Reverse Poynting Effects in the Torsion of Soft Biomaterials

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• 作者：Cornelius O. Horgan (1)
  Jeremiah G. Murphy (2)
  
  1. School of Engineering and Applied Science ; University of Virginia ; Thornton Hall ; Charlottesville ; VA ; 22904 ; USA
  2. Centre for Medical Engineering Research ; Dublin City University ; Glasnevin ; Dublin 9 ; Ireland
  
• 关键词：Incompressible fiber ; reinforced transversely isotropic nonlinearly elastic materials ; Soft biomaterials ; Papillary muscles ; Torsion of solid circular cylinders ; Reverse Poynting effect ; 74B20 ; 74G55
• 刊名：Journal of Elasticity
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：118
• 期：2
• 页码：127-140
• 全文大小：538 KB
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• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-2681

文摘

The torsion of solid cylindrical bodies has been widely investigated in the context of isotropic nonlinear elasticity theory with application to the behavior of rubber-like materials. More recently, this problem for anisotropic materials 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. Here we consider the torsion of a solid circular cylinder composed of a transversely isotropic incompressible material described by a strain-energy function that depends on the full set of relevant invariants. Three specific strain-energy density functions modeling soft tissues are considered in detail. These models are quadratic in the anisotropic invariants, linear in the isotropic strain invariants and are consistent with the linear theory. The classic Poynting effect found for isotropic 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 small angles of twist that are consistent with the physiological strain range, 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 biomaterials.