A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues I: A General Formulation
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Description
In this paper a theoretical framework for the study of residual stresses in growing tissues is presented using the theory of mixtures. Such a formulation must necessarily be a solid-multiphase model, comprising at least one phase with solid characteristics, owing to the fundamental role played by the incompatibility of strains in generating residual stresses. Since biological growth involves mass exchange between cellular and extracellular phases, field equations are presented for individual phases and for the mixture as a whole which incorporate this phenomenon. Appropriate constitutive equations are then deduced from first principles, appealing to the second law of thermodynamics. The analysis shows that the distinguishing feature of multiphase models involving mass exchange is the necessity to propose an additional constitutive postulate between the variables in the mass-balance equation in order to close the model. In particular, the defining characteristic of a solid-multiphase model which describes biological growth is a constitutive postulate which relates the process of interphase mass exchange (cell proliferation/cell death) with the expansion or contraction of the solid phase. Thus, the framework presented here represents a new class of mathematical models which extends the concepts of poroelasticity to accommodate continuous volumetric growth. A set of modelling equations is then proposed for the simplest case of a solid-multiphase model, being a biphasic mixture of a linear-elastic solid and an inviscid fluid.
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ID Code: | 10258 | ||||
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Item Type: | Contribution to Journal (Journal Article) | ||||
Refereed: | Yes | ||||
ORCID iD: |
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Measurements or Duration: | 24 pages | ||||
Keywords: | Constitutive Equations, Continuum Mechanics, Mixture Theory, Porous Media, Residual Stresses, Tissue Growth | ||||
DOI: | 10.1137/040607113 | ||||
ISSN: | 0036-1399 | ||||
Pure ID: | 34286855 | ||||
Divisions: | Past > QUT Faculties & Divisions > Faculty of Science and Technology Past > QUT Faculties & Divisions > Science & Engineering Faculty Current > Research Centres > Australian Research Centre for Aerospace Automation |
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Copyright Owner: | Consult author(s) regarding copyright matters | ||||
Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au | ||||
Deposited On: | 19 Oct 2007 00:00 | ||||
Last Modified: | 29 Apr 2024 12:41 |
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