The paper deals with several descriptions of the yield criteria, within the constitutive framework of anisotropic finite multiplicative elasto-plasticity. We put into evidence appropriate yield criteria, denned either in stress or strain spaces and we analyse the Eulerian setting attached to Sigma-models, first described in relaxed configuration, when Sigma represents the Mandel's stress measure or the quasistatic Eshelby stress tensor. We compare our anisotropic model with the elasto-plastic model, usually adopted in computational finite plasticity.
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