An efficient finite element based multigrid method for simulations of the mechanical behavior of heterogeneous materials
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ORIGINAL PAPER
An efficient finite element based multigrid method for simulations of the mechanical behavior of heterogeneous materials using CT images Xiaodong Liu1 · Julien Réthoré1
· Marie-Christine Baietto2 · Philippe Sainsot2 · Antonius Adrianus Lubrecht2
Received: 27 October 2019 / Accepted: 17 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract X-ray tomography techniques give researchers the full access to material inner structures. With such ample information, employing numerical simulation on real material images becomes more and more common. Material behavior, especially, of heterogeneous materials, e.g. polycrystalline, composite, can be observed at the microscopic scale with the computed tomography (CT) techniques. In this work, an efficient strategy is proposed to carry out simulations on large 3D CT images. A proposed matrix free type finite element based MultiGrid method is applied to improve convergence speed and to reduce memory space requirements. Homogenization techniques are used to obtain specific operators to enhance the convergence of the MultiGrid method when large material property variations are present. Hybrid parallel computing is implemented for memory space and computing time reasons. Free edge effects in a laminate composite with more than 16 billion degrees of freedom and crack opening in a cast iron are studied using the proposed strategy. Keywords Heterogeneous materials · Finite element method · MultiGrid · Homogenization · Mechanical behavior · Tomography images
1 Introduction One of the subjects of material science is to understand material behavior and then to improve material performance to respond to industrial requirements. However, to manufacture materials with such good performance, is not an easy job. Many defects are present in materials, e.g. voids, cracks or broken fibers in composite materials. CT images of such complex materials permit one to evaluate the presence of these defects. Nevertheless, the aim of researchers is to understand how these defects affect material performance. Numerical simulations are often used to analyze material performance. The main idea of this work is to carry out the calculation directly on CT images. This permits one to observe how the material structure affects its performance at the microscopic scale. However, these defects make the simulation expensive or even impractical. One of the most used methods is to
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Julien Réthoré [email protected]
1
GeM, CNRS UMR 6183, Centrale Nantes, 44321 Nantes, France
2
INSA-Lyon, CNRS UMR5259, LaMCoS, Univ Lyon, 69621 Lyon, France
homogenize materials, which means instead of focusing on the local defects, the material is supposed to be homogenized at a macroscopic scale. This technique is called homogenization. Hashin [13] explains how to predict the macroscopic property of a fiber composite from its microscopic structure. Özdemir et al. [25] presents the application of a homogenization method for the thermal conduction of heterogeneous materials. H
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