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Various stress return algorithms in elastoplastic analyses using the finite element method require the evaluation of the contact (or penetration) stress state (Figure 1), defining the transition from elastic to elastoplastic behaviour. Various iterative schemes are commonly used to evaluate contact stress state with a great degree of precision, as subsequent analysis process (forward Euler, mid‐point rule stress return scheme) is greatly affected by the evaluation of the contact stress state, as has been stressed by several authors.

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