Torsion of Incompressible Fiber-Reinforced Nonlinearly Elastic Circular Cylinders |
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Authors: | Email author" target="_blank">Cornelius?O?HorganEmail author Jeremiah?G?Murphy |
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Institution: | (1) Department of Civil Engineering, University of Virginia, P.O. Box 400742, Charlottesville, VA, 22904, U.S.A.;(2) Sezione di Ingegneria Industriale, Dipartimento di Ingegneria dell'Innovazione, Università degli Studi di Lecce, 73100 Lecce, Italy |
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Abstract: | 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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