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A Triphasic Theory for Growth in Biological Tissue – Basics and Applications

✍ Scribed by T. Ricken; A. Schwarz; J. Bluhm

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
413 KB
Volume
37
Category
Article
ISSN
0933-5137

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✦ Synopsis

Abstract

A triphasic model (solid, interstices filled with water containing nutrients) is proposed for the phenomenological description of transversely isotropic saturated biological tissues including the phenomena of growth. This is done within the framework of a macro‐mechanical description based on the Theory of Porous Media (TPM). Thereby, the constitutive equation of growth is determined by the state of stress and the local proportion of nutrients responsible for the mass exchange. The transversely isotropic behavior of the solid influences both the stress response and the internal fluid permeability, which is considered using an invariant formulation of the Helmholtz free energy and transversely isotropic permeability functions. After presenting the developed framework of the calculation concept including the representation of the governing weak formulations of the equations for large deformations, some representative numerical examples are examined.

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