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.