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Mathematics and Mechanics of Solids
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Helical Shear for Hardening Generalized Neo-Hookean Elastic Materials

Cornelius O. Horgan

Structural and Solid Mechanics Program, Department of Civil Engineering, University of Virginia, Charlottesville, VA 22904, USA

Giuseppe Saccomandi

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

The purpose of this research is to investigate the helical shear problem for a circular cylindrical tube composed of an isotropic hyperelastic incompressible material. Three specific constitutive models that account for hardening at large deformations are examined. These involve a strain-energy density which depends only on the first invariant of the Cauchy-Green tensor. For limiting values of a material parameter, all of these models reduce to the classical neo-Hookean form. The stress fields and displacements are characterized for each of these models. For two of the models considered, explicit closed-form analytic expressions are obtained. The results are compared with one another and with the predictions of the neo-Hookean model.

Key Words: helical shear • incompressible hyperelastic materials • strain hardening phenomena

Mathematics and Mechanics of Solids, Vol. 8, No. 5, 539-559 (2003)
DOI: 10.1177/10812865030085007
Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us   Add to Digg Digg   Add to Reddit Reddit   Add to Technorati Technorati    What's this?