Stochastic Macro Material Properties, Through Direct Stochastic Modeling of Heterogeneous Microstructures with Randomness

Abstract: In this paper, a simple and reliable procedure of stochastic compu-tation is combined with the highly accurate and efficient Trefftz Computational Grains (TCG), for a direct numerical simulation (DNS) of heterogeneous materi-als with microscopic randomness. Material properties of each material phase, and geometrical properties such as particles sizes and distribution, are considered to be stochastic with either a uniform or normal probabilistic distributions. The ob-jective here is to determine how this microscopic randomness propagates to the macroscopic scale, and affects the stochastic characteristics of macroscopic mate-rial properties. Four steps are included in this procedure: (1) using the Latin hy-percube sampling, to generate discrete experimental points considering each con-tributing factor (material parameters and volume fraction of each phase, etc.); (2) randomly generating Representative Volume Elements (RVEs) of the microstruc-ture for each discrete experimental point, and compute the effective macro-scale material properties at these points, using the computationally most efficient Tre-fftz Computational Grains; (3) relating the macro-scale material properties to th