Keywords: inverse structural engineering, optimisation, finite element analysis, deformation, material property, tracheal cartilage.

This paper describes an inverse methodology to characterise the constitutive material properties of the tracheal cartilage of the leatherback turtle (Dermochelys coriacea) and follows on from an earlier investigation [1]. The trachea of the leatherback turtle differs from terrestrials in that it consists of a near-continuous elliptical tube of uncalcified hyaline cartilage with minimal connective tissue between successive cartilaginous rings [2]. This arrangement appears to be structurally superior allowing the turtle to withstand colossal hydrostatic pressures experienced during deep dives (greater than 300m).

It is hypothesised that the integral difference between the load-displacement histories obtained from the material testing of a tracheal ring and from that of a corresponding finite element analysis (FEA) may be quantified. Using constrained optimisation the square of this quantity is minimised with respect to the constitutive material properties in the FEA.

A single tracheal ring taken from the cadaver of an adult Dermochelys coriacea was used in the compressive material testing. A corresponding model of the material testing was developed using a FEA software system. An artificial programming interface (API) was used to communicate with the FEA and optimise its load-displacement history with respect to the constitutive stress-strain relationship.

There is excellent agreement between the optimised load-displacement history and the history obtained from the material testing with minimal difference between the two curve overlays. In addition the curvature of the deformations predicted by the optimised FEA correlate strongly with those observed in the material testing suggesting that the values of the FEA material properties produced by the optimisation are reflective of those of the material. The tracheal cartilage was also found to display higher strength in compression than in tension, in line with other studies [3]. Altogether the results show clearly the benefits of applying the described inverse methodology to ascertain the material properties of the tracheal cartilage of the leatherback turtle.

1

C. Murphy, D. Kelliher, J. Davenport, "A Nonlinear Finite Element Inverse Approach to Characterise the Material Properties of Tracheal Cartilage: Preliminary Investigation", in "Proceedings of the ASME 2010 Summer Bioengineering Conference", American Society of Mechanical Engineers: Biomechanical Divison, June 16-19, Naples, Florida, 2010.

2

J. Davenport, J. Fraher, E. Fitzgerald, P. McLaughlin, T. Doyle, L. Harman, T. Cuffe, P. Dockery, "Ontogenetic Changes in Tracheal Structure Facilitate Deep Dives and Cold Water Foraging in Adult Leatherback Sea Turtles", Journal of Experimental Biology, 212, 3440-3447, 2009. doi:10.1242/jeb.034991

3

Z. Teng, I. Ochoa, J.A. Bea, M. Doblare, "Theoretical and Experimental Studies on the Nonlinear Mechanical Property of Tracheal Cartilage", in "Proceedings of the 29th Annual International Conference of the IEEE", EMBS Cité Internationale, Lyon, France, 2007. doi:10.1109/IEMBS.2007.4352477

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