite element method, which considers both the geometric nonlinearity resulting from large deformations and the material nonlinearity due to hyperelasticity. Four commonly used hyperelastic constitutive laws, namely the Mooney-Rivlin model, the neo-Hookean model, the Yeoh model, and the Ogden model, are employed to describe the nonlinear stress-strain relationship of the hyperelastic material. The convergence performance of the numerical model with respect to grid element and time step is thoroughly examined through several numerical examples. Subsequently, based on the developed numerical model, the nonlinear dynamic behaviors of the hyperelastic curved structures excited by uniform pressure loadings with single and dual frequencies are studied and compared using various constitutive laws. The material constants used in these constitutive laws are estimated based on the well-known Treloar's test data on vulcanized rubber material. Additionally, comprehensive parametric analyses are conducted on the nonlinear dynamic behaviors of the hyperelastic structure simulated by different constitutive laws. The deformation evolution process, resonance curves, time-frequency analysis, bifurcation diagrams, and phase portraits are employed to demonstrate the similarities and differences in the nonlinear dynamic behaviors (i.e., super- and sub-harmonic resonance, internal resonance, chaotic motion and bifurcations) of the hyperelastic structure modeled by different constitutive laws.

Eliminating the Misconceptions Regarding the Usage of Commercially Available Silicone Elastomers in Thin Film Actuators

Dielectric elastomers (DEs) are actively being studied to develop soft transducers including DE actuators (DEAs). Poly(dimethylsiloxane) is a popular elastomer component and known for yielding a relatively low dielectric constant (ε′) for DEAs. Herein, a novel polysiloxane‐based DE, namely, DOWSIL ME 7540 Electroactive Elastomer is reported, offering ε′ = 5.2–5.5 over a broad frequency range that is nearly two times as high as that for commercially popular SYLGARD 184 Silicone Elastomer as a comparative DE. Weibull analysis is useful for statistically evaluating dielectric strength (DS). ME 7540 DE attains DS = 63.8 V μm−1, which is only 16% lower than DS = 75.7 V μm−1 obtained with 184 DE. The material parameters obtained by fitting uniaxial extension results with the Yeoh model are used to simulate an equibiaxial stress–stretch ratio (λib) curve, with i = 1 or 2, and the relationship between voltage and λ1b. Simulation and actuation experiments confirm that ME 7540 DE performs better than 184 DE over one million cycles. With these advantages, ME 7540 DE will help accelerate not only fundamental studies but also developments in real‐life applications in the DEA field.

Development and biomechanical testing of full-scale human brain simulant

In 21st century, traumatic Brain Injuries (TBI) due to blast exposure or head impacts in contact sports, accidents are one of most critical research area. But the area of TBI is poorly investigated due to the limitation of brain tissue availability and related ethical/biosafety issues. In general, the brain tissue is difficult to acquire after the autopsy and test in laboratorial settings. In this work, a full-size human brain simulant was developed using a biofidelic multi-part polymeric material poured into a negative mould which was designed and 3D printed. Based on the number of mild to moderate traumatic brain injury cases reported in the literature, three TBI prominent locations were chosen. The prefrontal cortex of frontal lobe, top portion of parietal lobe and temporal lobe of right hemisphere of the brain were the locations where the experiments were conducted under compressive loading conditions. The load versus displacement data was recorded and converted to the stress-strain plots to analyse the result responses and its implications. Two constitutive hyperelastic models (Yeoh model and Neo-Hookean) were selected for curve fitting and characterizing the non-linear mechanical behavior of the full-scale brain model. Such precisely developed and characterized full-scale brain simulant has not been reported in the literature to date and would be beneficial for simulating a wide range of traumatic brain injuries and surgical training.

