Linear elasticity of planar Delaunay networks. III: Self-consistent approximations
type: Item
instance of: scholarly article
title: Linear elasticity of planar Delaunay networks. III: Self-consistent approximations
zbMATH Open document ID: 0852.73006
DOI: 10.1007/BF01215416
author: Martin Ostoja-Starzewski
author: I. Jasiuk
author: Khalid I. Alzebdeh
published in: Acta Mechanica
publication date: 1996-12-16T00:00:00Z
review text: [For parts I, II see the first author and \textit{C. Wang}, Acta Mech. 80, No. 1/2, 61-80 (1989; Zbl 0711.73275); ibid. 84, No. 1, 47-61 (1990; Zbl 0719.73047).] Two-phase Delaunay and regular triangular networks, with randomness per vertex, provide generic models of granular media consisting of two types of grains -- soft and stiff. We investigate effective macroscopic moduli of such networks for the whole range of area fractions of both phases and for a very wide range of stiffness of both phases. Results of computer simulations of such networks under periodic boundary conditions are used to determine which of several different self-consistent models can provide the best possible approximation to effective Hooke's law. The main objective is to find the effective moduli of a Delaunay network as if it was a field of inclusions, rather than vertices connected by elastic edges, without conducting the computer-intensive calculations of large windows.
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 74E30
zbMATH DE Number: 885789
zbMATH Keywords: effective Poisson's ratio
zbMATH Keywords: circular inclusion-matrix model
zbMATH Keywords: Voigt and Reuss bounds
zbMATH Keywords: two-dimensional matrix-inclusion composites
zbMATH Keywords: regular triangular networks
zbMATH Keywords: randomness
zbMATH Keywords: granular media
zbMATH Keywords: macroscopic moduli
zbMATH Keywords: effective Hooke's law
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01215416
OpenAlex ID: W2077626752
description: scientific article; zbMATH DE number 885789