A Bayesian Machine Learning Framework for Selection of the Strain Gradient Plasticity Multiscale Model

Abstract

Abstract A class of sequential multiscale models investigated in this study consists of discrete dislocation dynamics (DDD) simulations and continuum strain gradient plasticity (SGP) models to simulate the size effect in plastic deformation of metallic micropillars. The high-fidelity DDD explicitly simulates the microstructural (dislocation) interactions. These simulations account for the effect of dislocation densities and their spatial distributions on plastic deformation. The continuum SGP captures the size-dependent plasticity in micropillars using two length parameters. The main challenge in predictive DDD-SGP multi-scale modeling is selecting the proper constitutive relations for the SGP model, which is necessitated by the uncertainty in computational prediction due to DDD’s microstructural randomness. This contribution addresses these challenges using a Bayesian learning and model selection framework. A family of SGP models with different fidelities and complexities is constructed using various constitutive relation assumptions. The parameters of the SGP models are then learned from a set of training data furnished by the DDD simulations of micropillars. Bayesian learning allows the assessment of the credibility of plastic deformation prediction by characterizing the microstructural variability and the uncertainty in training data. Additionally, the family of the possible SGP models is subjected to a Bayesian model selection to pick the model that adequately explains the DDD training data. The framework proposed in this study enables learning the physics-based multiscale model from uncertain observational data and determining the optimal computational model for predicting complex physical phenomena, i.e., size effect in plastic deformation of micropillars.