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ABSTRACT:The development of a new strain energy function for hyperelastic solids based on the logarithmic strain measure is the objective of the present article. For all possible types of deformation it was shown that the proposed energy function is based on three independent material parameters. Using available experimental data for rubber-like materials from the literature, one may determined the materials parameters by a nonlinear fitting. The available domain of the strain energy function can be determined by plotting the third invariant of logarithmic strain vs the second one. The numerical integration of the experimental data of true stress as a function of the logarithmic strain for various types of deformation yields the strain energy function W, for rubber-like solids. The proposed model involves only one parameter that must be determined by fitting with the experimental data.

An atomistic structural mechanics method, which is based on the exclusive use of spring elements, is developed in order to study the radial elastic stiffness and vibrational characteristics of C 20 , C 60 , C 80 , C 180 , C 260 , C 320 , C 500 and C 720 molecules. According to the obtained results, the radial Young's modulus decreases non-linearly with respect to the radius of fullerene or equivalently with the number of carbon atoms. Similarly, the natural frequencies of the fullerenes are strongly dependent on their radius and their support conditions. The numerical results are compared with corresponding data given in the open literature, where possible.