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On the polynomial invariants of the elasticity tensor

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Abstract

We consider the old problem of finding a basis of polynomial invariants of the fourth rank tensorC of elastic moduli of an anisotropic material. DecomposingC into its irreducible components we reduce this problem to finding joint invariants of a triplet (a, b, D), wherea andb are traceless symmetric second rank tensors, andD is completely symmetric and traceless fourth rank tensor (D ∈ T 4 ss).We obtain by reinterpreting the results of classical invariant theory a polynomial basis of invariants forD which consists of 9 invariants of degrees 2 to 10 in components ofD. Finally we use this result together with a well-known descriptin of joint invariants of a number of second-rank symmetric tensors to obtain joint invariants of the triplet (a, b, D) for ageneric D.

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Authors and Affiliations

  1. Institute de Mécanique de Grenoble, France

    J. P. Boehler

  2. Yale University, 06520, New Haven, CT, USA

    A. A. Kirillov Jr. & E. T. Onat

Authors
  1. J. P. Boehler
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  2. A. A. Kirillov Jr.
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  3. E. T. Onat
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Boehler, J.P., Kirillov, A.A. & Onat, E.T. On the polynomial invariants of the elasticity tensor. J Elasticity 34, 97–110 (1994). https://doi.org/10.1007/BF00041187

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  • DOI: https://doi.org/10.1007/BF00041187

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