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The invariant representation of spins with applications in the theory of finite deformations

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Abstract

Based on the general solution given to a kind of linear tensor equations, the spin of a symmetric tensor is derived in an invariant form. The result is applied to find the spins of the left and the right stretch tensors and the relation among different rotation rate tensors has been discussed. According to work conjugacy, the relations between Cauchy stress and the stresses conjugate to Hill's generalized strains are obtained. Particularly, the logarithmic strain, its time rate and the conjugate stress have been discussed in detail. These results are important in modeling the constitutive relations for finite deformations in continuum mechanics.

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Authors and Affiliations

  1. Div. of Physics, Graduate School Univ. of Science and Technology of China, 100039, Beijing

    Wang Wenbiao

  2. Lab. for Non-linear Mechanics of Continuous Media, Institute of Mechanics, 100080, Beijing

    Duan Zhuping

Authors
  1. Wang Wenbiao
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  2. Duan Zhuping
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Additional information

The project is supported by the National Natural Science Foundation of China and the Chinese Academy of Sciences (No. 87-52).

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Wenbiao, W., Zhuping, D. The invariant representation of spins with applications in the theory of finite deformations. Acta Mech Sinica 6, 133–140 (1990). https://doi.org/10.1007/BF02488444

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  • DOI: https://doi.org/10.1007/BF02488444

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