## Treatise on materials science and technology, Volume 3 |

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Page 90

If we retain only linear terms in the displacement gradients, Eqs. (239) reduce to

r11 = (2n + X)um + i. ...

+ A)a + A(2a) or solving for a, (3A+2/0 Since in our case the only nonvanishing ...

If we retain only linear terms in the displacement gradients, Eqs. (239) reduce to

r11 = (2n + X)um + i. ...

**Substituting Eqs**. (242) into Eqs. (243) we obtain -P = (2/i+ A)a + A(2a) or solving for a, (3A+2/0 Since in our case the only nonvanishing ...

Page 95

(270) In this case the Jacobian matrix Eq. (169) and its transpose Eq. (170)

reduce to / l+ua 0 0 /=( va 1 0 | (271) \ wa 0 1 ... (272) \ 0 0 1

271) and (272) into Eq. (172) we find that the only non- vanishing strain

components are ...

(270) In this case the Jacobian matrix Eq. (169) and its transpose Eq. (170)

reduce to / l+ua 0 0 /=( va 1 0 | (271) \ wa 0 1 ... (272) \ 0 0 1

**Substituting Eqs**. (271) and (272) into Eq. (172) we find that the only non- vanishing strain

components are ...

Page 96

elastic constants we have (274) cj> = ^11711+c44(7?2 + 721+731+y?3) +

c111711+ic166[y11(yf2 + y|1 + y|1 + yf3)]. Differentiating Eq. (274) with respect to

the ...

**Substituting Eqs**. (273) in Eq. (268) and using Birch's values for the third- orderelastic constants we have (274) cj> = ^11711+c44(7?2 + 721+731+y?3) +

c111711+ic166[y11(yf2 + y|1 + y|1 + yf3)]. Differentiating Eq. (274) with respect to

the ...

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