Modelling of biomaterials as an application of the theory of mixtures
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Modelling of biomaterials as an application of the theory of mixtures
Original language description
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.
Czech name
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Czech description
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Classification
Type
C - Chapter in a specialist book
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA20-22092S" target="_blank" >GA20-22092S: Multiscale thermodynamics: boundary conditions, integration and applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Book/collection name
Modeling Biomaterials
ISBN
978-3-030-88083-5
Number of pages of the result
35
Pages from-to
105-139
Number of pages of the book
276
Publisher name
Birkhäuser Verlag
Place of publication
Basel
UT code for WoS chapter
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