Advanced Search

Journal Navigation

Journal Home

Subscriptions

Archive

Contact Us

Table of Contents

Sign In to gain access to subscriptions and/or personal tools.
Mathematics and Mechanics of Solids
This Article
Right arrow Full Text (PDF)
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to Saved Citations
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow Request Reprints
Right arrow Add to My Marked Citations
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Right arrow Citing Articles via Scopus
Google Scholar
Right arrow Articles by Horgan, C. O.
Right arrow Articles by Saccomandi, G.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Complore   Add to Connotea   Add to Del.icio.us   Add to Digg   Add to Reddit   Add to Technorati   Add to Twitter  
What's this?

Constitutive Modelling of Rubber-Like and Biological Materials with Limiting Chain Extensibility

Cornelius O. Horgan

Applied Mechanics Program, Department of Civil Engineering, University of Virginia, Charlottesville, VA 22904, USA

Giuseppe Saccomandi

Sezione di Ingegneria Industriale, Dipartimento di Ingegneria dell’Innovazione, Università degli Studi di Lecce, Lecce, 73100, Italy

Many rubber-like materials and soft tissues exhibit a significant stiffening or hardening in their stress-strain curves at large strains. The accurate modelling of this phenomenon is a key issue for a better understanding of the thermomechanics of rubber and the biomechanics of arteries, blood vessels, tendons and other biological tissues. In this paper, we consider several strain-energy functions that have been proposed to model this strain hardening effect in the framework of the theory of isotropic hyperelasticity. These models may be divided in two main families: power law models and limiting chain extensibility models, both of which are based on non-Gaussian statistics for their molecular structure. The known limiting chain extensibility models involve a constraint on the strain invariants. Here we consider alternative models which limit the maximum stretch. The two homogeneous deformations of uniaxial extension and pure shear are examined in detail. It is shown that simple modifications of the incompressible neo-Hookean or Varga materials to reflect limiting chain extensibility can be used to match well with the classic experimental data of Treloar. Some remarks on empirical inequalities and ellipticity are also given.

Key Words: nonlinear elasticity • limiting chain extensibility • material hardening • rubber-like materials • biological materials

Mathematics and Mechanics of Solids, Vol. 7, No. 4, 353-371 (2002)
DOI: 10.1177/108128028477
Add to CiteULike CiteULike   Add to Complore Complore   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us   Add to Digg Digg   Add to Reddit Reddit   Add to Technorati Technorati   Add to Twitter Twitter    What's this?


This article has been cited by other articles:


Home page
 Mathematics and Mechanics of SolidsHome page
M. F. Beatty
On Constitutive Models for Limited Elastic, Molecular Based Materials
Mathematics and Mechanics of Solids, July 1, 2008; 13(5): 375 - 387.
[Abstract] [PDF]

Home page
 Mathematics and Mechanics of SolidsHome page
J. G. Murphy
Some Remarks on Kinematic Modeling of Limiting Chain Extensibility
Mathematics and Mechanics of Solids, December 1, 2006; 11(6): 629 - 641.
[Abstract] [PDF]

Home page
 Mathematics and Mechanics of SolidsHome page
C. O. Horgan and G. Saccomandi
Helical Shear for Hardening Generalized Neo-Hookean Elastic Materials
Mathematics and Mechanics of Solids, October 1, 2003; 8(5): 539 - 559.
[Abstract] [PDF]