A closer look at the phase-field localization process, however, reveals that Eq.(28) may not be the best extension of Eq. (2). Based on the observed behavior of the 1D case in Sargado²⁵, a strict imposition of Eq.(27) may lead to an overestimate of the crack length. Consequently, one can use a modified version of Eq.(29) in which irreversibility is imposed only when\(\ \varphi\) exceeds a certain threshold, i.e.