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TECHNICAL BRIEF

A Theoretical Study of the In Vivo Mechanical Properties of Angiosperm Roots: Constitutive Theories and Methods of Parameter Estimation

[+] Author and Article Information
Alexander V. Sadovsky1

Institute for Genomics and Bioinformatics: Donald Bren School of Information and Computer Sciences, University of California, Irvine, CA 92697; California Institute for Telecommunications and Information Technology, University of California, Irvine, CA 92697sadovsky@math.uci.edu

Pierre F. Baldi

Institute for Genomics and Bioinformatics: Donald Bren School of Information and Computer Sciences, University of California, Irvine, CA 92697; California Institute for Telecommunications and Information Technology, University of California, Irvine, CA 92697pfbaldi@ics.uci.edu

Frederic Y.-M. Wan

Department of Mathematics, School of Physical Sciences, University of California, 267 Multipurpose Science & Technology Building, Irvine, CA; Department of Mechanical and Aerospace Engineering, School of Physical Sciences, University of California, Irvine, CA 92697fwan@math.uci.edu

1

Corresponding author.

J. Eng. Mater. Technol 129(3), 483-487 (Mar 20, 2007) (5 pages) doi:10.1115/1.2744435 History: Received September 21, 2006; Revised March 20, 2007

To investigate the constitutive relation of a plant tissue regarded as a deformable continuum, stress and strain must be determined experimentally for the same configurations. Such experiments are hindered by the inherent theoretical complexity of continuum mechanics, and by the technical difficulties of effecting external stress loads or body forces on the tissue without invasion, especially on a small scale. An understanding of appropriate mechanical problems and their solutions can help the experimentalist overcome these difficulties to a certain extent. Based on recent work on fiber-reinforced material, we formulate a constitutive theory for the root of different angiosperm species and suggest a set of loading conditions to determine the parameter values in a specific tissue sample. The loading conditions are formulated with a view toward experimental realization in vivo or with minimal invasion. For each loading condition, we formulate the corresponding mechanical problem and show how to obtain the values of the elastic parameters from known solutions. This framework can be used to analyze the interplay between mechanical and metabolic behavior in plants and to study the elastodynamics of plant tissues.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Possible fiber orientations in an outer epidermal wall of a cylindrical root: (A) circumferential and (B) longitudinal

Grahic Jump Location
Figure 2

A portion of the cylinder ΩL near the cross section z=0 under different loading conditions. (A) Loading condition 1. Constriction of the cylinder ΩL by a shrinking band, shown in longitudinal section: The normal stress load T∙r̂∣r=a equals −S0r̂ at r=a,∣z∣<h, and equals zero on the remaining portion of the lateral surface. (B) Loading condition 2. The lateral surface of the cylinder is subjected to the external stress loads ±S0ẑ applied, respectively, at the lines r=a,θ=±π∕2.

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