A constitutive model for ballistic gelatin at surgical strain rates

Abstract

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.

Response functions in linear viscoelastic constitutive equations and related fractional operators

“…The viscoelastic relaxation function can be expressed by a discrete relaxation spectrum through a decomposition as a Prony series φ p (t) with N p terms [33,34,41,44,95,116,122]:…”

“…Sometimes, only one term of the Prony series (i.e. N p = 1) is sufficient to capture the entire relation curve obtained experimentally [122] and then the relaxation function can be used in a modified form (5.1) as a model with four independent parameters that can be specified based on experimental results.…”

Linear Viscoelastic Responses: The Prony Decomposition Naturally Leads Into the Caputo-Fabrizio Fractional Operator

“…The viscoelastic relaxation function can be expressed by a discrete relaxation spectrum through a decomposition as a Prony series g P (t)with N φ terms [25,[59][60][61][62][63][64] with rate constants β i , namely…”

Constitutive modeling of nonlinear strain and time dependent behaviors of ballistic gelatin at low strain rates

“…[14] proposed tabulated hyperelasticity to capture strain ratedependence based on numerous actual stress-strain and strain rate curves from experimental tests. However, this method requires a sufficiently rich set of constituent curves to cover the desired range of loading conditions [15,16]. [15] employed an Ogden type strain energy density function for the nonlinear elastic response and a single Prony exponential term for the rate-dependent response of ballistic gelatin over multiple strain rates.…”

“…However, this method requires a sufficiently rich set of constituent curves to cover the desired range of loading conditions [15,16]. [15] employed an Ogden type strain energy density function for the nonlinear elastic response and a single Prony exponential term for the rate-dependent response of ballistic gelatin over multiple strain rates. The calibration of the material parameters was based on uniaxial compression tests with nominal compression strain rates in the range of 0.001/s~0.1/s.…”