Power-Laws hereditariness of biomimetic ceramics for cranioplasty neurosurgery

We discuss the hereditary behavior of hydroxyapatite-based composites used forcranioplastic surgery in the context of material isotropy. We classify mixtures ofcollagen and hydroxiapatite composites as biomimetic ceramic composites withhereditary properties modeled by fractional-order calculus. We assune isotropyof the biomimetic ceramic is assumed and provide thermodynamic of restric-tions for the material parameters. We exploit the proposed formulation of thefractional-order isotropic hereditariness further by means of a novel mechan-ical hierarchy corresponding exactly to the three-dimensional fractional-orderconstitutive model introduced