Stress Strain Fitting...(former Arrays)

>is easier to read the independent values on the horizontal scale and the dependent ones on the vertical one.<<br>
The independent variable is the pressure you apply, it plots on X
The dependent variable is the deformation, it plots on Y



You should worry most about the data you have collected, many of them show an unexplainable pressure cycle. Some you can defend and I can accept, typically the one I have worked. What you are not saying is about the pressure cycle you apply or attempt to apply [I mean the ones that makes sense]. That pressure cycle pattern, does it comes from a standard in that kind of testing or does it come from some invention. Up to the fracture, if you apply a linear pressure, it will surely fit well.
The other point is that you will not interpolate via "linterp" or a bspline [interp] on the non ascending part of the pressure cycle, unless the data are split and transformed . The attached demonstrates how to interpolate the ascending viscoelastic sites. The part after [polyline] is for a total pressure cycle in parametric form.

>My main goal is to see the best curve to fit experimental data. That is why, in the first place, I'm studying what others have proposed (i.e. Wang et. al). <<br>
The best fit up to fracture will largely depend upon the ascending pressure . When you plot sin(x), x is supposed linear. Sometimes transforming the independent variable helps the fit. You refer to Wang et al. but you haven't attached the PDF or else link to what you are reading, just to make sure it is understandable, and technically correct. Does Wang give the form of the pressure cycle or is it an invention. Why don't you make it linear up to the fracture ?

The last plot is a 2/2 rational approximation.

jmG

On 5/2/2010 3:28:18 PM, dvmoldovan wrote:
>The attached is the latest
>form for my calculations.
>Since some mistakes have found
>there way in (I'm sorry again
>for that, only today I
>"discovered" them), I feel
>it's mandatory to correct
>them. Insired by the work of
>jmG (thanks) you'll find some
>graphs at the end...
>
>Kind regards, Dumitru
______________________________

Mathcad is essentially a 0 ORIGIN based tool. Changing ORIGIN to 1 will result in many collabs not even considering the project. If you have done too much maths in ORIGIN 1, don't expect collabs to make your maths work to accommodate their help in ORIGIN 0. Your plot are in the reverse order, i.e: the independent variable "Load" plots on the Cartesian X and the dependent variable [deformation] plots on the Cartesian Y. The way you plot is not visible by inspection and it has to be re-plotted. Your data are still very confusing. No matter how much I have done, nothing is correct on the ground that you don't apply linear "Load pressure" but on a ramp basis, and some "Load pressure" are totally non sense. That means that fitting will be lot more difficult if the independent experimental variable is not linear. Explore the next graph and check the data that must be rejected. Altogether, there may be only one data set needed, and here again why not linear "Load pressure". So, before any math processing, make sure to consider only one data set for only one specimen. Then decide about more specimen and either check the "Load" is correct or run the experiment again. But in any and all cases, you have too many values from lab test::: What you are doing with the ramp load, you are collecting [stacking] a fine and a coarse experimental data set and that is not correct because for analysis, the collection has to be reverse engineered, undoing what shouldn't have been done in the first place.

This project looks simple but it is upside down.

It could be that the rational fraction represents the viscoelastic model for concrete. It shouldn't be more difficult to solve than the simple Maxwell model. As it looks, you are applying a pressure cycle but of such bizarre shape. Why not a simple triangular cycle. That would render the project visible by inspection with no torture of the mind and eventually with a non mirror return of the decreasing load, the deformation might be meaningless.

"In this pressure cycle that does NOT make sense unless justified, it can be seen that the deformation has in some ways followed the pressure load. In simple words: the specimen experimented is 'elastic'. "

jmG

On 5/4/2010 3:21:17 PM, rijackson wrote:
>On 5/4/2010 2:14:47 PM, dvmoldovan
>wrote:
>>Yes, richard that is what I
>>need. When talking about
>>column 2 you are referring
>>to..(what column/ in which
>>sheet?).
>
>It is getting hard to keep track of
>everything! Set c=2 in this sheet to see
>the data I am referring to:
>
>http://collab.mathsoft.com/~Mathcad2000/
>read?134452,11#134462
>
>Richard
________________________________

The Minerr Paul W. was passed in two styles: the short style as in the work sheet in reference, and the NULL style. The fastest when it works is the short style. However many fits will not be possible in short style, so here is the NULL style. The vector of initial values must be collected in vector, this is so because lots of fit can't go direct LM but a good approximation is obtained sometimes CG, sometimes QN ... thus much easier to plug coeff's. And because there is always an "AND", too many fits can only be done manual, thus you must be able to collect quite a few fits in vector.
In Mathcad it's best practice to respect the position of the arguments and parameters. Nothing wrong y(x,A,B,C,D) but it's not correct and creates lots of problems especially in collaboration ... it should be y(A,B,C,D,x).

