Write a MATLAB main function that will call subfunctions to accomplish the task described below.

All code must be contained within a single m$-$file and you should submit your lab m$-$file using Canvas.

Unless specified, you can handle the flow of the program however you choose.

Feel free to discuss the assignment, but you must do your own work.

Do not echo the results of the tasks below to the MATLAB Command Window.

Comment your work.

In mechanical testing, load cells and extensometers are often used to measure the response of a specimen to

loading. A load cell outputs a voltage that can be calibrated to measure load $($i$.$e$.$ force$)$ on a specimen.

Extensometers output a voltage that can be calibrated to measure the distance between the two extensometer

arms, which, when in contact with the specimen, will move when the specimen deforms and can be used to

measure specimen deformation.

A cylindrical specimen $($SI$-01)$ was glued into end caps for mechanical testing and tested using a transient

loading protocol consisting of a series of trapezoidal loading pulses followed by recovery periods. Deformation

data was collected using one load cell and $3$ extensometers: one extensometer $(E_1)$ was mounted across the

specimen end caps to record axial deformation and two and $\{$:$E_3)$ were mounted in contact with the specimen

to record deformation in two transverse directions. Data was collected at $200Hz$ for the length of the test $($e$.$g$.,$

data was collected every $\frac{1}{200}sec.$ for a time period before the specimens were loaded and then until the final

recovery period ended$).$ Extensometer data was recorded in $mm($after being converted from voltage$)$ and load

data was recorded in $N($after being converted from voltage$).$

Prior to testing, a set of deformation calibration equations were collected. All extensometer deformation $($d$)$ data

must be corrected by the following equations:

Extensometer $1$: $d_{1-\text{a}\text{c}\text{t}\text{u}\text{a}\text{l}}(mm)=0\mathrm{.}9924**d_{1-\text{m}\text{e}\text{a}\text{s}\text{u}\text{r}\text{e}\text{d}}+0\mathrm{.}00328$

Extensometer $2$: $d_{2-\text{a}\text{c}\text{t}\text{u}\text{a}\text{l}}(mm)={1\mathrm{.}3260}^{**}{d}_{2-\text{m}\text{e}\text{a}\text{s}\text{u}\text{r}\text{e}\text{d}}+0\mathrm{.}00696$

Extensometer $3$: $d_{3-\text{a}\text{c}\text{t}\text{u}\text{a}\text{l}}(mm)={1\mathrm{.}3765}^{**}{d}_{3-\text{m}\text{e}\text{a}\text{s}\text{u}\text{r}\text{e}\text{d}}-0\mathrm{.}000015$

Actual extensometer deformation data can be converted to strain data $($nondimensional$)$ by dividing by the

extensometer gage length. For $E_2$ and $E_3,$ the actual gage lengths $($gactual$)$ are determined as sum of

extensometer gage length and the average of the first $2000$ deformation measurements $($prior to load being

applied to the specimen$).$ The extensometer gage lengths for $E_2$ and $E_3$ are $7\mathrm{.}995mm$ and $8\mathrm{.}010mm,$

respectively. For $E_1,$ the $($effective$)$ gage length is determined as sum of the exposed length of the specimen

$($i$.$e$.$ length visible between the end caps$)$ and half of the length of specimen embedded within the endcaps. The

total length of the specimen was $24\mathrm{.}13mm$ and the length exposed between the end caps was $13\mathrm{.}72mm.$

Load cell data $(N)$ can be converted to stress data $(MPa)$ by dividing by the specimen area, with $1$MPa$=1N/$

$m{m}^2.$ The diameter of the cylindrical specimen was estimated as the mean of $g_{2-\text{a}\text{c}\text{t}\text{u}\text{a}\text{l}}$ and $g_{3-\text{a}\text{c}\text{t}\text{u}\text{a}\text{l}}.$

Tasks

Subfunction $1$: Read in the data $($provided in SI$-01.$xIsx$).$ Correct extensometer data and determine strain

data, as described above, using anonymous functions. $($Use one anonymous function to correct data for all

extensometers and use one anonymous function to determine strain for all extensometers$).$ Determine stress

data, as described above, using an anonymous function. Calculate a time vector for all recorded data

assuming that data collection started at time $=0sec.$

Subfunction $2$: Plot stress data and extensometer data as functions of time in individual plots all within the

same MATLAB figure. The stress vs time plot should be at the top of the figure with strain vs time plots

below in extensometer order $($e$.$g$.E_1,$ then $E_2,$ then $E_3).$ Label axes for each plot appropriately. Include a

title giving the specimen name at the top of the figure $($over the stress vs time plot$).$