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<p>It is well-known that analytic solutions for problems in nonlinear elasticity for incompressible isotropic hyperelastic materials can be obtained either by using constitutive models in terms of classical invariants of the right Cauchy-Green tensor or alternatively by using the principal stretches directly. In this paper, we describe an efficient procedure for transforming strain-energy densities expressed in terms of the principal stretches into their counterparts in terms of the invariants. To illustrate the results, applications to the problems of simple shear and pure torsion are described. It is demonstrated that the stretch formulation has some advantages in the former case while the principal invariant approach seems preferable for the torsion problem.</p>

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Some Remarks on the Principal Stretch Versus Invariant Formulation for Constitutive Modeling of Incompressible Isotropic Hyperelastic Materials

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  • 出版模式：

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  • 发表日期：

    2025年6月4日

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  • C. O. Horgan,
  • J. G. Murphy

摘要

It is well-known that analytic solutions for problems in nonlinear elasticity for incompressible isotropic hyperelastic materials can be obtained either by using constitutive models in terms of classical invariants of the right Cauchy-Green tensor or alternatively by using the principal stretches directly. In this paper, we describe an efficient procedure for transforming strain-energy densities expressed in terms of the principal stretches into their counterparts in terms of the invariants. To illustrate the results, applications to the problems of simple shear and pure torsion are described. It is demonstrated that the stretch formulation has some advantages in the former case while the principal invariant approach seems preferable for the torsion problem.