2. Matlab Applications
a) Parameter estimation (curve fitting)*
 Different ways to estimate parameters
 excel “solver”
A graphical user interface (curve fitting toolbox)
 Matlab command (nlinfit or fmincon)
 Example
 Creep compliance of a wheat protein film (determination of retardation
time and free dashpot viscosity in the Jefferys model)
J  J1 (1  exp(
t
ret
)) 
t
0
Note: creep is the tendency of a solid
material to slowly move or deform
permanently under the influence of stresses.
Where J is the strain, J1 is the retarded compliance (Pa-1); λret=µ1/G1 is
retardation time (s); µ0 is the free dashpot viscosity (Pa s); t is the time.
2. Matlab Applications
Parameter estimation - Creep compliance Experimental Data
Note: Unlike brittle fracture,
creep deformation does not
occur suddenly upon the
application of stress. Instead,
strain accumulates as a result
of long-term stress. Creep is a
"time-dependent"
deformation.
Chewing gum
t, Time (s)
300
600
900
1200
1500
1800
2100
2400
2700
3000
3300
3600
3900
4200
4500
4800
5100
5400
5700
6000
6300
6600
6900
7200
J, Strain (Mpa^-1)
0.17
0.265
0.318
0.348
0.366
0.376
0.382
0.386
0.388
0.39
0.392
0.393
0.395
0.396
0.397
0.398
0.4
0.401
0.402
0.403
0.404
0.405
0.406
0.408
Method 1) Using Excel Solver
4/13/2015
3
Method 2) CFTtoolbox
Parameter estimation - Creep compliance
 Use the command of >>cftool
3. Simulink
Simulink
Type “simulink” in
the command window
The graphic interfaces
Matlab
Tutorial example
x = sin (t)
simout
4/13/2015
Simulink example 2
Creep compliance of a wheat protein film
Using formaldehyde cross-linker
 Creep compliance of a wheat protein film (determination of retardation
time and free dashpot viscosity in the Jefferys model)
J  J1 (1  exp(
t
ret
)) 
t
0
Where J is the strain, J1 is the retarded compliance (Pa-1); λret=µ1/G1 is
retardation time (s); µ0 is the free dashpot viscosity (Pa s); t is the time.
 The recovery of the compliance is following the equation (t >t1):
J  J1 exp(
t  t1
ret
)
Where t1 is the time the stress was released.
Solve using Simulink model
Parameters: J1 = a = 0.38 Mpa-1; λret = b = 510.6 s; µ0 = c = 260800 Mpa s; t1=5000
4. Simulink examples
Creep compliance of a wheat protein film
Simulation result