Modeling the Failure of Structures With Stochastic Properties in a Sequentially Linear Analysis Framework

Abstract

Abstract. This paper investigates the influence of uncertain spatially varying material properties on the fracture behavior of structures made of softening materials. To model the structural failure, the sequentially linear solution procedure proposed by Rots (2001) is used, 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. The effect of uncertain material properties (Young's modulus, tensile strength, fracture energy) on the variability of the loaddisplacement curves and crack paths is examined. The uncertain properties are described by homogeneous stochastic fields using the spectral representation method in conjunction with translation field theory. 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 response statistics are affected by the spectral characteristics of the stochastic fields.