Numerical evaluation of micro- to macroscopic mechanical behavior of carbon-black-filled rubber

Tomita, Yoshihiro; Lü, Wei; Naito, Masato; Furutani, Y.

doi:10.1016/j.ijmecsci.2005.08.009

Cited by 30 publications

(30 citation statements)

References 17 publications

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“…(4) provides the relationship between the Jaumann rate of Kirchoff stress , ij Sˆ, and the strain rate , kl  , as in Tomita, et al (2006). The penalty method is introduced to enforce the deformation under constant volume.…”

Section: Generalization Of Constitutive Equationsmentioning

confidence: 99%

“…Furthermore, Bergstrom and Boyce (2000) introduced the first invariant amplification for the effective prediction of deformation of filled rubbers. Tomita, et al (2006) provided the slightly modified version of the original model (a) by introducing the nonaffine eight-chain model (Tomita, et.al., 1995) instead of the conventional eight-chain model. An extended version of the eight-chain model (b), consists of eight standard-like models with two Langevin springs  ,  , and a dashpot  (Tomita, et al, 2008b).…”

Section: Fig3 Deformation Of Molecular Chainsmentioning

confidence: 99%

“…The unit cell is sufficiently small as compared to the dimension of the entire body and Y-periodicity is assumed (Guedes and Kikuchi, 1990). Fig.7(a) indicates the stress-stretch relationship for unfilled rubber under cyclic loading (Tomita, et al, 2006). The dotted lines represent the experimental results.…”

Section: Deformation Behavior Of Unfilled Rubbermentioning

confidence: 99%

“…The Mullins effect for CB-filled rubber is marked compared to the unfilled rubber, which is closely related to the ultimate properties of filled rubber. Consequently, several mechanisms for the enhancement of the ultimate properties of filled rubber have been suggested (Mullins, 1969, Daunenberg, 1975, Tomita, et al, 2006. In this work, we focus our attention on the evaluation of the enhancement of deformation resistance and hysteresis loss caused by filling rubber with CB.…”

Section: Deformation Behavior Of Unfilled Rubbermentioning

confidence: 99%

“…The constitutive equations identified by the experimental results reproduce them well, however, owing to the complex microscopic deformation behaviors depending on the change of the volume fraction, heterogeneity of the sizes, and morphology of distributions of particles, the predictability of the effect of their changes on deformation behaviors would be limited. To solve the problems, we developed direct simulation methods of deformation behaviors of particles filled rubber (e.g., Tomita, et al, 2004Tomita, et al, , 2006 using finite element homogenization methods (e.g., Higa andLu, 2002) that have a potential to overcome the problems listed above.…”

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Constitutive equations of rubber based on molecular chain network model and evaluation of deformation behaviors of particle-filled rubbers

Tomita

2015

Mechanical Engineering Reviews

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Mechanical characteristics of polymers are markedly different depending on the temperature. At lower temperatures and up to a temperature known as the glass transition temperature Tg, polymers behave as glass-like materials with a high elasticity modulus and a low fracture strain. At higher temperatures than Tg, they behave as rubber-like materials with the ability to undergo large and reversible elastic deformations known as rubber elasticity. They are called hyperelastic materials and have a strain energy function W, a scalar function of the strain tensor, whose derivative with respect to the strain components determines the corresponding stress components (Fung, 1965). Many strain energy functions were proposed and were extensively used for the evaluation of the deformation behaviors of hyperelastic materials. The details of the concrete forms of strain energy functions and their experimental verifications were seen in Ogden (1977) and others.On the other hand, the constitutive equations of rubber elasticity using macromolecular network models were proposed based on the concept of a network of chains of randomly oriented rigid links that are connected at the chemical cross-links between macromolecules. The overall properties of the network are then obtained by summing the contributions of the individual chains. Non-Gaussian statistics were employed to single chain configurations taking into account the finite extendibility of molecular chains (Kuhn and Grun,1942, James andGuth, 1943). However, a rigorous treatment for summing the contributions of the individual chains, averaging process was not made available for arbitrary deformation until the development of computational resources. Many approximate methods have been proposed for the averaging process (James and Guth, 1943, Arruda and Boyce, 1993, Wu and van der Giessen, 1993 and have been employed toward the evaluation of the deformation behaviors of rubber.It is well known that the mechanical characteristics of rubbers are markedly improved by filling the hard particles. Therefore, their usage extends to an extensive range of engineering fields. Proper predictions of mechanical 1 AbstractThe constitutive equations for rubbers that are derived based on the molecular chain network model and their generalization to account for the non-affine deformation and viscoelastic deformation of rubbers are presented for the evaluation of the complex deformation behaviors under monotonic and cyclic deformation at different strain rates. Several applications of the constitutive equations using the finite element homogenization method for the evaluation of microscopic to macroscopic deformation behaviors of particles such as carbon black and silica-filled rubbers are addressed. The typical deformation behavior of rubbers and the essential mechanism of enhancement in the mechanical characteristics of particle-filled rubbers under monotonic and cyclic straining are clarified focusing on findings from our recent works.

