2 Matlab Applications a Parameter estimation curve fitting

2. Matlab Applications a) Parameter estimation (curve fitting)* v Different ways to estimate parameters v excel “solver” v. A graphical user interface (curve fitting toolbox) v Matlab command (nlinfit or fmincon) v Example v Creep compliance of a wheat protein film (determination of retardation time and free dashpot viscosity in the Jefferys model) 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, J 1 is the retarded compliance (Pa-1); λret=µ 1/G 1 is retardation time (s); µ 0 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. 392 0. 393 0. 395 0. 396 0. 397 0. 398 0. 401 0. 402 0. 403 0. 404 0. 405 0. 406 0. 408

Method 1) Using Excel Solver 11/5/2020 3

Method 2) CFTtoolbox Parameter estimation - Creep compliance v Use the command of >>cftool

3. Simulink Type “simulink” in the command window The graphic interfaces Matlab

Tutorial example x = sin (t) simout 11/5/2020

Simulink example 2 Creep compliance of a wheat protein film Using formaldehyde cross-linker v Creep compliance of a wheat protein film (determination of retardation time and free dashpot viscosity in the Jefferys model) Where J is the strain, J 1 is the retarded compliance (Pa-1); λret=µ 1/G 1 is retardation time (s); µ 0 is the free dashpot viscosity (Pa s); t is the time. v The recovery of the compliance is following the equation (t >t 1): Where t 1 is the time the stress was released. Solve using Simulink model Parameters: J 1 = a = 0. 38 Mpa-1; λret = b = 510. 6 s; µ 0 = c = 260800 Mpa s; t 1=5000

4. Simulink examples Creep compliance of a wheat protein film Simulation result