The importance of the second strain invariant in the constitutive modeling of elastomers and soft biomaterials

Horgan, Cornelius O.; Smayda, Michael

doi:10.1016/j.mechmat.2012.03.007

Cited by 81 publications

(47 citation statements)

References 40 publications

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“…We never observed an exact reproduction of the axial force through the simple shear approximation, however, simple shear can capture the correct trend for the axial force for some material models, e.g., Mooney-Rivlin. Models with a strain-energy function only dependent on I 1 , e.g., neo-Hookean, Yeoh and eight-chain models, unfortunately, do an inaccurate prediction of the normal stress b σ zz in the simple shear mode, namely zero [23]. Considering two actin network models, the torsion solution for the eight-chain model predicts a negative axial force which is in contrast to experimental results.…”

Section: Discussionmentioning

confidence: 86%

“…In analogy to (30) 1 , the error at γ ¼ 0:2 is e AB Mt ¼ 44%. Recall that the strain-energy function of the eightchain model is only dependent on the first invariant I 1 of the right Cauchy-Green tensor, and thus the simple shear solution predicts a zero normal stress b σ AB zz according to (18) 2 and [23]. The torsion of the cylinder gives again a negative normal stress.…”

Section: Eight-chain Modelmentioning

confidence: 99%

“…3(b), coincide. Recall, that for simple shear b σ YEOH zz ¼ 0 because ψ 2 ¼ 0, see (18) 2 and [22,23]. Considering, for example, the Yeoh model, Fig.…”

Section: Error Measures For the Torsion Couple And The Axial Forcementioning

confidence: 99%

See 2 more Smart Citations

Mechanical modeling of rheometer experiments: Applications to rubber and actin networks

Unterberger¹,

Weisbecker²,

Holzapfel³

2014

International Journal of Non-Linear Mechanics

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Section: Discussionmentioning

confidence: 86%

Section: Eight-chain Modelmentioning

confidence: 99%

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Mechanical modeling of rheometer experiments: Applications to rubber and actin networks

Unterberger¹,

Weisbecker²,

Holzapfel³

2014

International Journal of Non-Linear Mechanics

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“…The stress distribution on the artery for the two models is shown in Figure 9b, and the stress level was higher for polynomial model (0.79 MPa) due to more severe deformation. The importance of the second stretch invariant (I 2 ) has been discussed in Horgan and Smayda (2012) and Khajehsaeid et al (2013). It was reported that the strain-energy potential with the absence of I 2 is unable to capture some significant physical effects such as simple shear, strain stiffening at large stretches and torsion of a circular cylinder.…”

Section: Effect Of Artery Constitutive Models Second Stretch Invarianmentioning

confidence: 99%

A study of balloon type, system constraint and artery constitutive model used in finite element simulation of stent deployment

Schiavone

Zhao

2015

Mech Adv Mater Mod Process

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Background: Finite element is an effective tool to simulate stent expansion inside stenotic arteries, which provides an insightful understanding of the biomechanical behaviour of the whole stent-artery system during the procedure. The choice of balloon type, system constraint and artery constitutive model plays an important role in finite element simulation of stent deployment. Methods: Commercial finite element package ABAQUS was used to model the expansion of Xience stent inside a diseased artery with 40% stenosis. The arterial wall, consisting of intima, media and adventitia layers, and the stenotic plaque were described by different hyperelastic models. Both folded and rubber balloons were considered and inflated with a linearly increasing pressure of 1.4 MPa. Simulations were also carried out by considering free, partially and fully constrained arteries. Results: Folded balloon produces sustained stent expansion under a lower pressure when compared to rubber balloon, leading to increased stress level and enhanced final expansion for the system. Fully constrained artery reduces the stent expansion when compared to free and partially constrained arteries, due to the increased recoiling effect. Stress in the artery-plaque system has higher magnitude for stent expansion in a free artery due to more severe stretch. Calcified plaque limits stent expansion considerably when compared to hypocellular plaque. The negligence of the second stretch invariant in the strain energy potential leads to the disappearance of saturation behaviour during stent expansion. The use of anisotropic artery model reduces the system expansion at peak pressure when compared to the isotropic model, but with an increased final diameter due to reduced recoiling effect. The stress distribution in the artery-plaque system is also different for different combinations of artery and plaque constitutive models. Conclusions: Folded balloon should be used in the simulation of stent deployment, with the artery partially constrained using spring elements with a proper stiffness constant. The blood vessel should be modelled as a three-layer structure using a hyperelastic potential that considers both the first and second stretch invariants as well as the anisotropy. The composition of the plaque also has to be considered due to its major effect on stent deployment.

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“…Raghavan and Vorp (2000) It is worth noting also that we use the simplest model (3.2) to intact material behavior in view of the available experimental data. However, the account of the second principal invariant can be relevant for soft materials-see Horgan and Smayda (2012).…”

Section: Aaa Constitutive Models With Energy Limitersmentioning

confidence: 99%

Cavitation instability as a trigger of aneurysm rupture

Volokh

2015

Biomech Model Mechanobiol

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Aneurysm formation and growth is accompanied by microstructural alterations in the arterial wall. Particularly, the loss of elastin may lead to tissue disintegration and appearance of voids or cavities at the micron scale. Unstable growth and coalescence of voids may be a predecessor and trigger for the onset of macroscopic cracks. In the present work, we analyze the instability of membrane (2D) and bulk (3D) voids under hydrostatic tension by using two experimentally calibrated constitutive models of abdominal aortic aneurysm enhanced with energy limiters. The limiters provide the saturation value for the strain energy, which indicates the maximum energy that can be stored and dissipated by an infinitesimal material volume. We find that the unstable growth of voids can start when the critical stress is considerably less than the aneurysm strength. Moreover, this critical stress may even approach the arterial wall stress in the physiological range. This finding suggests that cavitation instability can be a rational indicator of the aneurysm rupture.

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The importance of the second strain invariant in the constitutive modeling of elastomers and soft biomaterials

Cited by 81 publications

References 40 publications

Mechanical modeling of rheometer experiments: Applications to rubber and actin networks

Mechanical modeling of rheometer experiments: Applications to rubber and actin networks

A study of balloon type, system constraint and artery constitutive model used in finite element simulation of stent deployment

Cavitation instability as a trigger of aneurysm rupture

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