A second order constitutive theory for hyperelastic materials |
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| Affiliation: | 1. Division of Mechanical Engineering, Department of Applied Mechanics and Engineering Science, University of California, San Diego, La Jolla, California 92093, USA;1. Centre for Theoretical Studies, Indian Institute of Technology Kharagpur, 721302, India;2. Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, 721302, India;1. Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, 730000, China;2. University of Chinese Academy of Sciences, Beijing, 100049, China;3. Key Laboratory of Nuclear Data, China Institute of Atomic Energy, Beijing, 102413, China;4. College of Physics and Electronic Information, Inner Mongolia University for the Nationalities, Tongliao, 028000, China |
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| Abstract: | The second order constitutive equation for a hyperelastic material with arbitrary symmetry is derived. In developing a second order theory, it is necessary to be discriminating in the choice of measures of deformation. Here the derivation is done in terms of the Biot strain, which has a direct physical interpretation in that its eigenvalues are the principal extensions of the deformation. The constitutive equation is specialized for the cases of isotropy and transverse isotropy. The isotropic equation derived here is compared with equations obtained by other authors in terms of the displacement gradient and the Green strain. |
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