Modelling of biomaterials as an application of the theory of mixtures

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00367710" target="_blank" >RIV/68407700:21340/21:00367710 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-030-88084-2_4" target="_blank" >https://doi.org/10.1007/978-3-030-88084-2_4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-88084-2_4" target="_blank" >10.1007/978-3-030-88084-2_4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Modelling of biomaterials as an application of the theory of mixtures

Popis výsledku v původním jazyce

An overview of the mixture theory is provided while building upon similarities with the classical single continuum theory. The mixture theory can be formulated on different levels of description, in terms of different state variables. The second law of thermodynamics is used as a fundamental constraint for obtaining the constitutive relations, the closures. For this purpose, one can either use a definition of entropy (Gibbs’ relation) or a definition of temperature, which is used to identify the entropy production. We discuss the significance and role of coupling in a model formulation and illustrate it using examples stemming from biology. The theory is applied to the formulation of a biphasic model of cartilage. The superiority of mixture theory over the single continuum framework is evident, but there is a trade-off in terms of more parameters that need to be estimated and the number of boundary conditions. In the latter, the difficulties are inherent to the theory and remain an open problem. They are not derivable and require further modelling, although there are situations where boundary conditions can be assessed. Upscaling methods might provide answers in certain situations as well as a new idea within GENERIC framework.

Název v anglickém jazyce

Modelling of biomaterials as an application of the theory of mixtures

Popis výsledku anglicky

An overview of the mixture theory is provided while building upon similarities with the classical single continuum theory. The mixture theory can be formulated on different levels of description, in terms of different state variables. The second law of thermodynamics is used as a fundamental constraint for obtaining the constitutive relations, the closures. For this purpose, one can either use a definition of entropy (Gibbs’ relation) or a definition of temperature, which is used to identify the entropy production. We discuss the significance and role of coupling in a model formulation and illustrate it using examples stemming from biology. The theory is applied to the formulation of a biphasic model of cartilage. The superiority of mixture theory over the single continuum framework is evident, but there is a trade-off in terms of more parameters that need to be estimated and the number of boundary conditions. In the latter, the difficulties are inherent to the theory and remain an open problem. They are not derivable and require further modelling, although there are situations where boundary conditions can be assessed. Upscaling methods might provide answers in certain situations as well as a new idea within GENERIC framework.

Druh

C - Kapitola v odborné knize

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA20-22092S" target="_blank" >GA20-22092S: Víceškálová termodynamika: okrajové podmínky, integrace a aplikace</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Modeling Biomaterials

ISBN

978-3-030-88083-5

Počet stran výsledku

35

Strana od-do

105-139

Počet stran knihy

276

Název nakladatele

Birkhäuser Verlag

Místo vydání

Basel

Kód UT WoS kapitoly

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