Computer Simulation of Stochastic Energy Fluctuations in Tensile Test of Elasto-Plastic Porous Metallic Material

Abstract

The main aim of this work is the computational implementation and numerical simulation of a metal porous plasticity model with an uncertain initial microdefects’ volume fraction using the Stochastic Finite Element Method (SFEM) based on the semi-analytical probabilistic technique. The metal porous plasticity model applied here is based on Gurson–Tvergaard–Needleman theory and is included in the ABAQUS finite element system, while the external probabilistic procedures were programmed in the computer algebra system MAPLE 2017. Hybrid usage of these two computer systems enabled the determination of fluctuations in elastic and plastic energies due to initial variations in the ratio of the metal micro-voids, and the calculation of the first four probabilistic moments and coefficients of these energies due to Gaussian distribution of this ratio. A comparison with the Monte-Carlo simulation validated the numerical efficiency of the proposed approach for any level of input uncertainty and for the first four probabilistic characteristics traditionally seen in the experimental series.