Stochastic Elasto-Plastic Analysis of Necking Bar with Random Tvergaard Coefficients

Abstract

This paper reports on the computational modelling of static extension tests of the round steel bar. The main objective was to apply the generalised stochastic perturbation technique implemented as the Stochastic Finite Element Method to carry out the numerical simulation of its elasto-plastic behaviour. This approach was based on: the general order Taylor expansion of all input random variables and the resulting state functions of their average means, as well as on the Least Squares Method employed to determine analytical functions of in-between design parameters and the given structural responses. Tvergaard coefficients were assumed as the uncorrelated Gaussian random variables to check the effect of material porosity uncertainty on the statistical scattering of its deformations and stresses. The computational implementation employed the FEM system ABAQUS and computer algebra system MAPLE, including polynomial and non-polynomial local response functions of the displacements, plastic strains and reduced stresses. Moreover, 4-node axisymmetric, continuum, reduced-integration FEM elements (CAX4R) were used in the conducted analyses. The basic probabilistic characteristics of the structural response (expectations, coefficients of variation, skewness and kurtosis) were determined throughout the entire deformation process as the functions of input uncertainty level. The obtained results were finally contrasted with the classical Monte-Carlo Simulation scheme and the semi-analytical technique for input coefficient of variation of porous plasticity coefficients not larger than 0.20.