Direct numerical simulations in solid mechanics for understanding the macroscale effects of microscale material variability

A fundamental challenge for the quantification of uncertainty in solid mechanics is understanding how microscale material variability is manifested at the macroscale. In an era of petascale computing and future exascale computing, it is now possible to perform direct numerical simulations (DNS) in solid mechanics where the microstructure is modeled directly in a macroscale structure. Using this DNS capability, we investigate the macroscale response of polycrystalline microstructures and the accuracy of homogenization theory for upscaling the microscale response. Using a massively parallel finite-element code, we perform an ensemble of direct numerical simulations in which polycrystalline microstructures are embedded throughout a macroscale structure. The largest simulations model approximately 420 thousand grains within an I-beam. The inherently random DNS results are compared with corresponding simulations based on the deterministic governing equations and material properties obtained from homogenization theory. Evidence is sought for both surface effects and other higher-order effects as predicted by homogenization theory for macroscale structures containing finite microstructures.