Critical (limiting, ultimate) state criteria in solid mechanics and, consequently, so called strength theories, by their physical sense, should be universal laws of nature. But well known strength criteria are separate for diverse materials types, have nothing in common with simple and universal fundamental laws of nature, and possess evident defects. For known criteria applicable to some very special cases only, generalization and correction methods to consider any (ductile or brittle, isotropic or anisotropic) materials under stationary or variable loading are founded. For this, scalar or vectorial reduced relative stresses are introduced that are equal to the reciprocals to sign-preserving individual safety factors. Each of these relative stresses is defined as a usual stress divided by the modulus of its limit (ultimate value) of the same sign by vanishing all the remaining stresses under the same other loading conditions. For the first time, general strength theory is developed and entire hierarchies of universal strength laws of nature are discovered.
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