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Finite Element Network Approximation of Conductivity in Particle Composites

Please always quote using this URN:urn:nbn:de:0296-matheon-9137
  • A new finite element method computes conductivity in some unstructured particle-reinforced composite material. The 2-phase material under consideration is composed of a poorly conducting matrix material filled by highly conducting circular inclusions which are randomly dispersed. The mathematical model is a Poisson-type problem with discontinuous coefficients. The discontinuities are huge in contrast and quantity. The proposed method generalizes classical continuous piecewise affine finite elements to special computational meshes which encode the particles in a network structure. Important geometric parameters such as the volume fraction are preserved exactly. The computational complexity of the resulting method is proportional to the number of inclusions and this is optimal in comparison to data complexity. The discretization error is proportional to the particle distance and does not depend on the conductivity contrast in the medium.

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Metadaten
Author:Daniel Peterseim, Carsten Carstensen
URN:urn:nbn:de:0296-matheon-9137
Referee:Harry Yserentant
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/11/10
Release Date:2011/11/10
Tag:discrete network; finite elements; high contrast; micro-structure
Institute:Research Center Matheon
Humboldt-Universität zu Berlin
Project:C Energy and Materials (Production)
MSC-Classification:65-XX NUMERICAL ANALYSIS
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Qxx Homogenization, determination of effective properties / 74Q20 Bounds on effective properties
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Qxx Homogenization, determination of effective properties
Preprint Number:824
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