A two-scale stochastic framework for predicting failure strength probability of heterogeneous materials

In the present study, a two-scale stochastic framework has been proposed for predicting the failure strength probability of heterogeneous materials. The analysis at both scales (meso and macro) is performed under plane stress condition. The meso-scale analysis is performed by XFEM whereas the macro-scale analysis is performed by FEM. The heterogeneities (pores and reinforced particles) are considered at meso-scale. The effect of shape, size, clustering and volume fraction of heterogeneities is analyzed at meso-scale. A new scheme is developed for modeling the arbitrary shape heterogeneities using periodic B-splines. An adaptive hanging node mesh refinement technique is employed to reduce the computational cost. Maximum principal stress failure criterion has been implemented for modeling both tensile and compressive behaviors at meso-scale. The volume fraction of pores and reinforcement particles is distributed stochastically to the elements at macro-scale. The average volume fraction of the pores is taken as 8%, 10%, 12% and 14% whereas the average volume fraction of the reinforced particles is kept constant at 20%. The statistical analysis of numerical data is performed through normal and Weibull distribution fits. K-S goodness of fit predicts that the numerical data is better fitted by the normal distribution.