Stress or strain?

This article is intended to reconcile the stress-based and strain-based formulations for material failure criteria, where a long-standing and deep division is present. The two approaches do not naturally agree with each other, and they do not genuinely complement each other, either. Most popular criteria are stress-based when originally proposed, including the maximum stress, Tresca, von Mises, Raghava–Caddell–Yeh and the Mohr criteria. Their formulations are unique and self-consistent, i.e. capable of reproducing the input data. Their strain-based counterparts, with the maximum strain criterion being considered as the strain-based counterpart of the maximum stress criterion, are neither unique nor necessarily self-consistent. It has been proven in this article that the self-consistent ones reproduce their respective stress-based counterparts identically in effect with a disadvantage of requiring an additional material property to apply, without a single benefit. For the Mohr criterion as a special case, a strain-based counterpart is simply infeasible in general. All undesirable features of strain-based criteria are rooted in a single source: the failure strains can only be measured under a uniaxial stress state, which corresponds to a combined strain state in general, not a uniaxial strain state! Given the arguments presented, the reconciliation proves to be biased completely towards the stress-based side if mathematics, logic and common sense prevail over perception and prejudice.