Speaker
Description
Human fibrous tissues display a non-local in time mechanical behaviour since they have memory of their past stress-strain history and consequently they can be defined as hereditary materials. In particular, this unconventional behaviour can be mathematically described by introducing a fractional intermediate non-additive rheological model, the so-called springpot [1], to avoid the drawbacks linked to the use of the classical models in the description of hereditary materials with continuous retardation/relaxation spectra. However, the use of an intermediate model prevents the correct description of the real multiphase structure of hereditary materials and this has led to the emergence of drawbacks such as the impossibility to derive a unique formulation for the free energy function for the thermodynamical characterization of these materials.
In previous studies, in order to overcome all these drawbacks, a new multiscale hierarchical mechanically-based model was proposed to describe hereditary materials [2]. Indeed this model presents a complete separation of the fluid and the solid phases and, at the same time, is characterized, at limit, by a continuous relaxation spectrum. The main limitation associated to the use of this model is that it neglects the contribution of inertial forces in its mechanical description and consequently it cannot be used to describe biological tissues which are subjected to dynamic loading conditions where inertial effects significantly influence the material behaviour.
Consequently, the main aim of this study turns out to be the modification of this multiscale model to describe biological tissues under dynamic conditions.
Additionally, a numerical analysis is proposed to assess the goodness of the proposed approach.
[1] Nutting, P. G. 1921, “A new general law of deformation”, Journal of the Franklin Institute, vol. 191.5, pp. 679-685.
[2] Di Paola, M., Zingales, M. 2012, “Exact mechanical models of fractional hereditary materials”, Journal of Rheology, vol. 56.5, pp. 983-1004.