On the symmetries of 2D elastic and hyperelastic tensors |
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| Authors: | Q -C He Q -S Zheng |
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| Institution: | (1) Département de Génie Mécanique, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland;(2) Department of Engineering Mechanics, Tsinghua University, 100084 Beijing, People's Republic of China |
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| Abstract: | A thorough investigation is made of the independent point-group symmetries and canonical matrix forms that the 2D elastic and hyperelastic tensors can have. Particular attention is paid to the concepts relevant to the proper definition of the independence of a symmetry from another one. It is shown that the numbers of all independent symmetries for the 2D elastic and hyperelastic tensors are six and four, respectively. In passing, a symmetry result useful for the homogenization theory of 2D linear elastic heterogeneous media is derived. |
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| Keywords: | elasticity hyperelasticity symmetry groups Kronecker isotropy anisotropy classification |
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