Restoration of the symmetries broken by reversible growth in hyperelastic bodies

In this paper, we interpret the development of material in homogeneities in continuum, hyper elastic bodies in the presence of reversible growth in terms of broken symmetries [1]. By applying Noether's Theorem [1, 2, 3, 4], we find a set of equations yielding the fields necessary to compensate...

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Bibliographic Details
Main Authors: Grillo Alfio, Federico Salvatore, Giaquinta Gaetano, Herzog Walter, La Rosa Guido
Format: Article
Language:English
Published: Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade 2003-01-01
Series:Theoretical and Applied Mechanics
Online Access:http://www.doiserbia.nb.rs/img/doi/1450-5584/2003/1450-55840304311G.pdf
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Summary:In this paper, we interpret the development of material in homogeneities in continuum, hyper elastic bodies in the presence of reversible growth in terms of broken symmetries [1]. By applying Noether's Theorem [1, 2, 3, 4], we find a set of equations yielding the fields necessary to compensate for the broken symmetry. As growth occurs, these fields provide for an instantaneously updated reference configuration of the body, and are responsible for the dynamical restoring of the body symmetries. In addition, we propose to use these compensating fields in order to generalize the definition of the transplant operator given in [5,6]. This work has been motivated by the current theoretical investigations on the biomechanical aspects of growth in particular cartilage.
ISSN:1450-5584