Power Law UMAT
Decemb er 19, 1995
1 Mechanics
No summmation in the following expressions!!
ij
=
S
ij
+
p
ij
(1)
p
=
ktr
(2)
For shear components introduce engineering strain:
ij
=2
ij
(3)
S
ii
=
2
3
0
m
;
1
0
ii
0
and
S
ij
=
1
3
0
m
;
1
0
ij
0
(4)
=
2
3
ij
ij
1
2
=
2
3
X
2
ii
+2
X
2
ij
1
2
(5)
=
2
3
X
2
ii
+
1
2
X
2
ij
1
2
@
ii
@
jj
=
ij
and
@
ij
@
kl
=
ik
jl
(6)
I
ij kl
=
1
2
(
ik
jl
+
il
jk
) (7)
J
=
@
ij
(
t
+
t
)
@
kl
(
t
+
t
)
=
@
ij
(
t
+
t
)
@
kl
(
t
+
t
)
(8)
1
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