Same remark about ORIGIN that should be left 0.

To fit a "normalised rational", only the first term need be valued, generally the value 1 is OK. Not detrimental in this 0...1 range of 'x' but it will soon fail with a much higher range of 'x' because if the higher order monomials are valued it pushes the solver out of capability.

Nothing wrong with the work sheet in reference, but not a model to follow, at least not for beginners learning "curve fitting" in Mathcad.



jmG

On 5/5/2010 7:51:16 AM, dvmoldovan wrote:
>Today I took the files as
>originated during testing and
>did a manual analysis on them.
>You were right Jean...the data
>was inconsistent (apparently
>the export to excel modifies
>the type of data from numbers
>to general). I also deleted
>steps that repeated themselfs
>so...the result
______________________________

Read carefully:

Mathcad was designed by visionary designers. They may never become as celebrated as Fourier, Laplace ... etc. Nevertheless, these guys were "Mathematicians". The Minerr is repertoried in the "Numerical Recipes", but it looks the Mathcad Minerr is a more powerful version. What I have done here is in gray and 'j yellow'. If you enable the 2nd constraint condition, it will force in some way the fit. The j 197 belongs to the 2nd data set, the value =1 is just demo, you could force by any unknown value to your appreciation " that is my fit to conserve".
There would be other ways to fit that rational, but too early. If you would want to fit globally, the fit can be wrapped in a piece of program that will do all at once, but you won't be able to force individually for a specific "forced plot". This fit is typically a "Gaussian" that might eventually fit better. But that will deviate [probably for better] from the Wang suggestion. Wang might have been short of models ?
Now you can see my point last night about "solving essentially equates to 0" and what I said about the 0 not necessarily being 0 but otherwise to accommodate a fit. Another point is about the text box , sometimes it's valuable to plug a solver in a text box, but usually it is of no advantage. If you have to push some regions down, you must leave some left margin to the text box, otherwise you can push only one step at the time, because the pointer always goes back the left and re-enters the text box and that screws things .

Resume:
j197 is for demo the 2nd data set, play with it for that fit and play with the conditional block = -1 or else to view the action.
Deactivate the 2nd conditional block to explore the other fits. You can leave the j 197, it will have no action on the fit and it will not turn the plots red because all the data set have > 197 points

About the text box:

It makes Mathcad read like newspaper, i.e: reads/calculates the text box top to bottom then jump on the right of the text box. Very convenient to put the working maths in text box and have the plot next right, like in text books. Text box it one of the features that makes Mathcad so gorgeous for technical presentation.

I will be out for the day, but that fitting session is in good hands with your new/revised data. Rational fractions tend to produce glitches. So, make sure you increment fine enough to insure no undesirable glitch appear, unexpected. Your ORIGIN didn't pest me up until now, but it will soon. There are some instances ORIGIN must be 1 or else but you redefine at the point needed in the work sheet and turn it back to 0 as soon as done with it. Where does that crazy ORIGIN= 1 comes from ? Just figure that many collabs have 1000's of modules based on ORIGIN=0 and every time they would have to adapt for helping "heretic visitors" , no way.

There is a lot of red in the 11 conversion, it might be that you have to define Mpa.

Jean

The results I obtained are consolidated in a way that the numerous Web sites discuss this problem.

Thanks for the clarification of the problem. With limited knowledge of the physical properties of the clay-aggregate cement mixture, plastic and chaotic deformation flows, I have shown the curve fits for these two regions and ignored the very meaningless part above the peak.

A relative of mine was West Virginia State Road Commissioner long ago, and I know the procedures he used to survey the tensile strength of small samples cast in a butterfly shape. We show treated wood small rural bridges outlast the old narrow rebar concrete bridges on the highways.