A three-dimensional visco-hyperelastic FE model for simulating the mechanical dynamic response of preloaded phalanges

This study lays the groundwork for a multi-scale strategy that will lead to a better understanding and prediction of the effects of vibration on the digital arterial network. This is accomplished by modelling the mechanical and biological factors that could disturb the basal vasoconstriction balance in the fingertip. The first stage of this novel approach involved building and validating an original dissipative constitutive law for the fingertip soft tissue for the purpose of finite element modelling of the mechanical response of preloaded phalanges in vibration. This visco-hyperelastic constitutive law was established by means of a two-stage procedure for combining a classical pure static nonlinear law with an original dissipative model. First, the parameters of an Ogden-Hill pure static nonlinear constitutive law were identified using a constrained optimisation algorithm. Second, an original viscous dissipation model was proposed in the spectral domain. This model is based on the linearization of the nonlinear quasi-linear viscoelasticity law and the use of a viscoelastic relaxation modulus, expressed as a continuous distribution of relaxation spectra suitable for living tissues. The experimental data used to fit this model were the static and dynamic stiffnesses of preloaded fingertips acquired from a group of 20 subjects. The relative errors between the measured and simulated stiffnesses were less than 5% in the static procedure and approximately 8% using dynamic analysis. The computed mechanical pressure and maximal tangential stress within the fingertip were high in the soft tissues close to the vibration excitation and also in the bones and interphalangeal cartilages far from the vibration source. Mechanical power was only dissipated significantly in the immediate vicinity of the contact area between the probe and the finger. The main contribution of this study was to implement and identify the parameters of a new spectral dissipative law for fingertip soft tissues. This work may apply in occupational health for modifying the vibration dose assessment or for the follow-up and screening of connective tissue diseases.