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In this paper, behavior of functionally graded rubbers with large deformation has been modeled under different loading conditions. Rubbers have been assumed incompressible hyperelastic material. In the first section of this paper, behavior of isotropic FG rubber has been investigated in uniaxial extension, equibiaxial extension and pure shear. In the second section, behavior of isotropic FG rubber is investigated in mechanical and thermal loads, simultaneously. For this purpose, multiplicative decomposition of deformation gradient tensor has been used. At last, behavior of transversely isotropic FG rubber has been investigated in uniaxial extension, equibiaxial extension and pure shear. Material properties vary continuously in different specific direction in FG hyperelastic materials. For modeling nonlinear behavior of hyperelastic materials, strain energy functions are used. Strain energy functions are function of invariants of left Cauchy-Green stretch tensor. Modification in strain energy functions required in order to use them for FG rubbers. For this purpose, material constants of strain energy functions have been assumed to vary exponentially in the axial direction of bar. Moreover, stretches in different points of the bar are considered to be function of material properties variation in the length direction. Analytical solution have been compared with experimental data and good agreement has been found between them, therefore proposed constitutive law has been modeled material behavior with a proper approximation.

Keywords: Hyperelastic material, Finite deformation, Rubber, Functionally Graded Materials, Transversely Isotropic

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