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A Coupled Experiment-finite Element Modeling Methodology for Assessing High Strain Rate Mechanical Response of Soft Biomaterials
Published on: May 18, 2015
Equivalence between short-time biphasic and incompressible elastic material responses
Gerard A Ateshian1, Benjamin J Ellis, Jeffrey A Weiss
1Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA.
Journal of Biomechanical Engineering
|June 1, 2007
Summary
This study reveals that short-term biphasic tissue responses are equivalent to incompressible elastic responses. This finding allows using simpler incompressible elastic models for analyzing porous-permeable tissues in biomechanics.
Area of Science:
- Biomechanics
- Biomaterials Science
- Computational Mechanics
Background:
- Porous-permeable tissues are frequently modeled using porous media theories, notably biphasic theory.
- Understanding the mechanical behavior of these tissues is crucial in various biomedical applications.
Purpose of the Study:
- To investigate the theoretical equivalence between short-time biphasic and incompressible elastic responses.
- To establish conditions under which simpler incompressible elastic models can substitute for complex biphasic models.
Main Methods:
- Derivation of the equivalence from first principles for arbitrary deformations and constitutive relations.
- Application of the equivalence to specific biomechanical problems: unconfined compression of a disk and articular contact.
- Utilizing two distinct constitutive relations for the solid matrix, including one accounting for anisotropic moduli.
Main Results:
- Demonstrated equivalence between short-time biphasic and incompressible elastic responses under general conditions.
- Validated the equivalence through simulations of disk compression and articular contact.
- Identified the time scale for this equivalence: short-term response deltat<
Conclusions:
- The short-time response of biphasic porous-permeable tissues can be accurately represented by incompressible elastic models.
- This equivalence provides a practical justification for employing existing finite element codes for incompressible elasticity in place of biphasic analyses for short-term phenomena.
- Caution is advised regarding specific finite element formulations, particularly those using uncoupled strain energy functions.
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