Stochastic macro material properties, through direct stochastic modeling of heterogeneous microstructures with randomness of constituent properties and topologies, by using Trefftz Computational Grains (TCG)

In this paper, a simple and reliable procedure of stochastic computation is combined with the highly accurate and efficient Trefftz Computational Grains (TCG), for a direct numerical simulation (DNS) of heterogeneous materials 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 objective here is to determine how this microscopic randomness propagates to the macroscopic scale, and affects the stochastic characteristics of macroscopic material properties. Four steps are included in this procedure: (1) using the Latin hypercube sampling, to generate discrete experimental points considering each contributing factor (material parameters and volume fraction of each phase, etc.); (2) randomly generating Representative Volume Elements (RVEs) of the microstructure for each discrete experimental point, and compute the effective macro-scale material properties at these points, using the computationally most efficient Trefftz Computational Grains; (3) relating the macro-scale material properties to the microscale random variables using the Kriging method; (4) taking advantage of the approximate macro-micro relation, and using the Monte Carlo simulation, to establish the probabilistic distribution of the macro-scale material properties. By considering the Al/SiC composite as an example, we give step-by step demonstration of the procedure, and give some comparisons with experimental results. The obtained probabilistic distributions of the effective macro-scale material properties have fundamental engineering merits, which can be used for reliability-based material optimization, and integrated-design of micro-as well as macro-structures. The studies in this paper are germane to the concepts of the Materials Genome Initiative (MGI), and Integrated Materials Science, Mathematics, Modeling, and Engineering (IMSMME).