“…For example, in [25], the combination use of (2) and the cohesive envelope of the exponential form are performed to simulate fatigue crack growth; however, this combination results in the contradictory damage evolution at δ n > δ 0 if a slightly larger value of σ f /σ max,0 is provided, and this problem can be solved by using (1). As mentioned above, the similar CCZM has been proposed to investigate the mixed mode fatigue crack growth in our previous simulations [29], the difference between these two models is that the current one does not introduce the monotonic damage, the material degradation under cyclic loadings is described uniformly by (2), and the monotonic damage is determined by the cohesive envelope implicitly. Actually, the combination of (1) and (2) has the capacity to simulate fatigue crack growth at the high ΔK levels, the applications need not be distinguished between monotonic damage and fatigue damage as introduced in [29], the key point in such simulations is the form of (1), and more details will be performed in Section 3.…”