Using Discrete Harmonic Expansions and Equilibrium Conditions to Estimate Intragrain Stress Distributions in Polycrystals from Grain-Averaged Data

TL;DR

This paper introduces a method using harmonic expansions and equilibrium conditions to estimate detailed intra-grain stress distributions in polycrystals from average stress data, enhancing the analysis capabilities of the MechMonics code.

Contribution

It presents a novel optimization-based approach to infer intra-grain stress variations from grain-averaged data, extending existing computational tools.

Findings

Successfully applied to synthetic data from virtual polycrystals.

Improves stress distribution estimation accuracy.

Integrates with open source MechMonics code.

Abstract

The application of harmonic expansions to estimate intra-grain stress distributions from grain-averaged stress data is presented that extends the capabilities of the open source code, MechMonics. The method is based on using an optimization algorithm to determine the harmonic expansion weights that reduce the violation of equilibrium while maintaining prescribed grain-averages. The method is demonstrated using synthetic data generated for uniaxial extension of a virtual polycrystal with the mechMet code.