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