Power-Laws hereditariness of biomimetic ceramics for cranioplasty neurosurgery

Abstract

In this paper the authors deals with the heredity behavior of hydroxyapatite-based composite used for cranioplastic surgery. It is shown that biomimetic prostheses, for their microstructural morphology, have a mechanical behavior that can be well described by an isotropic fractional-order hereditary model. The three-axial isotropic behavior is framed in the context of fractional-order calculus and same details about thermodynamical restrictions of memory functions used in the formulation of the three-axial isotropic constitutive equations. A mechanical model that corresponds, exactly, to the three-axial isotropic hereditariness is also introduced in the paper. File Name [File Type] cover letter.pdf [Cover Letter] power-laws-hereditariness second review.pdf [Response to Reviewers] power-laws-hereditariness.pdf [Response to Reviewers] Power_Laws_hereditariness_rev.pdf [Response to Reviewers] report.pdf [Review Reports] Paper Highlights-Bologna_Graziano-Deseri_Zingales.docx [Highlights] Power laws hereditariness.pdf [Manuscript File] Submission Files Not Included in this PDF File Name [File Type]power-laws-hereditariness (2).zip [LaTeX Source File] AbstractIn this paper the hereditary behavior of hydroxyapatite-based composites used for cranioplastic surgery is discussed in the context of material isotropy. Mixtures of collagen and hydroxiapatite composites are classified as biomimetic ceramic composites with hereditary properties modeled in the paper fractionalorder calculus. Isotropy of the biomimetic ceramic is assumed and the thermodynamic of restrictions among material parameters are provided. The proposed formulation of the fractional-order isotropic hereditariness has been further exploited by means of a novel mechanical hierarchy that corresponds, exactly, to the three-dimensional fractional-order constitutive model introduded in the paper. AbstractIn this paper the authors deal with the hereditary behavior of hydroxyapatitebased composites used for cranioplastic surgery. It is shown that biomimetic prosthesis, possess an isotropic fractional-order material hereditariness due to their microstructure architecture. The three-axial hereditariness is framed in the context of fractional-calculus providing details about thermodynamical restrictions of memory functions used in the formulation. A mechanical model that corresponds, exactly, to the three-axial fractional-order hereditariness is also introduced in the paper. AbstractWe discuss the hereditary behavior of hydroxyapatite-based composites used for cranioplastic surgery in the context of material isotropy. We classify mixtures of collagen and hydroxiapatite composites as biomimetic ceramic composites with hereditary properties modeled by fractional-order calculus. We assune isotropy of the biomimetic ceramic is assumed and provide thermodynamic of restrictions for the material parameters. We exploit the proposed formulation of the fractional-order isotropic hereditariness further by means of a novel mechanical hierarchy corresponding exactly to the three-di...

Advanced materials modelling via fractional calculus: challenges and perspectives

“…Other interesting contributions on thermodynamics in fractional-order viscoelasticity may be found in some recent papers [29]. A multiaxial model of fractional-order hereditariness for isotropic materials has been recently provided [30] upon introducing thermodynamic restrictions on the orders of the power laws involved in the mathematical models of transverse and axial creep as well as relaxation functions.…”

Fractional‐order poromechanics for a fully saturated biological tissue: Biomechanics of meniscus

“…10,11 In other studies, a power-law variation of the geometric and physical properties of the porous medium was considered, leading to a fractional-order relationship between incoming flow and pressure applied to the control section. 12 The common base of aforementioned approaches is represented by the linear elastic behavior of the fibrous tissue representing the meniscus. However, it is well-known as reported in relevant scientific literature that the stress in collagen tissue representing meniscus depends on past history of strain and not only on the actual value of the strain.…”

Mathematical modelling with experimental validation of viscoelastic properties in non-Newtonian fluids

“…The great potential of fractional-order impedance models (FOIMs) for capturing natural properties of materials in a variety of disciplines has been long recognized and established experimentally [10][11][12][13]. Applications in medicine and biology are most prevalent as these dynamical systems feature core properties such as multi-scale dynamics, diffusion, viscoelasticity and relaxation [8,[14][15][16]. The same properties are often used to model dynamics in the areas of geology, manufacturing, food industry and chemical products.…”