Efficient high-dimensional material reliability analysis with explicit voxel-level stochastic microstructure representation

Abstract

A novel efficient methodology for probabilistic material reliability analysis considering fine-scale microstructure stochasticity is proposed in this paper. Integrated computational material engineering requires efficient multiscale computational capabilities to enable computational design and validation. Two critical challenges are identified: handling uncertainties from microstructures and material properties; and handling the “curse of dimensionality” for probabilistic solvers. The proposed study addresses these two critical challenges. First, an analytical and hierarchical uncertainty quantification method is proposed for the explicit stochastic microstructure representation at the voxel-level. The hierarchy of uncertainties from both phase maps and uncertainties within each phase is modeled using an explicit Gaussian mixture random field. Analytical approximation for the arbitrary non-Gaussian random field is derived, which can facilitate the computation of gradient information in optimization. Following this, an efficient probabilistic solver using adjoint first-order reliability method combining the importance sampling is derived by formulating the material reliability analysis as a constrained optimization problem. The adjoint method is used to efficiently evaluate the responses and exact gradients with the help of the analytical Gaussian mixture random field. Several numerical examples for material reliability calculation with high-dimensional (voxel-level) random fields are subsequently employed to demonstrate and validate the proposed methodology. The results of the proposed method are quantitatively compared to those obtained via the classical first-order reliability method, direct Monte Carlo simulation, subset simulation, and the sequential importance sampling method. The comparisons indicate that the proposed method possesses high efficiency for high-dimensional material reliability problems.