Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T06:28:46.304Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized shear deformations for isotropic incompressible hyperelastic materials

Published online by Cambridge University Press:  17 February 2009

James M. Hill
James M. Hill
Affiliation:
Department of Mathematics, University of Wollongong, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For isotropic incompressible hyperelastic materials the single function characterizing generalized shear deformations or as they are sometimes called anti-plane strain deformations must satisfy two distinct partial differential equations. Knowles [5] has recently given a necessary and sufficient condition for the strain–energy function of the material which if satisfied ensures that the two equations have consistent solutions. It is shown here for the general material not satisfying Knowles' criterion that the only possible consistent solution of the two partial differential equations are those which are already known to exist for all strain–energy functions. More general types of generalized shear deformations for such meterials are shown to exist only for special or restricted form ot the strain-energy function. In derving these results we also obtain an alternative derivation of Knowles' criterion.

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 2 , December 1977 , pp. 129 - 141
Copyright
Copyright © Australian Mathematical Society 1977

References

REFERENCES

[1]Alexander, H., “A constitutive relation for rubber-like materials”, Int. J. Engng. Sci. 6 (1968), 549–563Google Scholar
[2]Gent, A. N. and Thomas, A. G., “Forms for the stored (strain) energy functions for vulcanized rubber”, J. of Polym. Sci. 28 (1958), 625–628.CrossRefGoogle Scholar
[3]Hart-Smith, L. J., “Elasticity parameters for finite deformations of rubber-like materials”, Z. angew. Math. Phys. 17 (1966), 608–626.CrossRefGoogle Scholar
[4]Hill, J. M., “Partial solutions of finite elasticity—Three dimensional deformations”, Z. angew. Math. Phys. 24 (1973), 609–618.CrossRefGoogle Scholar
[5]Knowles, J. K., “Anti-plane strain deformations for isotropic incompressible hyperelastic materials”, J. Austral. Math. Soc. 19 (Series B), (1977), 400–415.Google Scholar