Mathematical models and analysis of deformation processes in biomaterials with fractal structure

Yaroslav Sokolovskyy, Maryana Levkovych, Olha Mokrytska, Svitlana Yatsyshyn, Yaroslav Kaspryshyn, Christine Strauss

Veröffentlichungen: Beitrag zu KonferenzPaperPeer Reviewed

Abstract

Mathematical models of heat and mass transfer and deformation processes of biomaterials are investigated, taking into account such properties as memory-effect (eriditarity), self-organization, deterministic chaos, heterogeneity of structure, variability of rheological properties. The obtained results of numerical modelling of non-isothermal moisture transfer and deformation of biomaterials taking into account fractal structure make it possible to estimate – based on the type of material and its thermo-mechanical characteristics – the residual deformation of the material. A mathematical rheological model of two-dimensional visco-elastic deformation of biomaterials with regard to memory-effect and self-organization is constructed, which is described using equilibrium equations with fractional order. The relation between the two-dimensional stress-deformation state of biomaterials for the rheological models of Maxwell, Kelvin and Voigt, which are presented in the integral form, was obtained. The aspects of the algorithm of numerical implementation of two-dimensional mathematical model of visco-elastic deformation in fractured media are presented. The method of splitting fractional-differential parameters of models was adapted, which was used in the problems of identification of non-integer parameters of models. The results of the identification and numerical implementation of the mathematical model of heat and mass transfer processes of biophysical materials are considered, taking into account the fractal structure.

OriginalspracheEnglisch
Seiten133-144
Seitenumfang12
PublikationsstatusVeröffentlicht - 1 Jan. 2019
Veranstaltung2nd International Workshop on Informatics and Data-Driven Medicine, IDDM 2019 - Lviv, Ukraine
Dauer: 11 Nov. 201913 Nov. 2019

Konferenz

Konferenz2nd International Workshop on Informatics and Data-Driven Medicine, IDDM 2019
Land/GebietUkraine
OrtLviv
Zeitraum11/11/1913/11/19

ÖFOS 2012

  • 102020 Medizinische Informatik
  • 305905 Medizinische Informatik
  • 101028 Mathematische Modellierung

Zitationsweisen