Equivalence Between Short-Time Biphasic and Incompressible Elastic Material ResponsesSource: Journal of Biomechanical Engineering:;2007:;volume( 129 ):;issue: 003::page 405DOI: 10.1115/1.2720918Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response δt⪡Δ2∕∥C4∥∥K∥, where Δ is a characteristic dimension, C4 is the elasticity tensor, and K is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components.
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contributor author | Gerard A. Ateshian | |
contributor author | Benjamin J. Ellis | |
contributor author | Jeffrey A. Weiss | |
date accessioned | 2017-05-09T00:22:47Z | |
date available | 2017-05-09T00:22:47Z | |
date copyright | June, 2007 | |
date issued | 2007 | |
identifier issn | 0148-0731 | |
identifier other | JBENDY-26706#405_1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/135260 | |
description abstract | Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response δt⪡Δ2∕∥C4∥∥K∥, where Δ is a characteristic dimension, C4 is the elasticity tensor, and K is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Equivalence Between Short-Time Biphasic and Incompressible Elastic Material Responses | |
type | Journal Paper | |
journal volume | 129 | |
journal issue | 3 | |
journal title | Journal of Biomechanical Engineering | |
identifier doi | 10.1115/1.2720918 | |
journal fristpage | 405 | |
journal lastpage | 412 | |
identifier eissn | 1528-8951 | |
tree | Journal of Biomechanical Engineering:;2007:;volume( 129 ):;issue: 003 | |
contenttype | Fulltext |