Effective elastic properties of materials with high concentration of aligned spheroidal pores
type: Item
instance of: scholarly article
title: Effective elastic properties of materials with high concentration of aligned spheroidal pores
zbMATH Open document ID: 0581.73016
DOI: 10.1016/0020-7683(86)90095-8
author: Miroslav Hlaváček
published in: International Journal of Solids and Structures
publication date: 1986-01-01T00:00:00Z
review text: A model of elastic transversely isotropic porous materials is presented. It may have applications with cancellous bone. The arrangement of aligned spheroidal pores is obtained through a homological transformation from Hashin's composite-sphere model. The volume fraction C of the matrix is assumed small. Two extremal variational principles of the theory of elasticity yield some inequalities or bounds for the derivatives with respect to C at \(C=0\) of five macroscopic moduli. By using inhomogeneous stress boundary conditions for a hollow spheroidal element, the bounds are considerably improved. They coincide with the upper bounds for spherical pores. The bounds for the derivatives with respect to C at \(C=0\) of five moduli, obtained from a kinematically admissible displacement, are of a simple form and can be used for an approximation to five macroscopic moduli for \(C\ll 1\).
Mathematics Subject Classification ID: 74E10
Mathematics Subject Classification ID: 74E30
Mathematics Subject Classification ID: 74L15
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 3930429
zbMATH Keywords: small volume fraction
zbMATH Keywords: bounds for derivatives of five macroscopic moduli
zbMATH Keywords: elastic transversely isotropic porous materials
zbMATH Keywords: cancellous bone
zbMATH Keywords: arrangement of aligned spheroidal pores
zbMATH Keywords: homological transformation
zbMATH Keywords: Hashin's composite-sphere model
zbMATH Keywords: Two extremal variational principles
zbMATH Keywords: inhomogeneous stress boundary conditions
zbMATH Keywords: hollow spheroidal element
MaRDI profile type: Publication
full work available at URL: 0020-7683(86)90095-8
OpenAlex ID: W2121946863
description: scientific article; zbMATH DE number 3930429