Formulation of Constitutive Equations - Continuum Mechanics of Anisotropic Materials - page 119

a

W OA -> W OA + W AB
T A Fixed
T A -> T A + T B

A B

W OA + W AB ->
W OA + W AB + W BC

0 -> W OA

0 -> T A

T B Fixed
T A + T B -> T B

O C

T B -> 0
W OA + W AB + W BC ->
W OA + W AB + W BC + W CO

clockwise

b

W OC + W CB ->
W OC + W CB + W BA
T A Fixed
T A + T B -> T A

A B

W OC + W CB + W BA ->

W OC -> W OC + W CB

W OC + W CB + W BA + W AO

T B Fixed

T A -> 0

T B -> T A + T B

O C

0 -> T B
0 -> W OC

counterclockwise

Fig. 5.2 Illustrations of closed loading cycles. ( a ) Clockwise cycle O ! A ! B ! C ! O,
( b ) counterclockwise cycle O ! C ! B ! A ! O. See the text for further explanation

ð

A

ð

A

1

2 S ij T ð A Þ

E

dT

E i d T i ¼ T ð A Þ

i

W OA ¼ ¼ : (5.16H)

j

O O

The integral over the second loading sequence of the cycle, from T i to T i þ T i ,

T i

6¼ T i is a bit more complicated because the loading of the object begins from a