Mechanical Analyses using Discrete Harmonic Expansions of Grain-Based Field Data

TL;DR

This paper introduces a method to analyze grain-based field data using discrete harmonic modes, enabling efficient representation of stress distributions in polycrystals, supported by open-source software.

Contribution

It presents a novel methodology for computing and applying discrete harmonic modes to grain-based data, facilitating detailed mechanical analysis.

Findings

Effective representation of axial stress distributions during tensile loading

Methodology leverages orthogonality of harmonic modes for analysis

Open source code MechMonics available for researchers

Abstract

A methodology for computing expansion basis functions using discrete harmonic modes is presented. The discrete harmonic modes are determined grain-by-grain for virtual polycrystals for which finite element meshes are available. The expansion weights associated with representing field variables over grain domains are determined by exploiting the orthogonality of the harmonic modes. The methodology is demonstrated with the representation of the axial stress distributions during tensile loading of a polycrystalline sample. An open source code, MechMonics, is available to researchers wishing to use the methodology to analyze data.