Towards objective simulation of quasi-static failure using a bounded rate local model with damage

Today, the realistic simulation of complex industrial problems requires using industrial codes. For the simulation of failure in quasi-static, and if making use of implicit schemes, the convergence is often problematic. In order to ensure convergence and robustness, explicit algorithms are often used. In this case, mass and time scalings are used to allow for quasi-static simulations. How these techniques affect the failure prediction is nevertheless unclear. Moreover, in the case of damage model another difficulty arises, the one of spurious mesh dependency. In order to avoid this problem, the use of non-local models, as for example gradient ones, is the dominant approach. The implementation of such models in industrial software is cumbersome. A simpler possibility is to rely on bounded rate approaches (Allix in Int J Damage Mech 22:808–828, 2013). In fact, these approaches require only local modifications of the constitutive relation. Nevertheless, they have been much less studied and require dynamic analyses to ensure adapted regularisation effects. Considering these two issues, we study, in this paper, the possibility of combining explicit simulations with bounded rate models with damage. The aim is to enable relevant quasi-static damage simulations to perform up to failure. In this context, one main issue concerns the proposal of adapted scaling techniques. This problem is addressed through examples concerning the simulation of failure and the computation of the burst rotating speed of an axisymmetric disk.