Suggestions for predicting the displacement of a graph or force estimation.

Stelios Fanourakis 님이 질문을 제출함. 13 Oct 2019

최근 활동 Daniel M 님이 댓글을 추가함. 21 Oct 2019

조회 수: 2(최근 30일)

Hello

This question is aimed mostly to engineers but whoever believes he can handle it may give his valuable advice.

I have a tabular data set of Load/Displacements in Newton/mm of a material using an Instron Machine, applying compressive forces.

Those data are my reference or gold standard. The same material is depicted on images where unknown forces are applied to the object and the object deforms as it is a rubber material. I want to estimate the forces caused that deformation.

My idea is developing a model that measures each column of the image that the object is depicted under strain. I measure the heigh of the object in each image column and find the difference from the gold standard that I have. Sounds simple right? I was thinking an interpolation method to bridge the gaps between the gold standard and the measured data from the images. E.g. if the gold standard data for 5 Newton is 2 mm displacement from its original position (undeformed material), then how many newtons are required to displace the same object at 5 mm from its original position. Something like that.

Can you help with suggestions and ideas please?

Thanks in advance

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Daniel M 13 Oct 2019

This is a cool idea. I think it is pretty straightforward, although I don't have any experience with image processing. So the basic idea, is you have data of stress vs strain, and you know that Hooke's law describes the behaviour during the linear portion of the curve (before plastic deformation occurs).

So, get a fit for the linear portion. Since it is linear and there is no force at rest, it should literally just be y = mx. Then process your images to get displacement (x), and plug it into your model and it should output the stress.

I'm sure you could try to create a model to include the nonlinear aspects too. But it would be very complicated to do from first principles. You would probably be better off just doing a spline. But the plastic region of your data will have a much higher variance than the elastic, so this could make it tricky. Hope you have a lot of data.

So, no need to interpolate, do it properly and for your data. You will need a different fit for each material though, because they will all have their different properties such as Young's modulus and futility, yield strength, strain-hardening etc. And I'm not sure where you will apply this too, because real-life material behaviour can vary from a lab setting. Materials in real applications can have defects, degradation, different climate, etc.

Daniel M 21 Oct 2019

Is stress not just force divided by cross sectional area?

Do NOT use a 7th order polynomial for anything. Create a function that describes your model, fit the coefficients of your model for each material you have. Then when you need to get stress from a displacement, just plug it into the function you have created with the corresponding coefficients. You do not need to interpolate anything if you have a parametric equation describing the characteristics of your system.

Stelios Fanourakis 21 Oct 2019

In other words you tell me to use only the Ogden model. Maybe modified to give me stress out of loads and strain out of displacements.

stress = force / area is for linear objects. Mine since is a nonlinear one, should be more complicated

Daniel M 21 Oct 2019

I suggest you try and get your pipeline working on a simple, linear material first. Then, once you have confirmed it works the way you like, to go back and upgrade it to the nonlinear regime.

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