Beam model for the elastic properties of material with spherical voids
Heitkam
S
author
Drenckhan
W
author
Weaire
D
author
Froehlich
J
author
2016
The elastic properties of a material with spherical voids of equal volume are analysed using a new model, with particular attention paid to the hexagonal close-packed and the face-centred cubic arrangement of voids. Void fractions well above 74 % are considered, yielding overlapping voids as in an open-cell foam and hence a connected pore structure. The material is represented by a network of beams. The elastic behaviour of each beam is derived analytically from the material structure. By computing the linear elastic properties of the beam network, the Young's moduli and Poisson ratios for different directions are evaluated. In the limit of rigidity loss, a power law is obtained, describing the relation between Young's modulus and void fraction with an exponent of 5/2 for bending-dominated and 3/2 for stretching-dominated directions. The corresponding Poisson ratios vary between 0 and 1. With decreasing void fraction, these exponents become 2.3 and 1.3, respectively. The data obtained analytically and from the new beam model are compared to finite element simulations carried out in a companion study, and good agreement is found. The hexagonal close-packed void arrangement features anisotropic behaviour, comparable to that of fibre-reinforced materials. This may give rise to new applications of open-cell materials.
exported from refbase (http://www.ics-cnrs.unistra.fr/publication/show.php?record=14245), last updated on Tue, 07 Nov 2017 16:46:16 +0100
text
10.1007/s00419-015-1102-8
Heitkam_etal2016
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Archive Of Applied Mechanics
2016
continuing
periodical
academic journal
86
1-2, Si
165
176
0939-1533