Tensorial Polar Decomposition of 2D fourth order tensors

Abstract : One studies the structure of 2D symmetric fourth order tensors, i.e. having both minor and major indicial symmetries. Verchery polar decomposition is rewritten in a tensorial form entitled Tensorial Polar Decomposition. Main result is that any 2D symmetric fourth order tensor can be written in terms of second order tensors only in a decomposition that makes explicitly appear invariants and symmetry classes. The link with harmonic decomposition is made thanks to Kelvin decomposition of its harmonic term.
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Boris Desmorat, Rodrigue Desmorat. Tensorial Polar Decomposition of 2D fourth order tensors . Comptes Rendus Mécanique, Elsevier Masson, 2015, 343 (9), pp.471-475. ⟨10.1016/j.crme.2015.07.002⟩. ⟨hal-01455305⟩

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