Probabilistic elasto-plasticity: solution and verification in 1D

In this paper, a solution is presented for evolution of probability density function (PDF) of elastic–plastic stress–strain relationship for material models with uncertain parameters. Developments in this paper are based on already derived general formulation presented in the companion paper. The solution presented is then specialized to a specific Drucker–Prager elastic–plastic material model. Three numerical problems are used to illustrate the developed solution. The stress–strain response (1D) is given as a PDF of stress as a function of strain. The presentation of the stress–strain response through the PDF differs significantly from the traditional presentation of such results, which are represented by a single, unique curve in stress–strain space. In addition to that the numerical solutions are verified against closed form solutions where available (elastic). In cases where the closed form solution does not exist (elastic–plastic), Monte Carlo simulations are used for verification.