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Geometry definition and unstructured grid generation for simulating nanostructured materials

Patrick Laug 1, * 
* Corresponding author
1 Gamma3 - Automatic mesh generation and advanced methods
Inria Paris-Rocquencourt, ICD - Institut Charles Delaunay
Abstract : A sample of nanostructured material contains particles of different sizes, typically ranging from 5 to 30 nanometers. These particles can be experimentally observed and their size distribution measured. A geometric model of such a sample consists in a parallelepiped filled with non-overlapping spheres (or, in 2D, a rectangle filled with circles) whose radii follow the given size distribution. In the first part of this talk, a new method for constructing these geometric models will be introduced. The algorithm, based on an advancing front approach, is almost linear in complexity, robust and fast in both 2D and 3D. A simple technique, using Laguerre or power diagrams, can also be used to transform spheres into polyhedra (or 2D circles into polygons) providing more realistic shapes. In the second part of this talk, methods for generating unstructured grids of these models will be presented. These grids are necessary to simulate the mechanical behavior of nanostructured materials with the finite element method. The convergence of this method and the accuracy of the calculated solution strongly depend on the quality of the generated meshes. Therefore, we propose an adaptive scheme governed by a metric map taking into account the geometry and the proximity of the particles. For models having a large number of particles, we propose two domain decomposition methods to parallelize the global process including mesh generation and finite element computation. Several numerical examples will be shown to illustrate our approach (hereafter, two geometric models can be seen in figure 1 and their corresponding adapted grids in figure 2). This work has been carried out in collaboration with H. Borouchaki (Prof. at the University of Technology of Troyes, France), J. Lu (Prof. at the Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong) and A. Benabbou (PhD).
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Submitted on : Tuesday, January 28, 2014 - 2:04:19 PM
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  • HAL Id : hal-00937457, version 1



Patrick Laug. Geometry definition and unstructured grid generation for simulating nanostructured materials. ISGG - 11th International Society on Computing Grid Generation Conference, May 2009, Montréal, Canada. ⟨hal-00937457⟩



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