  Fatigue simulation requires accurate modeling of unloading and reloading.
However, classical ductile damage models treat deformations after complete
failure as irrecoverable -- which leads to unphysical behavior during
unloading. This unphysical behavior stems from the continued accumulation of
plastic strains after failure, resulting in an incorrect stress state at crack
closure. As a remedy, we introduce a discontinuity strain in the additive
elasto-plastic strain decomposition, which absorbs the excess strain after
failure. This allows representing pre- and post-cracking regimes in a fully
continuous setting, wherein the transition from the elasto-plastic response to
cracking can be triggered at any arbitrary stage in a completely smooth manner.
Moreover, the presented methodology does not exhibit the spurious energy
release observed in hybrid approaches. In addition, our approach guarantees
mesh-independent results by relying on a characteristic length scale -- based
on the discretization's resolution. We name this new methodology the
discontinuous strain method. The proposed approach requires only minor
modifications of conventional plastic-damage routines. To convey the method in
a didactic manner, the algorithmic modifications are first discussed for one-
and subsequently for two-/three-dimensional implementations. Using a simple
ductile constitutive model, the discontinuous strain method is validated
against established two-dimensional benchmarks. The method is, however,
independent of the employed constitutive model. Elastic, plastic, and damage
models may thus be chosen arbitrarily. Furthermore, computational efforts
associated with the method are minimal, rendering it advantageous for
accurately representing low-cycle fatigue but potentially also for other
scenarios requiring a discontinuity representation within a plastic-damage
framework.
