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Modeling material stress using integrated Gaussian Markov random fields.

Peter W Marcy¹, Scott A Vander Wiel¹, Curtis B Storlie²

¹Statistical Sciences Group (CCS-6), Los Alamos National Laboratory (LANL), Los Alamos, NM, USA.

Journal of Applied Statistics

|June 16, 2022

Summary

This study models stress distribution in tantalum grains using advanced statistical methods. The research introduces a novel approach to analyze complex material stress fields for improved material science understanding.

Keywords:

Bayesian analysis Gaussian Markov random field blind deconvolution large-scale inverse problem materials science process convolution robust regression

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Studying Large Amplitude Oscillatory Shear Response of Soft Materials

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Published on: April 25, 2019

Area of Science:

Materials Science
Computational Mechanics
Statistical Modeling

Background:

Numerical solutions of constitutive models yield von Mises stress fields in discretized material volumes.
Understanding stress distribution within tantalum grains is crucial for material performance.
Existing methods may face challenges with complex geometries and large datasets.

Purpose of the Study:

To develop an intricate statistical model for the spatial field of von Mises stress in tantalum grains.
To fundamentally incorporate grain geometry into the stress field analysis.
To enable efficient Bayesian analysis of complex stress data.

Main Methods:

A statistical model relating the 3D stress field to stochastic processes on grain boundaries.
Utilizing a latent Gaussian Markov random field (GMRF) for boundary node neighborhoods.
Employing parallel computing, sparse matrix methods, and block update strategies for computational efficiency.
Incorporating an auxiliary variables approach to handle data outliers.

Main Results:

A robust statistical framework for analyzing von Mises stress fields in tantalum grains.
Demonstration of integrating grain geometry into stress field modeling.
Successful application of computational techniques to overcome Bayesian analysis challenges.
Accommodation of outliers in the stress data through auxiliary variables.

Conclusions:

The developed statistical model provides a powerful tool for understanding stress heterogeneities in polycrystalline materials.
The combination of computational techniques facilitates efficient analysis of complex, high-dimensional material stress data.
This work advances the integration of statistical modeling and numerical simulations in materials science.