Biomechanical properties of nasal tissues

Introduction. Plastic rhinosurgery and augmentation rhinoplasty are very relevant today. Especially in relation to patients with congenital saddle deformity of the nasal dorsum, as well as patients with iatrogenic disorders of the nose shape, which dramatically reduce the quality of human life. There are violations of the function of the nose. The purpose of the work. Purpose. Within the framework of the necessity of performing silicone implantation rhinoplasty, the strength, elastic and hyperelastic properties of the soft tissues of the nasal fascia and periosteum were studied, the dynamic viscosity of the tissues of the nasal fascia and periosteum was evaluated, determining their relaxation properties using elastic, hyperelastic and rheological models. Methods. Linear, bilinear (with two Young modules), exponential, hyperelastic (neohookean, Mooney-Rivlin, Ogden, Yeoh, polynomial and Veronda-Westmann) and elastic-viscous (Maxwell) models of biological tissues were used. We used the Mathcad 15.0 computer algebra system and the universal package of interdisciplinary programs ANSYS Multiphysics Software (version 2022 R2). The accuracy of replacing the properties of real tissues with the results of calculations was calculated on the basis of indicators of descriptive statistics (standard deviation, maximum absolute error, maximum relative error and correlation coefficient). Results. It is proved that the bilinear model for the exact reproduction of the stress-strain curve assumes at the molecular level of tissues an initial linear reaction of elastin fibers, passing at ε=εcr into the final linear reaction of the collagen matrix. It was found that the properties of the periosteum (correlation coefficient R=0.9999) and nasal fascia (correlation coefficient R=0.9999) are described most adequately by the 5-parametric polynomial model of the 2nd order and the Yeoh model of the 3rd order (R=0.999 and R=1, respectively), the least accurately by the simple 1-parameter neohookean model (R=0.898 for the periosteum and R=0.905 for the fascia). Among elastic models, the exponential dependence characterizes the behavior of nasal materials quite well. Conclusion. Biomechanically verified that the periosteum is thicker, stronger and more rigid than the fascia. The established very high viscosity values indicate the slowness of relaxation processes in tissues. The periosteum relaxes tension more slowly, which improves the result of implant fixation. On the contrary, the relaxation time of the periosteum is higher than that of the fascia, from which it is concluded that it is preferable not to cut the periosteum during subcostal implantation.

A new method for selecting and evaluating the hyperelastic model of tread rubber material under rolling contact condition

The selection and evaluation of the hyperelastic model of tread rubber material were of great value and significance to the clarification and application of the mechanical properties of tread rubber material. In this article, a non-contact tread rubber material rolling test bench was established. The improved digital image correlation method was used to calculate the strain rate distribution of the marked point under different test conditions. Combined with the stress distribution of the marked point, the rolling dynamic stress-strain characteristics of tread rubber material were obtained. Based on rubber material models under different tensile test modes, the parameter inversion identification of the hyperelastic model was completed, and the influence of the tensile test mode on the parameter inversion of the tread rubber hyperelastic model was revealed. A new method for selecting and evaluating the hyperelastic model of tread rubber material under rolling contact conditions was proposed. The selection criterion for the hyperelastic model of tread rubber material was developed under different rolling conditions. The experimental and analytical results show that the nonlinear degree of the constitutive relation of the hyperelastic model decreased with the increase in rolling speed. Compared with hyperelastic models under different tensile modes, the fitting error of the Yeoh model was less than 3%, and the overall fitting error of the Yeoh model was less than 2%. Therefore, the Yeoh model had better stability and accuracy and was more suitable for describing the rolling mechanical properties of tread rubber under rolling contact conditions.

Insights on the J‐integral expression of pure shear carbon black filled natural rubber specimen and predicting the crack growth rate using finite element method

AbstractThe J‐integral approach manifests itself in an efficient way to determine the crack growth and failure mechanism of tread and sidewall compounds used in tyres. Therefore, for a pure shear (PS) specimen of carbon black filled natural rubber, the J‐integral formula was vivisected, and the material parameters were defined using the concepts of solid mechanics considering the planar stress conditions. Theoretical calculations, experimental observations, and finite element analysis were executed to calculate the J value for different strain percentages. Different hyperelastic material models were used to understand the hyperelastic behavior of the test compound, but Yeoh model was found to be the best fit with the least error against the experimental test data. The frequency sweep dynamic mechanical analyzer test was done to observe the viscoelastic response of the material. It was observed that the J value decreased with decreasing contour radius and had exhibited stark difference with the global tearing energy values, indicating the effects of stress softening and the dependence of J value on the elastic characteristics of the material. Further, the J value attained from finite element methods for a random strain 22% was used to predict the crack growth rate of the pre‐notched PS specimen.Highlights J‐integral formula for pure shear specimen using solid mechanics approach. J value comparison of theoretical, experimental, and finite element methods. Dependence of J value on the elastic characteristics of the material. Different hyperelastic models compared and Yeoh model chosen for analysis. Prediction of crack growth rate at a random strain percentage.