A recent article by Vigdergauz considered two-component, linearly elastic plates. It showed the existence of spatially periodic microstructures producing plates of extremal rigidity. For the microstructures which maximize or minimize the effective bulk modulus, Vigdergauz asserted that the effective behavior was isotropic. We show this is wrong: the effective tensor is in fact anisotropic.
Issue Section:
Brief Notes
1.
Gibson
L. J.
Ashby
M. F.
Schajer
G. S.
Robertson
C. I.
1982
, “The mechanics of two-dimensional cellular materials
,” Proceedings of the Royal Society of London, A
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, pp. 25
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.2.
Grabovsky
Y.
1995
, discussion
, ASME JOURNAL OF APPLIED MECHANICS
, Vol. 62
, p. 550
550
.3.
Grabovsky
Y.
Kohn
R. V.
1995
, “Microstructures minimizing the energy of a two phase elastic composite in two space dimensions. II: the Vigdergauz microstructure
,” Journal of the Mechanics and Physics of Solids
, Vol. 43
, pp. 949
–972
.4.
Vigdergauz
S.
1994
, “Two-Dimensional Grained Composites of Extreme Rigidity
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 61
, pp. 390
–394
.
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