From image data towards microstructure information -- accuracy analysis at the digital core of materials

TL;DR

This paper develops a unified error analysis framework for image-based microstructure representations, distinguishing modeling and discretization errors to improve simulation accuracy in computational solid mechanics.

Contribution

It introduces a novel error analysis approach for uniform and adaptively coarsened microstructure discretizations, aiding in reliable digital twin development.

Findings

Quantitative relation between modeling and discretization errors

Impact of errors on microscale and macroscale simulations

Validation of the approach on a two-phase material

Abstract

A cornerstone of computational solid mechanics in the context of digital transformation are databases for microstructures obtained from advanced tomography techniques. Uniform discretizations of pixelized images in 2D are the raw-data point of departure for simulation analyses. This paper proposes the concept of a unified error analysis for image-based microstructure representations in uniform resolution along with adaptively coarsened discretizations. The analysis distinguishes between a modeling error due to finite, possibly coarsened image resolution and a discretization error, investigates their quantitative relation, spatial distributions and their impacts on the simulation results both on the microscale and the macroscale in the context of computational homogenization. The assessment of accuracy and efficiency is carried out for an exemplary two-phase material. Beyond the example considered here the concept is a rational tool in the transformation of raw image data into microstructure information adapted to particular simulation needs and endows the digital twin of real microstructures with validated characteristics for reliable, predictive simulations.