A three-dimensional network model for rubber elasticity: The effect of local entanglements constraints

Bechir, Hocine; Chevalier, Luc; Idjeri, Mourad

doi:10.1016/j.ijengsci.2009.10.004

Cited by 26 publications

(13 citation statements)

References 36 publications

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“…The free energy of the constraint network is idealized using the standard three-chain energy function and the free energy of the unconstrained idealized network is constructed by means of the eight-chain model. Therefore, according to Bechir et al [20], the total free energy function of this model is merely a combination of the two chain models, that is, 8 3…”

Section: Bechir Modelmentioning

confidence: 99%

“…For the sake of modifications over the classical one, some models increase the number of parameters to fit the data, for example, Bechir model [20], whereas some remain with the two parameters, for example, the bootstrapped eightchain model [18]. Some well-known modified versions of the Arruda-Boyce model are the modified Flory-Erman model [8,21], Gornet-Desmorat (GD) model [19], bootstrapped eight-chain model [18], Bechir model [20], Meissner-Matejka model [22], and the Kroon model [6]. When a modified model is proposed aiming to show better results in contrast to the original eight-chain model, the modified version is usually compared with the original one but the comparison among the variants of the eightchain model are not demonstrated so far in the literature.…”

Section: Introductionmentioning

confidence: 99%

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Eight-chain and full-network models and their modified versions for rubber hyperelasticity: a comparative study

Hossain

Amin

Kabir

2015

Journal of the Mechanical Behavior of Materials

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The eight-chain model, also known as ArrudaBoyce model, is widely used to capture the rate-independent hyperelastic response of rubber-like materials. The parameters of this model are physically based and explained from micromechanics of chain molecules. Despite its excellent performance with only two material parameters to capture bench measurements in uniaxial and pure shear regime, the model is known to be significantly deficient in predicting the equibiaxial data. To ameliorate such drawback, over the years, several modified versions of this successful model have been proposed in the literature. The so-called full-network model is another micromechanically motivated chain model, which has also few modified versions in the literature. For this study, two modified versions of the full-network model have been selected. In this contribution, five modified versions of the Arruda-Boyce model and two modified versions of full-network model are critically compared with the classical eight-chain model for their adequacy in representing equibiaxial data. To do a comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous deformation modes, that is, uniaxial tension, equibiaxial tension, and pure shear have been derived and the performances of the selected models are analysed. The comparative study demonstrates that modified Flory-Erman model, Gornet-Desmorat (GD) model, Meissner-Matějka model, and bootstrapped eight-chain model predict well the three deformation modes compare to the classical eight-chain model.

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Section: Bechir Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Eight-chain and full-network models and their modified versions for rubber hyperelasticity: a comparative study

Hossain

Amin

Kabir

2015

Journal of the Mechanical Behavior of Materials

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“…Fine meshes are defined for cords in the first and second belt layers, as well as the carcass layer, for detailed analysis. e various rubber materials in the three-dimensional model are represented by isotropic incompressible C3D8RH elements, and the stress-strain relations of rubber materials are described with hyperelastic models [13]. e finite element model has 10,721 elements of carcass rubber and 10,102 elements in the belt and the carcass layers.…”

Section: Finite Element Modeling Of a Radial Tirementioning

confidence: 99%

Experiment and Analysis of Cord Stress on High‐Speed Radial Tire Standing Waves

Sun

Huang

Zhou

et al. 2019

Shock and Vibration

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This paper elaborates on the production mechanisms of standing waves during high-speed tire rolling and analyzes the relationship between the change of wavelength of sidewall waves and the vehicle velocity, from an oblique wave point of view. A finite element model for a 195/65R15 radial tire is established with the nonlinear analysis software ABAQUS, based on the tire structure and cord parameters. This paper comparatively analyzes the finite element simulation results and experimental results of the tire load-sinkage relation and the load vs inflatable section width relation and finds little difference between the simulation and experimental results. A similar analysis studies the change in the wavelength of sidewall standing waves at different vehicle velocities during high-speed tire rolling. The calculated value by the oblique wave approach, the value by simulation, and the experimental results demonstrate high consistency, concluding that during high-speed tire rolling, the wavelength of sidewall standing waves increases with vehicle velocity. Thus, the accuracy of the finite element model is verified under both static and dynamic conditions. Under a constant tire pressure and load, the impact of velocity change on tire-cord stress during high-speed tire rolling is studied based on the finite element model so as to identity the relation between the cord stress and standing waves.

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“…Various reinforcement and toughening strategies have been introduced to toughen the elastomers [11][12][13][14], including hydrogen bonds [21], coordination bonds [22], sacrificial bonds and dynamic bonds [23,24]. Several phenomenological and viscoelastic models have been formulated to describe their toughening mechanisms and mechanical behaviours [25][26][27][28][29][30]. However, scaling laws of condensed-matter physics, which are self-consistent and connect molecular segment, macromolecule chain with elasticity of polymer network, have not been well understood [31,32].…”

Section: Introductionmentioning

confidence: 99%

Self-consistent Sierpinski iteration of toughening mechanism in elastomer undergoing scaled segment-chain-network

Xing

2023

Proc. R. Soc. A.

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Understanding working principles and toughening mechanisms of soft elastomers has been a huge challenge due to their significant scaling effects from molecules to bulk polymer. In this study, by combining Sierpinski fractal and scaling theory, an extended Kelvin model is developed to investigate the mechanical behaviour of the soft elastomer undergoing scaled segment-chain-network. According to the scaling theory, a radial distribution function was initially introduced to explain the diffusion and relaxation behaviours of molecular segments with the Sierpinski fractal features. The self-consistent iteration of the Sierpinski fractal is then used to describe the scaling effects of segments and networks. Rubber elasticity of the polymer network is further formulated based on the self-consistent iteration equation and scaling theory. A constitutive stress–strain relationship is also derived to explore the toughness mechanism and working principle in the polymer elastomer. Finally, the effectiveness of the proposed model is verified using finite-element analysis and experimental results reported in the literature, to explore a scaling insight into toughening mechanisms of elastomers governed by the self-consistent Sierpinski iteration.

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A three-dimensional network model for rubber elasticity: The effect of local entanglements constraints

Cited by 26 publications

References 36 publications

Eight-chain and full-network models and their modified versions for rubber hyperelasticity: a comparative study

Eight-chain and full-network models and their modified versions for rubber hyperelasticity: a comparative study

Experiment and Analysis of Cord Stress on High‐Speed Radial Tire Standing Waves

Self-consistent Sierpinski iteration of toughening mechanism in elastomer undergoing scaled segment-chain-network

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