A description of arterial wall mechanics using limiting chain extensibility constitutive models

Horgan, Cornelius O.; Saccomandi, Giuseppe

doi:10.1007/s10237-002-0022-z

Cited by 130 publications

(127 citation statements)

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“…Horgan & Saccomandi (2002, 2006 for a review of such models and their applications to strain-stiffening rubber-like and biological tissues. Application of the Gent model to the mechanics of arterial walls is discussed by Horgan & Saccomandi (2003), Holzapfel (2005) and Ogden & Saccomandi (2007). The Gent model has been shown to be a viable alternative to the classical Fung exponential model that has had widespread application in the biomechanics of soft tissues.…”

Section: Shear Stress Response For Soft Tissuesmentioning

confidence: 99%

“…Based on the experimental work of Lawton & King (1951) on oscillations of human thoracic aorta segments, Horgan & Saccomandi (2003) proposed values of the limiting chain parameter in the isotropic Gent model. In the absence of experimental data corresponding to the new model (3.4), here, we simply use the same values for the parameter J as were proposed by Horgan & Saccomandi (2003) for the Gent model.…”

Section: Effects Of Fibre Orientationmentioning

confidence: 99%

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Simple shearing of soft biological tissues

Horgan

Murphy

2010

Proc. R. Soc. A.

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Shearing is induced in soft tissues in numerous physiological settings. The limited experimental data available suggest that a severe strain-stiffening effect occurs in the shear stress when soft biological tissues are subjected to simple shear in certain directions. This occurs at relatively small amounts of shear (when compared with the simple shear of rubbers). This effect is modelled within the framework of nonlinear elasticity by consideration of a class of incompressible anisotropic materials. Owing to the large stresses generated for relatively small amounts of shear, particular care must be exercised in order to maintain a homogeneous deformation state in the bulk of the specimen. The results obtained are relevant to the development of accurate shear test protocols for the determination of constitutive properties of soft tissues. It is also demonstrated that there is a fundamental ambiguity in determining the normal stresses in simple shear when soft tissues are modelled as incompressible hyperelastic materials owing to the arbitrary nature of the hydrostatic pressure term. Two physically well-motivated approaches to determining the pressure are presented here, and the resulting hydrostatic stresses are compared and contrasted. The possible generation of cavitational damage owing to critical hydrostatic stress levels is briefly discussed.

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Section: Shear Stress Response For Soft Tissuesmentioning

confidence: 99%

Section: Effects Of Fibre Orientationmentioning

confidence: 99%

Simple shearing of soft biological tissues

Horgan

Murphy

2010

Proc. R. Soc. A.

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“…(Horgan and Saccomandi, 2003;Li and Robertson, 2009;Tsamis et al, 2013), damage and remodeling (Ferrara and Pandolfi, 2008;Ni Annaidh et al, 2012;Sánchez et al, 2014). As a consequence of the intrinsically patient-specific nature and of the microstructural complexity of biological tissues, their modeling is very challenging and still incomplete.…”

Section: Introductionmentioning

confidence: 99%

Statistical characterization of the anisotropic strain energy in soft materials with distributed fibers

Gizzi

Pandolfi

Vasta

2016

Mechanics of Materials

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a b s t r a c tWe discuss analytical and numerical tools for the statistical characterization of the anisotropic strain energy density of soft hyperelastic materials embedded with fibers. We consider spatially distributed orientations of fibers following a tridimensional or a planar architecture. We restrict our analysis to material models dependent on the fourth pseudo-invariant I 4 of the Cauchy-Green tensor, and to exponential forms of the fiber strain energy function aniso . Under different loading conditions, we derive the closed-form expression of the probability density function for I 4 and aniso . In view of bypassing the cumbersome extension-contraction switch, commonly adopted for shutting down the contribution of contracted fibers in models based on generalized structure tensors, for significant loading conditions we identify analytically the support of the fibers in pure extension. For uniaxial loadings, the availability of the probability distribution function and the knowledge of the support of the fibers in extension yield to the analytical expression of average and variance of I 4 and aniso , and to the direct definition of the average second Piola-Kirchhoff stress tensor. For generalized loadings, the dependence of I 4 on the spatial orientation of the fibers can be analyzed through angle plane diagrams. Angle plane diagrams facilitate the assessment of the influence of the pure extension condition on the definition of the stable support of fibers for the statistics related to the anisotropic strain energy density.

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“…As an example, slight compressibility (volumechange of up to roughly 3%) resulted in circumferential stresses in the arterial wall up to 100% higher compared to the incompressible case for the physiological pressure of 100 mmHg as documented in [21,8]. For almost-incompressible materials ε = µ/κ is usually a small parameter, but not zero, and the interested reader is referenced to a detailed analysis of such cases for ε ≪ 1 in [14,15].…”

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confidence: 99%