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Deformation patterning in finite-strain crystal plasticity by spectral homogenization with application to magnesium

Vidyasagar, A. and Tutcuoglu, Abbas D. and Kochmann, Dennis M. (2018) Deformation patterning in finite-strain crystal plasticity by spectral homogenization with application to magnesium. Computer Methods in Applied Mechanics and Engineering, 335 . pp. 584-609. ISSN 0045-7825. http://resolver.caltech.edu/CaltechAUTHORS:20180308-105420394

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Abstract

Complex microstructural patterns arise as energy-minimizers in systems having non-convex energy landscapes such as those associated with phase transformations, deformation twinning, or finite-strain crystal plasticity. The prediction of such patterns at the microscale along with the resulting, effective material response at the macroscale is key to understanding a wide range of mechanical phenomena and has classically been dealt with by simplifying energy relaxation theory or by expensive finite element calculations. Here, we discuss a stabilized Fourier spectral technique for the homogenized response at the level of a representative volume element (RVE). We show that the FFT-based method admits sufficiently high resolution suitable to predict the emergence of energy-minimizing microstructures and the resulting effective response by computing the approximated quasiconvex energy hull. We test the method in the classical single-slip problem in single- and bicrystals. Especially the latter goes beyond the scope of traditional finite element and analytical relaxation treatments and hints at mechanisms of pattern formation in polycrystals. We also demonstrate that the chosen spectral finite-difference approximation, important for removing ringing artifacts in the presence of high contrasts, adds a natural regularization to the non-convex minimization. Finally, the technique is applied to polycrystalline pure magnesium, where we account for the competition between dislocation-mediated plasticity and deformation twinning. These inelastic deformation mechanisms result in complex texture evolution paths at the polycrystalline mesoscale and are simulated within RVEs of varying grain size and texture by a constitutive crystal plasticity model with an effective, volume fraction-based description of twinning.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.cma.2018.03.003DOIArticle
https://www.sciencedirect.com/science/article/pii/S0045782518301208PublisherArticle
ORCID:
AuthorORCID
Kochmann, Dennis M.0000-0002-9112-6615
Additional Information:© 2018 Elsevier B.V. Received 5 December 2017, Revised 28 February 2018, Accepted 2 March 2018, Available online 7 March 2018. This research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-12-2-0022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
Funders:
Funding AgencyGrant Number
Army Research LaboratoryW911NF-12-2-0022
Subject Keywords:Homogenization; Spectral methods; Polycrystal; Microstructure; Magnesium
Record Number:CaltechAUTHORS:20180308-105420394
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180308-105420394
Official Citation:A. Vidyasagar, Abbas D. Tutcuoglu, Dennis M. Kochmann, Deformation patterning in finite-strain crystal plasticity by spectral homogenization with application to magnesium, Computer Methods in Applied Mechanics and Engineering, Volume 335, 2018, Pages 584-609, ISSN 0045-7825, https://doi.org/10.1016/j.cma.2018.03.003.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85202
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Mar 2018 21:40
Last Modified:23 Mar 2018 20:22

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