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Constitutive Models for Compressible Nonlinearly Elastic Materials with Limiting Chain Extensibility

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Abstract

Constitutive models are proposed for compressible isotropic hyperelastic materials that reflect limiting chain extensibility. These are generalizations of the model proposed by Gent for incompressible materials. The goal is to understand the effects of limiting chain extensibility when the compressibility of polymeric materials is taken into account. The basic homogeneous deformation of simple tension is considered and simple closed-form relations for the deformation characteristics are obtained for slightly compressible materials. An explicit first-order approximation is obtained for the lateral contraction and for the Poisson function in terms of the axial extension which is shown to be valid for each of two specific compressible versions of the Gent model. One of the main results obtained is that the effect of limiting chain extensibility is to stiffen the material relative to the neo-Hookean compressible case.

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Authors and Affiliations

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

    Cornelius O. Horgan

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

    Giuseppe Saccomandi

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  1. Cornelius O. Horgan
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  2. Giuseppe Saccomandi
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Correspondence to Cornelius O. Horgan.

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Mathematics Subject Classifications (2000)

74B20, 74G55.

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Horgan, C.O., Saccomandi, G. Constitutive Models for Compressible Nonlinearly Elastic Materials with Limiting Chain Extensibility. J Elasticity 77, 123–138 (2004). https://doi.org/10.1007/s10659-005-4408-x

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  • DOI: https://doi.org/10.1007/s10659-005-4408-x

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