A constitutive model for ballistic gelatin at surgical strain rates

This paper describes a constitutive model for ballistic gelatin at the low strain rates experienced, for example, by soft tissues during surgery. While this material is most commonly associated with high speed projectile penetration and impact investigations, it has also been used extensively as a soft tissue simulant in validation studies for surgical technologies (e.g. surgical simulation and guidance systems), for which loading speeds and the corresponding mechanical response of the material are quite different. We conducted mechanical compression experiments on gelatin specimens at strain rates spanning two orders of magnitude (~0.001-0.1s(-1)) and observed a nonlinear load-displacement history and strong strain rate-dependence. A compact and efficient visco-hyperelastic constitutive model was then formulated and found to fit the experimental data well. An Ogden type strain energy density function was employed for the elastic component. A single Prony exponential term was found to be adequate to capture the observed rate-dependence of the response over multiple strain rates. The model lends itself to immediate use within many commercial finite element packages.