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Here, there is a difference between the material failure criterion and the specific structure failure criterion. In general, the nucleation of material damage is not necessarily a condition for the failure of the structure as a whole (subcritical damage), also the structure can lose its functionality without accompanying material damage (loss of stability, change of shape, etc.). If for a specific structure and for specific conditions it is more convenient for you to use simplified criteria, for example, strain-based one, then it should still be justified quantitatively, including on the basis of generally accepted criteria for the materials fracture.