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Published on: November 20, 2014
Anisotropic hydraulic permeability under finite deformation
Gerard A Ateshian1, Jeffrey A Weiss
1Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA.
Journal of Biomechanical Engineering
|November 2, 2010
Summary
This study introduces a new framework for modeling anisotropic transport in biological tissues undergoing large deformations. It provides a general approach to describe how tissue structure and strain influence permeability and diffusivity.
Area of Science:
- Biomechanics
- Continuum Mechanics
- Materials Science
Background:
- Biological tissues exhibit anisotropic transport properties due to their structure.
- Large deformations in tissues can further induce or modify anisotropy.
- Existing frameworks lack a general approach for constitutive relations of anisotropic transport under finite deformations.
Purpose of the Study:
- To develop a general framework for constitutive relations of anisotropic transport properties under finite deformations.
- To provide conditions for ensuring positive semidefiniteness of permeability or diffusivity tensors.
- To illustrate strain-induced anisotropy in porous-deformable media.
Main Methods:
- Utilizing representation theorems for symmetric tensor-valued functions.
- Formulating constitutive relations for orthotropic, transversely isotropic, and isotropic materials.
- Applying the framework to analyze finite torsion of a cylinder with axial permeation.
Main Results:
- Demonstrated that large strains can induce greater anisotropy in transport properties.
- Showcased how torsion can lead to helical flow patterns in solid-fluid mixtures.
- The general formulation allows for both affine and nonaffine reorientation of material symmetry directions with strain.
Conclusions:
- This study addresses a critical gap in biomechanics literature concerning anisotropic transport under large deformations.
- The proposed framework offers guidelines and formulations for modeling strain-dependent anisotropic transport in porous media.
- The findings are crucial for understanding and predicting transport phenomena in deformable biological tissues.
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