Stress-strain response of quasi-incompressible thin biological tissue layers by means of spherical compression tests

Characterization of the mechanical behavior of soft biological tissues is of interest given its wide range of applications in the medical field.Among various techniques, indentation experiments have the advantage to be applied through micro to macro-scales.This work focuses on spherical compressor that allows keeping the sample intact and close to in vivo mechanical conditions.As the compressor displacement is not necessarily equal to the penetration depth, gaining access to the stress-strain curves remains a challenge. Recent studies propose modifications to the Hertz theory but none considers the interaction of the sample with the testing support during the test as well as the gravity effect, which may also affect the measurement of penetration depth.\\Thanks to finite element method, we developed a method to get access to the stress-strain response of thin layer of biological material undergoing spherical compression tests with unbound samples to the supporting base. It allowed the evaluation of effective stress and strain values thanks to the experimental force and displacement data for various sample thicknesses. As a conclusion, the use of the commonly adopted penetration depth as a model parameter should be avoided. The method was developed using neo-Hookean constitutive relation and the results can be extended for other hyperplastic constitutive laws.Of course, the combination of anisotropic, viscous and multiphase aspects would allow a closer approximation of what occurs physiologically in biological tissues. Although, this approach will allow first identification that will feed more sophisticated simulations able to consider all above mentioned phenomena.