Von Mises Failure Criterion in Mechanics of Materials: How to Efficiently Use it Under Interval and Fuzzy Uncertainty

One of the main objective of mechanics of materials is to predict when the material experiences fracture (fails), and to prevent this failure. With this objective in mind, it is desirable to use it ductile materials, i.e., materials which can sustain large deformations without failure. Von Mises criterion enables us to predict the failure of such ductile materials. To apply this criterion, we need to know the exact stresses applied at different directions. In practice, we only know these stresses with interval or fuzzy uncertainty. In this paper, we describe how we can apply this criterion under such uncertainty, and how to make this application computationally efficient.