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Applications of Wavelets in the Representation and Prediction of Transformation in Shape-Memory Polycrystals

Shmuel, Gal and Thorgeirsson, Adam Thor and Bhattacharya, Kaushik (2014) Applications of Wavelets in the Representation and Prediction of Transformation in Shape-Memory Polycrystals. In: TMS 2014 Supplemental Proceedings. Wiley & Sons Inc. , Hoboken, NJ, pp. 527-534. ISBN 978-1-118-88972-5. http://resolver.caltech.edu/CaltechAUTHORS:20150623-085602848

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Abstract

In recent years, new developments in materials characterization techniques have led to a vast amount of data on the microstructure of polycrystals. Simultaneously, improvements in computational capabilities have enabled accurate full-field simulations for the micro-mechanical fields developing in polycrystalline aggregates. These show that in phenomena including phase transformation, localized bands of deformation percolate in a complex way across various grains. Our objective is to develop a methodology for analyzing, storing and representing microstructure data and, in turn, to identify the relevant information dictating the macroscopic behavior in superelastic polycrystals. To this end, wavelets are used in a case study of a polycrystalline aggregate in anti-plane shear. It is demonstrated how the transformation fields developing within the material can be efficiently represented by thresholding their wavelet expansion, maintaining more than 90% of the L_2 norm of the original field, while using approximately 10% of the number of terms in the original data. The macroscopic stress-strain relation resulting from solving the governing equations using a thresholded transformation strain is shown to be in a good agreement with the exact relation. Finally, the set of the functions retained in the expansion after thresholding was found to be similar in adjacent loading steps. Motivated by these observations, we propose a new wavelet-based algorithm for calculating the developing fields in phase transforming polycrystals.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/9781118889879.ch64DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/9781118889879.ch64/summaryPublisherArticle
https://link.springer.com/chapter/10.1007/978-3-319-48237-8_64PublisherArticle
ORCID:
AuthorORCID
Bhattacharya, Kaushik0000-0003-2908-5469
Additional Information:© 2014 The Minerals, Metals & Materials Society. Published Online: 24 Jan 2014. Published Print: 1 Feb 2014. We gratefully acknowledge the support of the US Air Force Office of Scientific Research through the MURI grant ’Managing the Mosaic of Microstructure’ (FA9550-12-1-0458). The first author also wishes to thank Dr. A. W. Richards for many helpful discussions.
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-12-1-0458
Subject Keywords:Wavelets, Polycrystals, Phase transformation
Record Number:CaltechAUTHORS:20150623-085602848
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150623-085602848
Official Citation:Shmuel G., Thorgeirsson A.T., Bhattacharya K. (2014) Applications of Wavelets in the Representation and Prediction of Transformation in Shape-Memory Polycrystals. In: The Minerals, Metals & Materials Society (eds) TMS 2014: 143rd Annual Meeting & Exhibition. Springer, Cham
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:58436
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:23 Jun 2015 16:52
Last Modified:14 Jun 2017 19:20

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