2. Matlab Applications 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) a) Parameter estimation (curve fitting)* 0 1 )) exp( 1 ( t t J J ret Where J is the strain, J 1 is the retarded compliance (Pa -1 ); λ ret =µ 1 /G 1 is retardation time (s); µ 0 is the free dashpot viscosity (Pa s); t is the time. Note: creep is the tendency of a solid material to slowly move or deform permanently under the influence of stresses.
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2. Matlab Applications
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)
a) Parameter estimation (curve fitting)*
01 ))exp(1(
tt
JJret
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.
Note: creep is the tendency of a solid material to slowly move or deform permanently under the influence of stresses.
2. Matlab Applications
Parameter estimation - Creep compliance Experimental Datat, Time (s) J, Strain (Mpa^-1)
300 0.17600 0.265900 0.318
1200 0.3481500 0.3661800 0.3762100 0.3822400 0.3862700 0.3883000 0.393300 0.3923600 0.3933900 0.3954200 0.3964500 0.3974800 0.3985100 0.45400 0.4015700 0.4026000 0.4036300 0.4046600 0.4056900 0.4067200 0.408
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
Method 1) Using Excel Solver
04/18/23 3
Method 2) CFTtoolbox
Use the command of >>cftool
Parameter estimation - Creep compliance
3. Simulink
The graphic interfaces
Matlab
Simulink
Type “simulink” in the command window
Tutorial example
04/18/23
x = sin (t)
simout
Simulink example 2
Creep compliance of a wheat protein filmUsing formaldehyde cross-linker
Creep compliance of a wheat protein film (determination of retardation
time and free dashpot viscosity in the Jefferys model)
01 ))exp(1(
tt
JJret
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):
)exp( 11
ret
ttJJ
Where t1 is the time the stress was released.
Parameters: J1 = a = 0.38 Mpa-1; λret = b = 510.6 s; µ0 = c = 260800 Mpa s; t1=5000Solve using Simulink model
4. Simulink examples
Creep compliance of a wheat protein film
Simulation result
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