Failure Formulations in Modular Plasticity Models
Computational prediction of ductile failure remains a challenging and important problem as demonstrated by the recent Sandia Fracture Challenges. In addition to emphasizing the complexity of such problems, the variety of solution strategies also highlighted the number of possible approaches to this problem. A common engineering approach for such efforts is to use a failure model in conjunction with element deletion. In the second Sandia Fracture Challenge, for instance, nine of the fourteen teams used some form of element deletion. For such schemes, a critical decision pertains to the selection of the appropriate failure model; of which many may be found in the literature (see the review of Corona and Reedlunn). The variety may also be observed in the aforementioned second Sandia Fracture Challenge in which at least eight different failure criteria are listed for the nine element deletion based approaches. The selection of the appropriate failure model is a difficult challenge depending on the material being considered and such criteria can variously depend on stress state (i.e. triaxiality, Lode angle) and loading conditions (i.e. strain rate, temperature). Separate implementations of each criteria with different plasticity models can be a repetitive and cumbersome process which may limit available models for an engineering analyst. To mitigate this issue, an effort was pursued to flexibly implement failure models in which different failure models could be specified and utilized within the same elastic-plastic constitutive routine by simply changing the input syntax. Similarly, the same models are implemented across a suite of elastic-plastic formulations enabling consistent definitions. As will be discussed later, a specific "modular failure" model is also implemented which allows for the selection or specification of different dependencies depending on the current need. At this stage, this effort is limited to defining failure models; progression/damage evolution in the constitutive model is not treated and left to future efforts.