Deformation induced loss of ellipticity in an anisotropic circular cylindrical tube

Hamdaoui, Mustapha El; Merodio, J.; Ogden, Ray W.

doi:10.1007/s10665-017-9904-z

Cited by 11 publications

(3 citation statements)

References 10 publications

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“…Mathematically, it turns out that, fiber kinking is related to marginal loss of the strong ellipticity condition [16][17][18]. Similar phenomena were also observed in the framework of simple shear and rectilinear shear [19,20].…”

Section: Introductionsupporting

confidence: 56%

On behavior of transversely isotropic incompressible hyperelastic materials under multiaxial stretching

Methia

Bechir

Yaya

2023

Preprint

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Nowadays, mechanical behavior of soft materials are characterized by using standard tests: uniaxial traction, simple shear (or combination) and equibiaxial tension. However, the multiaxial testing data are necessary in order to characterize the anisotropy, which is posing formidable technical challenges. We propose a new method to investigate multiaxial behavior of fiber-reinforced hyperelastic solids. The test protocol consists to deform a thin rectangular sample by coupling both the pure shear and simple shear loadings. The specimen is mounted and oriented by an angle in the plane of a special device, which is attached to a universal testing machine. So, the direction of stretching is dictated by in such way that, the stress-strain relations depend on and magnitude of the displacement prescribed on the sample edge, i.e. . The shape factor of the sample is assumed to dictate the direction of transverse isotropy in the reference configuration. Thereby, the direction of stretching could be taken neither parallel nor perpendicular to the stretching-direction. But also, it could be chosen parallel to the direction of transverse isotropy. Based on, we have revisited the standard results, established new ones, and investigated the anisotropy. We demonstrated that, the Cauchy stress fields are depending on the multiaxiality in the core region of the sample. So, the experimental data arising from this test could be used for both parameter calibration and/or validation of transversely isotropic incompressible hyper elastic models.

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Section: Introductionsupporting

confidence: 56%

On behavior of transversely isotropic incompressible hyperelastic materials under multiaxial stretching

Methia

Bechir

Yaya

2023

Preprint

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“…El Hamdaoui et al 23 have analyzed the ellipticity condition in an isotropic tube that is subjected to a combined deformation, such as axial extension with axial and azimuthal shear wherein basic equations were derived, and loss of ellipticity was examined for this material.…”

Section: Introductionmentioning

confidence: 99%

Evaluating the response of a modified Gent-Thomas strain energy function having limiting chain extensibility condition in torsion and azimuthal shear

Sayyad

Imam

Haghighi

2021

Polymers and Polymer Composites

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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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“…[130], [131], [179]). In particular, great research efforts have been accomplished towards the comprehensive understanding of the role of residual stresses in biomechanical systems and materials [86], [111], [156], [161] or anisotropic circular cylindrical tube [42]. Hence, the residually stressed material models have received a great deal of attention.…”

Section: Model Frameworkmentioning

confidence: 99%

Application of Sensitivity analysis (SA) by means of statistical techniques in nonlinear elastic constitutive models including residual stress

Asghari

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This thesis deals with applying the sensitivity analysis methods that consideration of different functions on the non-linear elastic constitutive models in particular a circular cylindrical tube with radial and circumferential residual stresses and in some different types of pressure-inflation relation in a pressurized and axially stretched tube.Considering the inflation of hyperelastic cylinders in the framework of non-linear elastic constitutive models imposed to an axial stretch and torsion in the presence of residual stress has been done in this work. The constitutive relation of the material depends on various parameters such as the cylinder geometry, the different loading parameters, the prescribed stretches, and the magnitude of the residual stresses. Applying sensitivity analysis methods with attention to a statistical approach determined how the variations of the input variables affect the output variables.After reviewing on applied sensitivity analysis and recapping on basic contents of the non-linear elastic constitutive models, through the implementation of Sobol and the Fourier Amplitude Sensitivity Test (FAST) methods, the most important parameters of the system under the applied pressure and axial force such as the thickness of the tube or axial and azimuthal stretch are gained in the first part of the thesis. Then, the complicated form of the mechanical problem is expressed which is the problem of mixed extension, inflation, and torsion of a circular cylindrical tube in the presence of residual stress which the input parameters in the material model are distributed according to three probability distribution methods, namely the uniform, the gamma, and the normal distribution. In other words, the relation between various parameters as they relate to the inflation pressure, the moment, and the reduced axial force is studied with the help of two sensitivity analysis methods, namely, the Sobol method and FAST method. Both methods found their application in relatively complex models, especially when these models show a non-linear and non-monotonic behaviour. After that, the pressure-inflation relation in a pressurized and axially stretched tube is studied in fiber-reinforcement materials with different natural configurations. The material consists of an isotropic ground substance that is reinforced by two families of fibers. The natural configuration of the fibers may differ from that of the ground substance and the fibers are taken to be dispersed. The sensitivity analysis is applied by means of statistical simulation in the "R" program to determine how the uncertainties of the cylinder stretch, the fiber dispersion, and the fiber natural configuration affect the required inflation pressure. The V implementation of the Sobol and FAST methods allows us to account for the interplay of different parameters and to identify the most influential parameters in the pressure-inflation relation.

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Deformation induced loss of ellipticity in an anisotropic circular cylindrical tube

Cited by 11 publications

References 10 publications

On behavior of transversely isotropic incompressible hyperelastic materials under multiaxial stretching

On behavior of transversely isotropic incompressible hyperelastic materials under multiaxial stretching

Evaluating the response of a modified Gent-Thomas strain energy function having limiting chain extensibility condition in torsion and azimuthal shear

Application of Sensitivity analysis (SA) by means of statistical techniques in nonlinear elastic constitutive models including residual stress

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