This paper aims at enhancing the capability of the smoothing gradient-enhanced damage method in modeling localization failure, especially mixed-mode fracture in quasi-brittle materials, e.g., double edge notch — DEN by Nooru-Mohamed test. As a novelty, we integrate an alternative technique for estimation of the equivalent strain based on Ottosen’s failure criterion, the four-parameter strain equivalent method that characterizes the sensitivity of deformation stages and loading path conditions, into our damage theory to form a new approach for better capturing the mixed-mode fracture behavior. Our approach allows to use the same low-order finite elements for approximation of both displacements and equivalent strain fields without any stress oscillation, highly suitable for practice. The new approach owns several desirable features of an advanced method including mesh insensitivity, and numerical examples in two-dimension indicate the applicability of the developed model in capturing the crack paths observed in experiments. Interpreting principal stresses in the failure envelopes further sheds light on insight into the damage behavior of the developed model.
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