Stochastic aspects of localised failure: material and boundary imperfections

This paper presents the application of the finite element reliability method to the evaluation of the statistical properties of localisation phenomena. Material and boundary constraint imperfections are considered. The latter are imposed through Lagrange multipliers. The evaluation of the sensitivity to the stochastic basic variables, which is needed in the reliability method, is outlined. Numerical simulations of mode-I and mode-II localisation phenomena are presented.