Shear of rubber tube springs

Suh, Jong Beom; Gent, A. N.; Kelly, S. Graham

doi:10.1016/j.ijnonlinmec.2007.07.002

Cited by 10 publications

(3 citation statements)

References 14 publications

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“…In the case of a nearly incompressible material (with Poisson's ratio = 0.490, for example) we have shown that the in-plane stress components computed by the HGO-C model are reduced by an order of magnitude. Bulk modulus sensitivity has been pointed out for isotropic models by Gent et al (2007) and Destrade et al (2012), and for the HGO-C model by Ní Annaidh et al (2013b). Here, we have demonstrated that a ratio of bulk to shear modulus of κ 0 /µ 0 = 2 × 10 6 (equivalent to a Poisson's ratio of 0.49999975) is required to compute correct results for the HGO-C model.…”

Section: Discussionsupporting

confidence: 52%

A robust anisotropic hyperelastic formulation for the modelling of soft tissue

Nolan

Gower

Destrade

et al. 2014

Journal of the Mechanical Behavior of Biomedical Materials

195

105

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The Holzapfel-Gasser-Ogden (HGO) model for anisotropic hyperelastic behaviour of collagen fibre reinforced materials was initially developed to describe the elastic properties of arterial tissue, but is now used extensively for modelling a variety of soft biological tissues. Such materials can be regarded as incompressible, and when the incompressibility condition is adopted the strain energy Ψ of the HGO model is a function of one isotropic and two anisotropic deformation invariants. A compressible form (HGO-C model) is widely used in finite element simulations whereby the isotropic part of Ψ is decoupled into volumetric and isochoric parts and the anisotropic part of Ψ is expressed in terms of isochoric invariants. Here, by using three simple deformations (pure dilatation, pure shear and uniaxial stretch), we demonstrate that the compressible HGO-C formulation does not correctly model compressible anisotropic material behaviour, because the anisotropic component of the model is insensitive to volumetric deformation due to the use of isochoric anisotropic invariants. In order to correctly model compressible anisotropic behaviour we present a modified anisotropic (MA) model, whereby the full anisotropic invariants are used, so that a volumetric anisotropic contribution is represented. The MA model correctly predicts an anisotropic response to hydrostatic tensile loading, whereby a sphere deforms into an ellipsoid. It also computes the correct anisotropic stress state for pure shear and uniaxial deformation. To look at more practical appli- cations, we developed a finite element user-defined material subroutine for the simulation of stent deployment in a slightly compressible artery. Significantly higher stress triaxiality and arterial compliance are computed when the full anisotropic invariants are used (MA model) instead of the isochoric form (HGO-C model).Keywords: Anisotropic, Hyperelastic, Incompressibility, Finite element, Artery, Stent Nomenclature I -identity tensor Ψ -Helmholtz free-energy (strain-energy) function Ψ vol -volumetric contribution to the free energy Ψ aniso -anisotropic contribution to the free energy Ψ iso -isotropic contribution to the isochoric free energy Ψ aniso -anisotropic contribution to the isochoric free energy σ -Cauchy stress σ -deviatoric Cauchy stress q -von Mises equivalent stress σ hyd -hydrostatic (pressure) stress F -deformation gradient J -determinant of the deformation gradient; local ratio of volume change C -right Cauchy-Green tensor I 1 -first invariant of C I 4,6 -anisotropic invariants describing the deformation of reinforcing fibres F -isochoric portion of the deformation gradient C -isochoric portion of the right Cauchy-Green deformation tensor I 1 -first invariant of C I 4,6 -isochoric anisotropic invariants a 0i , i = 4, 6 -unit vector aligned with a reinforcing fibre in the reference configuration a i , i = 4, 6 -updated (deformed) fibre direction (= Fa 0i ) κ 0 -isotropic bulk modulus µ 0 -isotropic shear modulus k i , i = 1, 2 -anisotropic material co...

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Section: Discussionsupporting

confidence: 52%

A robust anisotropic hyperelastic formulation for the modelling of soft tissue

Nolan

Gower

Destrade

et al. 2014

Journal of the Mechanical Behavior of Biomedical Materials

195

105

View full text Add to dashboard Cite

show abstract

“…This effect is usually negligible for elastic deformations, because of the small strains, , generally involved with colloidal materials 10 (e.g., [115,117]), but may be important in plastic deformation. Given that a shear stress can be expressed in terms of (normal) principal stresses, in turn decomposed into isotropic and deviatoric parts, it is not surprising that Poisson's ratio might play an important role; experimental measurements confirm a very high sensitivity to ], including a transition from tensile to compressive 22 for very small deviations from ] = 1/2 [104,118]. In practice the sign of the normal stresses themselves depends on the boundary conditions, or any superimposed isotropic stress [104,118].…”

Section: Influence Of Shear Strain and Strain Rate On Normal Stressesmentioning

confidence: 99%

“…10. Within elastic solids, the normal stresses set up in some cases of shear deformation could lead to changes in volume, if not resisted, and potentially progress to failure [104,118]; these underlying stresses could be a useful way to describe the dilatancy upon shearing that is a feature of "critical state" soil mechanics [93]-or general shearenhanced volumetric strain [113]-although this link does not appear to have been investigated previously.…”

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confidence: 99%

Normal Stress Differences and Yield Stresses in Attractive Particle Networks

Verrelli

Kilcullen

2016

Advances in Condensed Matter Physics

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The nature of attractive particulate networks, yield stresses, and normal stress differences is systematically reviewed, each in terms of the relevant definitions, underlying mechanisms, and current measurement techniques. With this foundation, experimental observations of normal stress differences in some suspensions and colloidal systems are surveyed, along with constitutive models that allow for normal stress differences to arise prior to yielding. Yield stresses are a hallmark of attractive colloidal systems and vital in their processing. In contrast, little attention has been given to the role of normal stress differences in these systems. The presence or absence of normal stress differences necessarily affects the isotropy of the normal stress field through the solid particulate phase (treated as a continuum), in turn affecting estimation of yield stress. Given the importance of yield stresses in dealing with practical industrial problems, and in understanding fundamental behaviours, it is important to ensure that yield measurements can be relied upon.

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Probabilistic Model of Fatigue Damage Accumulation in Rubberlike Materials

Larin

2015

Strength Mater

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Shear of rubber tube springs

Cited by 10 publications

References 14 publications

A robust anisotropic hyperelastic formulation for the modelling of soft tissue

A robust anisotropic hyperelastic formulation for the modelling of soft tissue

Normal Stress Differences and Yield Stresses in Attractive Particle Networks

Probabilistic Model of Fatigue Damage Accumulation in Rubberlike Materials

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