Stochastic failure analysis of structures with softening materials

Abstract

This paper investigates the influence of uncertain spatially varying material properties on the fracture behavior of structures with softening materials. Structural failure is modeled using the sequentially linear analysis (SLA) proposed by Rots (2001), which replaces the incremental nonlinear finite element analysis by a series of scaled linear analyses and the nonlinear stress–strain law by a saw-tooth curve. In this paper, SLA is implemented in the framework of a stochastic setting. The proposed approach constitutes an efficient procedure avoiding the convergence problems encountered in regular nonlinear FE analysis. Two benchmark structures are analyzed and comparisons with nonlinear analysis results are provided. The effect of uncertain material properties described by homogeneous stochastic fields (Young’s modulus, tensile strength, fracture energy) on the variability of the load–displacement curves is examined. The response variability is computed by means of direct Monte Carlo simulation. The influence of the variation of each random parameter as well as of the probability distribution, coefficient of variation and correlation length of the stochastic fields is quantified. It is shown that the load–displacement curves and the failure probability of the structures are affected by the statistical characteristics of the stochastic fields.