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Invariant characteristic representations for classical and micropolar anisotropic elasticity tensors

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Abstract

By extending and developing the characteristic notion of the classical linear elasticity initiated by Lord Kelvin, a new type of representation for classical and micropolar anisotropic elasticity tensors is introduced. The new representation provides general expressions for characteristic forms of the two kinds of elasticity tensors under the material symmetry restriction and has many properties of physical and mathematical significance. For all types of material symmetries of interest, such new representations are constructed explicitly in terms of certain invariant constants and unit vectors in directions of material symmetry axes and hence they furnish invariants which can completely characterize the classical and micropolar linear elasticities. The results given are shown to be useful. In the case of classical elasticity, the spectral properties disclosed by our results are consistent with those given by similar established results.

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Authors and Affiliations

  1. Department of Mathematics, Peking University, 100871, Beijing, China

    H. Xiao

  2. Institute of Mathematics, Peking University, 100871, Beijing, China

    H. Xiao

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  1. H. Xiao
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Xiao, H. Invariant characteristic representations for classical and micropolar anisotropic elasticity tensors. J Elasticity 40, 239–265 (1995). https://doi.org/10.1007/BF00043958

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  • DOI: https://doi.org/10.1007/BF00043958

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