The effect of pore shape on the Poisson ratio of porous materials
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Published version
Author(s)
Lutz, Melanie P
Zimmerman, Robert W
Type
Journal Article
Abstract
A brief review is given of the effect of porosity on the Poisson ratio of a porous material. In contrast to elastic moduli such as K, G, or E, which always decrease with the addition of pores into a matrix, the Poisson ratio ν may increase, decrease, or remain the same, depending on the shape of the pores, and on the Poisson ratio of the matrix phase, νo. In general, for a given pore shape, there is a unique critical Poisson ratio, νc, such that the addition of pores into the matrix will cause the Poisson ratio to increase if νo<νc, decrease if νo>νc, and remain unchanged if νo=νc. The critical Poisson ratio for spherical pores is 0.2, for prolate spheroidal pores is close to 0.2, and tends toward zero for thin cracks. For two-dimensional materials, νc=1/3 for circular pores, 0.306 for squares, 0.227 for equilateral triangles, and again approaches 0 for thin cracks. The presence of a “trapped” fluid in the pore space tends to cause νc to increase, and for the range of parameters that may occur in rocks or concrete, this increase is more pronounced for thin crack-like pores than for equi-dimensional pores. Measurements of the Poisson ratio therefore may allow insight into pore geometry and pore fluid. If the matrix phase is strongly auxetic, small amounts of porosity will generally not cause the Poisson ratio to become positive.
Date Issued
2021-08-01
Date Acceptance
2021-05-12
Citation
Mathematics and Mechanics of Solids, 2021, 26 (8), pp.1191-1203
ISSN
1081-2865
Publisher
SAGE Publications
Start Page
1191
End Page
1203
Journal / Book Title
Mathematics and Mechanics of Solids
Volume
26
Issue
8
Copyright Statement
© The Author(s) 2021. This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage).
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000675517100008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Technology
Physical Sciences
Materials Science, Multidisciplinary
Mathematics, Interdisciplinary Applications
Mechanics
Materials Science
Mathematics
Porous materials
Poisson ratio
effective medium theory
auxetic materials
ELASTIC-MODULI
DIFFERENTIAL SCHEME
2-DIMENSIONAL PORES
SHEAR COMPLIANCE
COMPRESSIBILITY
CAVITIES
SOLIDS
Publication Status
Published
Date Publish Online
2021-06-22