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The equivalent stress hypotheses allow us to compare an arbitrary stress state witha uni-dimesional one. These hypotheses are empirical, so some plausibilitycriteria are needed. Diversity of such criteria shows that the hypotheses ofstrength are still being developed. However as a whole they can be systemised.Six modelling principles are suggested, leading to a small number of “allpurpose”models. These models contain well-established hypotheses and can beapplied to different material classes.The various forms of the meridian being of practical relevance can be received forthese models. Unlike the known models, here the rotational, triangular orhexagonal symmetry in the deviatoric plane can be obtained independently fromthe compressibility. Meaningful are only the models with trigonal symmetry. Inorder to compute the parameters of the models a simple optimisation routine aswell as certain constraints are proposed.