Mechanics of Soft Tissues: Reflecting on Roads Traveled And The Road Just Taken

Prof. Alan D. Freed (Saginaw Valley State University, MI, USA)

Friday 8th March, 2013 15:00-16:00 Maths 203

Abstract

A decade ago I was asked to assist The Cleveland Clinic in their efforts to model the viscoelastic response of heart valves, with the objective being a material model suitable for implementation into finite element codes.  This was an abrupt change from my prior activities on rocket engine technologies for the Agency—NASA.  This talk reflects on my road of discovery, finishing with my vision of what lies ahead.

Having no prior experience in the field of biomechanics allowed me to enter into it without bias, which has been my advantage.  After an introduction to soft tissues from a mechanics perspective, I will explain why not having prior exposure to the field allowed me to seek what I consider to be a simpler mathematical description for soft tissue mechanics, both elastic and viscoelastic.  Early investigations determined the viscoelastic response of tissues to obey fractional-order kinetics.   To construct a viable 3D viscoelastic model would require an appropriate 3D elastic model to describe the tissue’s quasi-static behavior.  My first attempt to describe the finite quasi-elastic response of these materials was to move from a stress—strain or hyper-elastic model to a stress-rate—strain-rate or hypo-elastic model.  This lead to a simpler theoretical structure for soft tissues, but it lacked a clear and simple thermodynamic interpretation. 

About two years ago, Prof. Rajagopal introduced me to his idea of an implicit elastic solid from which I was able to construct an elegant elastic theory for tissues derived straight from thermodynamics.  To apply the theory to lung, a novel isotropic—deviatoric split in a differential change of the deformation gradient was introduced that separates work into independent isotropic and deviatoric contributions.  An alternative to the classical hyper-elastic theory, i.e., an implicit theory of elasticity, is now in place, which is suitable for describing soft tissues.  Applicability of this novel theory, simple in structure, is demonstrated by its ability to capture the complex mechanical response exhibited by this class of materials. 

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