Stochastic Finite Element Method Elasto-Plastic Analysis of the Necking Bar With Material Microdefects

Abstract

The main aim of this work is to study a significance of structural microdefects and their uncertainty in structural steel on its elastoplastic large deformations subjected to tensile test with the use of the generalized stochastic perturbation method. Elastoplastic behavior of the macroscopically homogeneous material is defined by the Gurson–Tvergaard–Needleman (GTN) constitutive model, where Young's modulus and this model constants q1 and q2 are consecutively randomized according to the Gauss probability distribution. The stochastic finite element method (SFEM) analysis has been carried out in the system abaqus for the problem of necking under tension to compute the first four probabilistic moments and coefficients of displacements, deformations, and stresses. The tenth-order perturbation scheme has been implemented via statistically optimized least-squares method (LSM) determination of the structural nodal polynomial response functions. A comparison with Monte Carlo simulation (MCS) as well as the semi-analytical integral technique based on the same polynomial bases confirms applicability of the method proposed for the input uncertainty not larger than 0.10. Further numerical experiments with this constitutive law including stochastic nucleation and/or coalescence would be necessary to better understand deformations and stresses of stochastic porous plastic materials. This model may find its applications in various stress states of the plastic materials with voids as well as in numerical simulations of the composite materials with imperfect interphases, for instance, where some parameters exhibit initial Gaussian statistical scattering.