two aforementioned issues, the first may be remedied by making use of alternative formulations as discussed in [@Pham2011]. On the other hand, the dependency of mechanical response on $\ell$ is not yet fully understood. It has been suggested recently [e.g. @Bourdin2014] that the latter should be viewed as a material parameter that is closely connected to the crack nucleation stress. While we consider the two points raised above as distinct issues, we nonetheless recognize that they are also closely inter-related, in particular because the first often exacerbates the second.

Our contribution in the following work is twofold. First, we provide a conceptual explanation of how the choice of length scale can result to either delay or acceleration of failure under quasi-static conditions. Secondly, we introduce a new family of degradation functions that allows for correctly reproducing the onset of failure for reasonably chosen arbitrary values of the regularization parameter. The latter point is important since the problem of regularization-dependent material response is not solved in the alternative formulations previously mentioned, and furthermore is not only confined to brittle fracture as demonstrated in the numerical results of [@Areias2016] on cracking in elastoplastic materials. Enthusiasm in the relatively new phase-field paradigm has 