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Section: Generalization Of Constitutive Equationsmentioning

confidence: 99%

Section: Fig3 Deformation Of Molecular Chainsmentioning

confidence: 99%

Section: Deformation Behavior Of Unfilled Rubbermentioning

confidence: 99%

Section: Deformation Behavior Of Unfilled Rubbermentioning

confidence: 99%

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confidence: 99%

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Constitutive equations of rubber based on molecular chain network model and evaluation of deformation behaviors of particle-filled rubbers

Tomita

2015

Mechanical Engineering Reviews

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Effective properties and size effects in filled polymers

Johlitz¹,

Steeb²,

Jänicke³

et al. 2008

GAMM-Mitteilungen

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Filled polymers are of special interest according to their superior mechanical properties. Special attention is given to nano-filled polymers where not only the volume fraction but also the internal surface has a significant contribution to the effective properties. In the present contribution the increase in stiffness with decreasing size of the fillers at constant volume fraction of the fillers is modelled by a phenomenological, i.e. continuum-based, approach taking into account large deformations. The proposed multiphase model allows for a systematic investigation of increasing surface-to-volume ratio which becomes important for micro-and nanosized fillers. The numerical treatment of the proposed model is based on a coupled Galerkin finite element formulation.

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Strain Softening of Bimodal Isoprene Rubber Vulcanizates

Hou

Xia

Song

et al. 2021

Macro Materials & Eng

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Isoprene rubber (IR) vulcanizates soften upon large‐amplitude oscillational shear and large‐strain cyclic tensile deformation. The mechanisms of these two strain softening behaviors remain unclarified and methods for reducing the accompanied mechanical dissipations are not well established. Herein IR/liquid isoprene rubber bimodal blends are cured into vulcanizates with similar cross‐linking densities. The results indicate that, in comparison with the pure IR network, the bimodal networks demonstrate lowered loss modulus and loss tangent at low strain amplitudes during oscillational shear and reduced loading−unloading dissipation energy at large strains during cyclic tensile deformation. The latter is ascribed to the weakened strain‐induced crystallization (SIC) as disclosed by in situ wide angle X‐ray diffraction. To the best of the current knowledge, the depression of SIC and thus dissipation energy in cyclic deformation is seldom reported for rubber materials. This work provides a new perspective for preparing rubber materials with balanced deformation resistance and mechanical hysteresis.

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Numerical evaluation of micro- to macroscopic mechanical behavior of carbon-black-filled rubber

Cited by 30 publications

References 17 publications

Constitutive equations of rubber based on molecular chain network model and evaluation of deformation behaviors of particle-filled rubbers

Constitutive equations of rubber based on molecular chain network model and evaluation of deformation behaviors of particle-filled rubbers

Effective properties and size effects in filled polymers

Strain Softening of Bimodal Isoprene Rubber Vulcanizates

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