A multi-scale modelling strategy to predict the vibration effects on the digital vascular network. First stage: validation of a finite element model at the macroscopic scale for a pre-loaded and vibrated distal phalanx.

This study lays the foundation for a multi-scale strategy which would be able in the future to predict and to better understand the action of the vibrations on the digital arterial network by modeling some mechanical-biological coupling effects unbalancing the basal vasoconstriction. The first step of this original approach deals with the construction and the validation of a finite element model at the macroscopic scale for a pre-stressed vibrated distal phalanx. Experimental data required for fitting the model are the static and dynamic stiffness acquired for a group of 20 subjects. These measurements show that the human phalanx behaves mechanically in the same way that a complex rubber with stiffening in frequency and softening in amplitude. The visco-hyper-elastic constitutive law is implemented in two stages. Firstly, the parameters of a purely non-linear static law of Ogden-Hill are identified by using constrained optimization algorithms. Then, a viscous dissipative model is defined from the linearization of a nonlinear viscoelasticity law (Quasi Linear Viscoelasticity) and from relaxation spectra. The relative error between measured and computed stiffness is lower than 5 % for the static case and around 8 % for the dynamic case. Two application examples exhibit that the dissipated vibrated power and the induced temperature rise are localized in the contact zone between the indenter and the phalanx.