A cubic element of material with Young's modulus

E

and Poisson's ratio

v

is subjected to normal stresses

\\\\sigma _(1),\\\\sigma _(2)

and

\\\\sigma _(3)

, resulting in strains

\\\\epsi _(1),\\\\epsi _(2)

and

\\\\epsi _(3)

.\ (a) Find an expression for the dilatation

\\\\Delta

when a unit cube (side length 1) experiences strains of

\\\\epsi _(1),\\\\epsi _(2)

and

\\\\epsi _(3)

, assuming that the strains are elastic and therefore small

(1)

.

2. A cubic element of material with Young's modulus E and Poisson's ratio v is subjected to normal stresses 1,2 and 3, resulting in strains 1,2 and 3. (a) Find an expression for the dilatation when a unit cube (side length 1) experiences strains of 1,2 and 3, assuming that the strains are elastic and therefore small (