Page 239 - Introduction to Continuum Mechanics

224 The Elastic Solid

(a)

(b)the strain energy function U is given by

Solution, (a) Since for linearly elastic solid 7/j = C,^/£^, therefore

therefore,

(b) From

we have

i.e.,

Changing the dummy indices, we obtain

But, CMIJ = Cijffi, therefore

Adding Eqs. (v) and (vii), we obtain