Multi-fidelity microstructure-induced uncertainty quantification by advanced Monte Carlo methods

TL;DR

This paper introduces a multi-fidelity uncertainty quantification method using advanced Monte Carlo techniques to efficiently assess microstructure variations' impact on material properties in CPFEM simulations.

Contribution

It develops a unified multi-fidelity framework employing MLMC and MIMC methods to reduce computational costs in microstructure-induced uncertainty quantification.

Findings

Multi-level Monte Carlo methods significantly reduce simulation costs.

Adaptive fidelity exploitation improves accuracy with fewer microstructure samples.

The approach extends to multi-model frameworks combining different constitutive models.

Abstract

Quantifying uncertainty associated with the microstructure variation of a material can be a computationally daunting task, especially when dealing with advanced constitutive models and fine mesh resolutions in the crystal plasticity finite element method (CPFEM). Numerous studies have been conducted regarding the sensitivity of material properties and performance to the mesh resolution and choice of constitutive model. However, a unified approach that accounts for various fidelity parameters, such as mesh resolutions, integration time-steps, and constitutive models simultaneously is currently lacking. This paper proposes a novel uncertainty quantification (UQ) approach for computing the properties and performance of homogenized materials using CPFEM, that exploits a hierarchy of approximations with different levels of fidelity. In particular, we illustrate how multi-level sampling methods, such as multi-level Monte Carlo (MLMC) and multi-index Monte Carlo (MIMC), can be applied to assess the impact of variations in the microstructure of polycrystalline materials on the predictions of homogenized materials properties. We show that by adaptively exploiting the fidelity hierarchy, we can significantly reduce the number of microstructures required to reach a certain prescribed accuracy. Finally, we show how our approach can be extended to a multi-fidelity framework, where we allow the underlying constitutive model to be chosen from either a phenomenological plasticity model or a dislocation-density-based model.