A new material identification pattern for the fractional Kelvin–Zener model describing biomaterials and human tissues

Abstract The aim of this study is to describe several biomaterials and tissues using a simple material identification pattern applied to the fractional Kelvin–Zener model of viscoelastic body and standard mechanical tests. Each of the descriptions comprises the order of fractional derivative of stress and strain, modulus of elasticity, and stress and strain relaxation constants that obey restrictions imposed by the Clausius–Duhem inequality. These four parameters are obtained by use of the Laplace transform, Post's inversion formula and Newton's method. The suggested approach can serve as an alternative to quasilinear viscoelasticity providing a physically uniform quantitative measure for biomaterials/tissues comparison and can be applied to real data. It works for nonsmooth inputs too. Regarding biomaterials the comparison between an etched poly lactic-co-glycolic acid membrane and the corresponding composite scaffold was made. With respect to human tissues the tympanic membrane, the stapedial tendon, and the stapedial annular ligament were described. The obtained mechanical response for examined cases is in agreement with the experimentally recorded one.