Pure azimuthal shear of isotropic, incompressible hyperelastic materials with limiting chain extensibility

The purpose of this paper is to investigate the torsion and azimuthal shear of an incompressible hyperelastic cylinder having a modified Gent-Thomas strain energy with limiting chain extensibility condition. First, the torsional response of the modified Gent-Thomas model is obtained analytically and compared with those of Gent-Gent, Gent-Thomas, and Carroll strain energy models where the former model incorporates the limiting chain extensibility condition while the latter two are phenomenological models. The results show the modified Gent-Thomas model to be in better agreement with the experimental data of Rivlin and Saunders on torsion than the other three models. To further evaluate the response of the modified Gent-Thomas model, azimuthal shear deformation of an incompressible hyperelastic cylinder with the modified Gent-Thomas, Gent-Thomas, Gent-Gent, and Carroll strain energies is considered, where the angular displacement in azimuthal shear is determined analytically for the first three models and numerically for the fourth model. It is shown that the strain hardening effect, predicted either by the limiting chain extensibility condition for the modified Gent-Thomas and Gent-Gent models or phenomenologically by the Carroll model, is quite significant in the azimuthal shear response of the incompressible cylinder.

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Remarks on nonlinear elastic waves with null conditions

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2020039 ◽

2020 ◽

Vol 26 ◽

pp. 121

Author(s):

Dongbing Zha ◽

Weimin Peng

Keyword(s):

Initial Data ◽

Global Existence ◽

Elastic Waves ◽

Wave Equations ◽

Alternative Proof ◽

Classical Solutions ◽

Small Initial Data ◽

Hyperelastic Materials ◽

Variational Structure ◽

Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

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An Alternative Technique to Evaluate Crack Propagation Path in Hyperelastic Materials

Tire Science and Technology ◽

10.2346/1.3684484 ◽

2012 ◽

Vol 40 (1) ◽

pp. 42-58 ◽

Cited By ~ 6

Author(s):

R. R. M. Ozelo ◽

P. Sollero ◽

A. L. A. Costa

Keyword(s):

Constitutive Model ◽

Crack Propagation ◽

Experimental Tests ◽

Growth Direction ◽

Propagation Path ◽

J Integral ◽

Alternative Technique ◽

Crack Propagation Path ◽

Hyperelastic Materials ◽

Material Constitutive Model

Abstract REFERENCE: R. R. M. Ozelo, P. Sollero, and A. L. A. Costa, “An Alternative Technique to Evaluate Crack Propagation Path in Hyperelastic Materials,” Tire Science and Technology, TSTCA, Vol. 40, No. 1, January–March 2012, pp. 42–58. ABSTRACT: The analysis of crack propagation in tires aims to provide safety and reliable life prediction. Tire materials are usually nonlinear and present a hyperelastic behavior. Therefore, the use of nonlinear fracture mechanics theory and a hyperelastic material constitutive model are necessary. The material constitutive model used in this work is the Mooney–Rivlin. There are many techniques available to evaluate the crack propagation path in linear elastic materials and estimate the growth direction. However, most of these techniques are not applicable to hyperelastic materials. This paper presents an alternative technique for modeling crack propagation in hyperelastic materials, based in the J-Integral, to evaluate the crack path. The J-Integral is an energy-based parameter and is applicable to nonlinear materials. The technique was applied using abaqus software and compared to experimental tests.

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An octahedral stress-based fracture criterion for hyperelastic materials

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406220972136 ◽

2020 ◽

pp. 095440622097213

Author(s):

A Hamdi ◽

A Boulenouar ◽

N Benseddiq

Keyword(s):

Pure Shear ◽

Thermoplastic Elastomer ◽

Styrene Butadiene Rubber ◽

Butadiene Rubber ◽

Principal Stresses ◽

Hyperelastic Materials ◽

Biaxial Tests ◽

Set Up ◽

Loading Modes ◽

Styrene Butadiene

No uniﬁed stress-based criterion exists, in the literature, for predicting the rupture of hyperelastic materials subjected to mutiaxial loading paths. This paper aims to establish a generalized rupture criterion under plane stress loading for elastomers. First, the experimental set up, at breaking, including various loading modes, is briefly described and commented. It consists of uniaxial tests, biaxial tests and pure shear tests, performed on different rubbers. The used vulcanizate and thermoplastic rubber materials are a Natural Rubber (NR), a Styrene Butadiene Rubber (SBR), a Polyurethane (PU) and a Thermoplastic elastomer (TPE). Then, we have investigated a new theoretical approach, based upon the principal stresses, to establish a failure criterion under quasi-static loadings. Thus, we have proposed a new analytical model expressed as a function of octahedral stresses. Quite good agreement is highlighted when comparing the ultimate stresses, at break, between the experimental data and the prediction of the proposed criteria using our rubber-like materials.

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