On probabilistic yielding of materials

Uncertainty in material properties can have large effect on numerical modeling of solids and structures. This is particularly true as all natural and man-made materials exhibit spatial non-uniformity and point-wise uncertainty in their behaviors. A methodology that accounts for the probabilistic yielding of elastic-plastic materials is presented. The recently developed Eulerian-Lagrangian form of the Fokker-Planck-Kolmogorov equation is used to obtain a second-order exact solution to elastic-plastic constitutive differential equations. In this paper that solution is used in deriving the weighted probabilities of elastic, elastic-plastic behavior and yielding. A number of examples for two commonly used material models, von Mises and Drucker-Prager, illustrated the findings.