Microstructure model reduction and uncertainty quantification in multiscale deformation processes

The quantification and propagation of uncertainty in multiscale deformation processes is considered. A reduced-order model for representing the data-driven stochastic microstructure input is presented. The multiscale random field representing the random microstructure is decomposed into few modes in different scales (the Rodrigues space for representing texture on mesoscale and the continuum macroscale space). Realizations from a stochastic simulation are used to obtain a small number of modes approximating the stochastic field. An example of a multiscale closed-die forging problem is provided in which the effects of uncertain initial geometry and texture on the macroscale properties are studied.