A Novel Equation of Motion to Predict Elastoplastic Deformation of 1-D Stochastic Bars

Abstract

AbstractBased on stochasticity in local and nonlocal deformation-gamuts, a stochastic nonlocal equation of motion to model elastoplastic deformation of 1-D bars made of stochastic materials is proposed in this study. Stochasticity in the energy-densities as well as energy-states across the spatial domain of given material and stochasticity in the deformation-gamuts parameters are considered, and their physical interpretations are discussed. Numerical simulations of the specimens of two distinct materials, subjected to monotonic as well as cyclic loadings, are carried out. Specimens are discretized using stochastic as well as uniform grids. Thirty realizations of each stochastic process are considered. The mean values of the results from all realizations are found to be in good agreement with deterministic values, theoretical estimations and experimental results published in open literature.