Reactive Constrained Mixtures for Modeling the Solid Matrix of Biological Tissues

This article illustrates our approach for modeling the solid matrix of biological tissues using reactive constrained mixtures. Several examples are presented to highlight the potential benefits of this approach, showing that seemingly disparate fields of mechanics and chemical kinetics are actually...

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Bibliographic Details
Published in:Journal of elasticity 2017-12, Vol.129 (1-2), p.69-105
Main Authors: Nims, Robert J., Ateshian, Gerard A.
Format: Article
Language:English
Subjects:
Automotive Engineering
Chemical bonds
Classical Mechanics
Energy dissipation
Free energy
Modelling
Physics
Physics and Astronomy
Reaction kinetics
Recruitment
Reforming
Tissues
Viscoelasticity
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Summary:This article illustrates our approach for modeling the solid matrix of biological tissues using reactive constrained mixtures. Several examples are presented to highlight the potential benefits of this approach, showing that seemingly disparate fields of mechanics and chemical kinetics are actually closely interrelated and may be elegantly expressed in a unified framework. Thus, constrained mixture models recover classical theories for fibrous materials with bundles oriented in different directions or having different reference configurations, that produce characteristic fiber recruitment patterns under loading. Reactions that exchange mass among various constituents of a mixture may be used to describe tissue growth and remodeling, which may also alter the material’s anisotropy. Similarly, reactions that describe the breaking and reforming of bonds may be used to model free energy dissipation in a viscoelastic material. Therefore, this framework is particularly well suited for modeling biological tissues.
ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-017-9630-9