Computational homogenization of polycrystalline materials with the Virtual Element Method

authored by: Michele Marino, Blaž Hudobivnik, Peter Wriggers
Abstract: Homogenized properties of polycrystalline materials are needed in many engineering applications. The present work investigates the effectiveness of computational homogenization approaches based on the Virtual Element Method (VEM). Advantages and/or disadvantages of the VEM formulation with respect to traditional FEM approaches are explored by means of a number of numerical examples. Representative volume elements with different geometrical and material properties are investigated. Both two-and three-dimensional applications, as well as both linear and nonlinear homogenization schemes, are presented. The results show the accuracy of a VEM-based approach. On the contrary, traditional FEM-based homogenization schemes suffer with increasing grains anisotropy, requiring a high number of degree of freedoms for maintaining an acceptable accuracy. In conclusion, VEM is a promising methodology for the homogenization of polycrystalline materials. The advantage of VEM when compared to FEM is of engineering relevance for facing the challenging case of materials with strong and heterogeneous anisotropies. In fact, it is shown that VEM formulations are free from anisotropic locking.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 355
Pages: 349-372
No. of pages: 24
ISSN: 0045-7825
Publication date: 01.10.2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2019.06.004 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{f541a5e7c6f24a98a94d4eaa41bee0b4,
title = "Computational homogenization of polycrystalline materials with the Virtual Element Method",
abstract = "Homogenized properties of polycrystalline materials are needed in many engineering applications. The present work investigates the effectiveness of computational homogenization approaches based on the Virtual Element Method (VEM). Advantages and/or disadvantages of the VEM formulation with respect to traditional FEM approaches are explored by means of a number of numerical examples. Representative volume elements with different geometrical and material properties are investigated. Both two-and three-dimensional applications, as well as both linear and nonlinear homogenization schemes, are presented. The results show the accuracy of a VEM-based approach. On the contrary, traditional FEM-based homogenization schemes suffer with increasing grains anisotropy, requiring a high number of degree of freedoms for maintaining an acceptable accuracy. In conclusion, VEM is a promising methodology for the homogenization of polycrystalline materials. The advantage of VEM when compared to FEM is of engineering relevance for facing the challenging case of materials with strong and heterogeneous anisotropies. In fact, it is shown that VEM formulations are free from anisotropic locking.",
keywords = "Anisotropic locking, Computational homogenization, Nonlinear homogenization, Polycrystalline materials, Virtual element method",
author = "Michele Marino and Bla{\v z} Hudobivnik and Peter Wriggers",
note = "Funding Information: M. Marino acknowledges that this work has been carried out within the framework of the SMART BIOTECS alliance between the Technical University of Braunschweig and the Leibniz University Hannover. This initiative is financially supported by the Ministry of Science and Culture (MWK) of Lower Saxony, Germany.",
year = "2019",
month = oct,
day = "1",
doi = "10.1016/j.cma.2019.06.004",
language = "English",
volume = "355",
pages = "349--372",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}