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Surface stress and the equilibrium shape of an elastic crystal
1.Cf. M. M. Nicolson, Proc. R. Soc. A 228, 490 (1955).
2.M. E. Gurtin and A. I. Murdoch, Arch. Ration. Mech. Anal. 57, 291 (1975);
2.M. E. Gurtin and A. I. Murdoch, 59, 389 (1975)., Arch. Ration. Mech. Anal.
3.R. Shuttleworth, Proc. Phys. Soc. A 63, 444 (1950).
4.C. Herring, The Physics of Powder Metallurgy (McGraw‐Hill, New York, 1951).
5.Cf., e.g., M. E. Gurtin, Handbuch der Physik (Springer, Berlin, 1972), Vol. VIa/2.
6.Here subscripts have the range of the integers 1, 2; summation convention is used; is the Kronecker delta.
7.Cf. M. E. Gurtin and A. I. Murdoch, J. Appl. Phys. (to be published). In their notation and
8.Reference 7, Eq. (1.2).
9.Reference 7, Eq. (1.3).
10.Reference 4. Herring omits mention of the term from the outset.
11.We follow Herring (Ref. 4) in taking σ negative. For σ positive one simply reverses the direction of the displacement field.
12.Of course, this displacement is independence of the length l. On the other hand, for a length change of l to l/C the stress at corresponding points changes from to
13.Surface buckling due to surface compression has been studied by F. Andreussi and M. E. Gurtin (unpublished). There it is essential that the term be included.
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