Problem 13.2
Ice crystals are hexagonal with five independent elastic compliance coefficients
(units of 10−11 m2/N): s11 = 10.1, s12 = −4.1, s13 = −1.9, s33 = 8.3,
s44 = 32.5. The full matrix is given in Table 13.3.
Show that the elastic compliance surface for ice is cylindrically symmetric
about the hexagonal axis (Z3 = [001]) by deriving s
1111
= s
11 in spherical
coordinates θ and φ. Prove that
s
11
= s11 sin4 θ + s33 cos4 θ + (s44 + 2s13) sin2 θ cos2 θ.
Plot Young’s Modulus (E = 1/s
11) as a function of θ in the Z1–Z3 plane.
Ice crystals are hexagonal with five independent elastic compliance coefficients
(units of 10−11 m2/N): s11 = 10.1, s12 = −4.1, s13 = −1.9, s33 = 8.3,
s44 = 32.5. The full matrix is given in Table 13.3.
Show that the elastic compliance surface for ice is cylindrically symmetric
about the hexagonal axis (Z3 = [001]) by deriving s
1111
= s
11 in spherical
coordinates θ and φ. Prove that
s
11
= s11 sin4 θ + s33 cos4 θ + (s44 + 2s13) sin2 θ cos2 θ.
Plot Young’s Modulus (E = 1/s
11) as a function of θ in the Z1–Z3 plane.