Volumetric Growth of Thermoelastic Materials and Mixtures

Stephen M. Klisch, University of California - San Diego
Anne Hoger, University of California - San Diego

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The final, definitive version of this paper has been published in Mathematics and Mechanics of Solids by SAGE Publications, Ltd. All rights reserved. © Sage Publications. The definitive version is available online at http://dx.doi.org/10.1177/10812865030084003.

NOTE: At the time of publication, the author Stephen Klisch was not yet affiliated with Cal Poly.

Abstract

The proteoglycan and collagen constituents of cartilage serve distinct mechanical roles. Changes to the mechanical loading conditions during cartilage growth lead to changes in the concentrations of these molecules and, consequently, the mechanical properties. The main aim of this paper is to present a theory that can describe the mechanical aspects of cartilage growth. The model for cartilage growth is based on a general thermomechanical theory for a mixture of an arbitrary number of growing elastic constituents and an inviscid fluid. Our development of a growth mixture theory is accomplished in two steps. First, the thermodynamics of growing elastic materials are considered. The resulting theory of growing thermoelastic materials is extended to continuum mixture theory. Using this general growth mixture theory, we then propose a cartilage growth model that includes two special types of internal constraints that are relevant to cartilage.