Page 215 - Introduction to Continuum Mechanics

200 Stress

(c) For a unit area in the deformed state in the €3 direction, its undeformed area dA 0 n 0 is
given by Eq. (3.28.6). That is

With detF = 1, and the matrix F given above, we obtain

Thus, n 0 = 62 and

gives

i.e, ^ = 2503 MPa. We note that this vector is in the same direction as the Cauchy stress vector,
its magnitude is one fourth of that of the Cauchy stress vector, because the undeformed area
is 4 times that of the deformed area.
(d) We have, from Eq. (4.10.9)

Thus,

We see that this pseudo stress vector is in a different direction from that of the Cauchy stress
vector. (We note that the tensor F transforms e 2 into the direction of e 3 .)