Finite elasticity formulations for evaluation of ligamentous tissue

The variety of techniques used to measure the cross-sectional area of soft connective tissues during mechanical testing lead to inconsistencies in elastic descriptions. This study compares the numerical differences between finite elasticity (Eularian and Lagrangian formulations) and infinitesimal elasticity when considering stress, strain and elastic modulus of ligamentous tissue. Our results found stress differences (Cauchy versus Kirchhoff) of 22.4%, strain differences (engineering versus Green versus Almansi) as large as 14% and elastic modulus differences (Eularian versus Lagrangian) of 44% from ligament tissue sampled from rats. It is therefore critical to maintain consistent (energy conjugate) elastic formulations for reporting mechanical evaluation of soft hydrated tissue.