246448680 Linear Viscoelasticity
29
Linear Viscoelasticity
description
vis
Transcript of 246448680 Linear Viscoelasticity
General Constitutive Law
))()((0 t
dtE
))()((1
0 t
dtKE
*)( KIE We can re-write this in the form:
*)( IE
If we define *)1( EE
than we generalize the Elastic law:
E
It might be shown that *)1(1
*1
11K
EE
and, for example:
)1(2
EG
Linear Viscoelasticity
0
0
0
zzzyzxz
yyzyyxy
xxzxyxx
Fzyx
Fzyx
Fzyx
)(2
1
i
j
j
iij x
u
x
u
ijijij 2
(no time, so far)
*)1(*);1(
Laplace…
;)()((0
dtt
;)1()(
ijijij )1(2)1(
Laplace transform of this function leads to
Similarly for
Finally:
)(2
1
i
j
j
iij x
u
x
u
0, jjij F
Examples of Operators
t
ctK )(
0
)(
t
ctK
10;)(
t
ctK
Boltzmann kernel
Boltzmann without singularity
No infinite rate of deformation
0
0ln1
t
cE
1
1
1t
c
E