Biological Growth in Bodies with Incoherent Interfaces

A general theory of thermodynamically consistent biomechanical--biochemical growth in a body, considering mass addition in the bulk and at an incoherent interface, is developed. The incoherency arises due to incompatibility of growth and elastic distortion tensors at the interface. The incoherent in...

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Bibliographic Details
Published in:arXiv.org 2017-10
Main Authors: Swain, Digendranath, Gupta, Anurag
Format: Article
Language:English
Subjects:
Biomechanics
Boundary value problems
Evolution
Incompatibility
Kinematics
Laws
Residual stress
Tensors
Wound healing
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Summary:A general theory of thermodynamically consistent biomechanical--biochemical growth in a body, considering mass addition in the bulk and at an incoherent interface, is developed. The incoherency arises due to incompatibility of growth and elastic distortion tensors at the interface. The incoherent interface therefore acts as an additional source of internal stress besides allowing for rich growth kinematics. All the biochemicals in the model are essentially represented by nutrient concentration fields, in the bulk and at the interface. A nutrient balance law is postulated which, combined with mechanical balances and kinetic laws, yields an initial-boundary-value problem coupling the evolution of bulk and interfacial growth, on one hand, and the evolution of growth and nutrient concentration on the other. The problem is solved, and discussed in detail, for two distinct examples: annual ring formation during tree growth and healing of cutaneous wounds in animals.
ISSN:2331-8422
DOI:10.48550/arxiv.1710.02853