Finite extension and torsion of papillary muscles: A theoretical framework

Humphrey, Jay D.; Barazotto, R.L.

doi:10.1016/0021-9290(92)90094-h

Cited by 31 publications

(17 citation statements)

References 22 publications

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“…We confine attention here to the resultant applied moment and axial force necessary to maintain the deformation. On using the results of Humphrey et al [14] and converting to the notation of the present paper we obtain (3.6) and …”

Section: Torsion Of a Solid Circular Cylindermentioning

confidence: 91%

“…3, we review known results for the problem of torsion of a solid circular cylinder composed of an incompressible transversely-isotropic hyperelastic material. We summarize results obtained by Humphrey et al [14] for a class of strain-energies. It is important to note that these results are exact solutions for the general class of transversely-isotropic materials considered and reduce to the celebrated results of Rivlin [26] for the case of isotropy.…”

Section: Introductionmentioning

confidence: 88%

“…Thus the fibers are considered to be helically wound throughout the cylinder. As remarked in Humphrey et al [14] if the majority of perimysial fibers in papillary muscles coincide with the long axis, one has ψ = π/2 and A = (0, 0, 1) and this special case will be considered in detail in the sequel. For general angles ψ , on using the notation c = cos ψ, s = sin ψ , we find that…”

Section: Torsion Of a Solid Circular Cylindermentioning

confidence: 96%

“…General expressions for the physical components of the Cauchy stresses for the case where W = W (I 1 , I 4 ) are given by Humphrey et al [14] and by Humphrey [13]. We confine attention here to the resultant applied moment and axial force necessary to maintain the deformation.…”

Section: Torsion Of a Solid Circular Cylindermentioning

confidence: 98%

“…More recently, this problem has attracted attention in the literature on biomechanics of soft tissues and has been applied, for example, to study the mechanical behavior of passive papillary muscles of the heart (see, e.g., Humphrey et al [14], Criscione et al [1], Humphrey [13], Taber [29]). A recent study by Kanner and Horgan [15] in a nonlinear elasticity framework was concerned with the effects of strain-stiffening on the response of solid circular cylinders in the combined deformation of torsion superimposed on axial extension.…”

Section: Introductionmentioning

confidence: 99%

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Torsion of Incompressible Fiber-Reinforced Nonlinearly Elastic Circular Cylinders

Horgan

Murphy

2010

J Elast

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Torsion of solid cylinders in the context of nonlinear elasticity theory has been widely investigated with application to the behavior of rubber-like materials. More recently, this problem has attracted attention in investigations of the biomechanics of soft tissues and has been applied, for example, to examine the mechanical behavior of passive papillary muscles of the heart. A recent study in nonlinear elasticity was concerned specifically with the effects of strain-stiffening on the torsional response of solid circular cylinders. The cylinders are composed of incompressible isotropic nonlinearly elastic materials that undergo severe strain-stiffening in the stress-stretch response. Here we investigate similar issues for fiber-reinforced transversely-isotropic circular cylinders. We consider a class of incompressible anisotropic materials with strain-energy densities that are of logarithmic form in the anisotropic invariant. These models reflect stretch induced strain-stiffening of collagen fibers on loading and have been shown to model the mechanical behavior of many fibrous soft biological tissues. The consideration of anisotropy leads to a more elaborate mechanical response than was found for isotropic strain-stiffening materials. The classic Poynting effect found for rubber-like materials where torsion induces elongation of the cylinder is shown to be significantly different for the transversely-isotropic materials considered here. For sufficiently large anisotropy and under certain conditions on the amount of twist, a reverse-Poynting effect is demonstrated where the cylinder tends to shorten on twisting The results obtained here have important implications for the development of accurate torsion test protocols for determination of material properties of soft tissues.

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Section: Torsion Of a Solid Circular Cylindermentioning

confidence: 91%

Section: Introductionmentioning

confidence: 88%

Section: Torsion Of a Solid Circular Cylindermentioning

confidence: 96%

Section: Torsion Of a Solid Circular Cylindermentioning

confidence: 98%