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has been cited by the following article:

• TITLE: Continuum Constitutive Modeling for Isotropic Hyperelastic Materials

  AUTHORS: Fuzhang Zhao

  KEYWORDS: Continuum Constitutive Modeling, Hyperelastic Material, Ellipsoidal Deformation, Stretch, Stored Energy Function, Stress Work Done

  JOURNAL NAME: Advances in Pure Mathematics, Vol.6 No.9, August 2, 2016

  ABSTRACT: The partial differential equation for isotropic hyperelastic constitutive models has been postulated and derived from the balance between stored energy and stress work done. The partial differential equation as a function of three invariants has then been solved by Lie group methods. With geometric meanings of deformations, the general solution boils down to a particular three-term solution. The particular solution has been applied for several isotropic hyperelastic materials. For incompressible materials, vulcanized rubber containing 8% sulfur and Entec Enflex S4035A thermoplastic elastomer, three coefficients have been determined from uniaxial tension data and applied to predict the pure shear and equibiaxial tension modes. For a slightly compressible rubber material, the coefficients have also been extracted from the confined volumetric test data.