COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Commun. Numer. Meth. Engng 2000; 00:1–6 Prepared using cnmauth.cls [Version: 2002/09/18 v1.02] On Probabilistic Yielding of Materials Boris Jeremi´ c and Kallol Sett Department of Civil and Environmental Engineering, University of California, Davis, CA, 95616, U.S.A. SUMMARY 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 material exhibit spatial non- uniformity and point-wise uncertainty in material behavior. Presented is the methodology that accounts for probabilistic yielding of elastic–plastic materials. The recently developed Eulerian–Lagrangian form of Fokker–Planck–Kolmogorov equation is used to obtain 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 findings. Copyright c 2000 John Wiley & Sons, Ltd. * Correspondence to: Boris Jeremi´ c, Department of Civil and Environmental Engineering, One Shields Ave., University of California, Davis, CA, 95616, U.S.A. jeremic@ucdavis.edu Contract/grant sponsor: NSF; contract/grant number: CMMI-0600766 Copyright c 2000 John Wiley & Sons, Ltd.