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.