Page 117 - Introduction to Continuum Mechanics

102 Kinematics of a Continuum

Example 3.8.2
Given the displacement field

(a)Find the unit elongation and the change of angle for the two material elements
cDv ' = dXi*i and dXs ' = dX^i that emanate from a particle designated by X = «i—«2-
(b)Find the deformed position of these two elements dK- ^ and dX^ '.

and therefore the strain matrix is

Since EH = £"22 ~ 2^» DOtri elements have a unit elongation of 2x10 . Further, since
£"12 = 0, these line elements remain perpendicular to each other.
(b) From Eq. (3.7. la)

and similarly

The deformed position of these elements is sketched in Fig. 3.5. Note from the diagram that