Experiment-based validation and uncertainty quantification of coupled multi-scale plasticity models

Anisotropic materials, such as zirconium require the inclusion of evolution of the crystal structure in the finite element model representations of the mechanical behavior, naturally leading to coupled meso- and macro-scale plasticity models. For achieving such models, partitioned techniques where isolated models that resolve system behavior at different scales are coupled through iterative exchange of inputs and outputs are widely used. In this treatment, a finite element at the macro-scale provides strain information to a meso-scale visco-plastic self-consistent model to represent micro-scale properties. These properties are then returned to the macro-scale for new stress and strain calculations. During this iterative process, biases and uncertainties inherent within constituent model predictions propagate between constituents. This propagation creates a need for a multi-scale approach for experiment-based validation and uncertainty quantification, in which separate effect experiments conducted within each constituent’s domain test the validity of the independent constituents in their respective scales and integral-effect experiments executed within the coupled domain validate the entire coupled system. In this paper the authors implement a multi-scale experiment-based validation approach utilizing both separate and integral-effect experiments. Results demonstrate that training an independent error model for the bias of the constituent model utilizing separate-effect experiments as means of appropriately bias-correcting constituent model predictions during coupling iterations results in an improved predictive capability. This improvement is demonstrated through the use of integral-effect experiments.