project from solid mechanics

It might help others to make suggestions to you if you make a list of courses that you have taken in solid mechanics.  You can also find some student projects posted on iMechanica.  The are projects for a first year graduate course in solid mechanics

I don't know exactly what's your definition of basics of solid mechanics, like those can be found in text books or literatures? Or you would like to do some oringinal work?

For Mohr's circle you may consider 3D case and prove the valid area is that bounded by three circles.

You may also try finite element method, vibration, waves or large deformation.

As Zhigang suggested, to have a look at http://www.imechanica.org/taxonomy/term/307

about 1st year graduate students' elasticity projects will help a lot. 

Dear Tuhin,

I will try to help you with your problem, I think the best way to help you is to present some way to educate yourself in the field of fracture mechanics, since both of your suggested topics lie within this field. Of course, stay on imechanica for more interesting topics!

Despite the fact that I don't know your level of overall knowledge or even expertise in solid mechanics. If you are really new to this field, you might first consider a course or some courses on continuum mechanics, (elasticity theory, maybe plasticity, etc.) If you are already familiar with tensor calculus and some solid mechanics basics, you should take a look at this link http://www.mate.tue.nl/~piet/

Click Fracture Mechanics > Sheets This link is the online course material of a course I took on fracture mechanics in my home university in Eindhoven, The Netherlands. Topics are listed and you can easily educate yourself a way into this field, which in a few days should lead to a profound understanding of the project descriptions presented to you.

I hope my advice can be of some assistance in your decision-making process.

Best regards,

Martijn

(I) Experimental Study of 2D Stress Fields

The objective is to develop a first-hand understanding of how the stress field is related to the strain and displacement fields, esp. in a 2D situation.

Take a thin sheet of rubber. You may obtain the piece after cutting a large balloon. You may also want to try the very inexpensive pieces of discarded tubes of truck tires available near any mechanic shop.

Fix a flat rectangular piece of rubber with suitable adhesive to two flat solid battens (e.g. wooden or plastic rulers usually found in the school compass-box).

Firmly attach one of the two battens to some stationary object protruding outside like a cantilever (e.g., drop the assembly from a side of a lab desk).

Firmly fix a cardboard box (or a plastic lunch-box) to the bottom batten.

Fill the box with sand. The box will serve to statically load the rubber sheet through the battens. The advantage with using sand is that you can increase the load so very gradually. (But take care to fill it slowly and uniformly so as not to generate moments in the batten!)

(i) Using sand portions of pre-measured (known) weights, find the load-displacement curve. Here, you may want to use thin long strips of rubber--not "rectangular sheets". Look up the rubber strength data in handbooks and find out in advance the largest section that you could take to the breaking point with manageable weights. For rubber, the load-displacement curve won't be linear. So, you will have to repeat the experiment a number of times to get good repeatability, esp. at points on the graph where the local slope undergoes changes.

(ii) Analyze how you will apply statistics to the experimental data here. Note, due to nonlinearity, you will need something more than the plain least-squares fit. Hint: Bring in measures of confidence level. Use scatter plots imaginatively in your presentation.

(iii) Develop numerical programs in the language of your choice to do statistical analysis and to find the curve of best fit.

(iv) This is very interesting. Start with a large rubber sheet. Mark a square grid (or only the grid points) with a ball-pen, or screen-print one on the rubber sheet, in its undeformed state. (If screen-printing, take care that the bulge due to printing does not interfere with mechanical properties.)

Then, load the sheet using sand and photograph the grid at various loading levels. (Perhaps, even a digital camera in a mobile phone could give you enough resolution.)

Measure the displacement of each grid point from the photograph. (Take care to include a fixed ruler or so within the field of the photograph for comparison sake.)

Calculate the strain field from the measured displacement field.

Calculate the stress field from the strain field. Use the stress-strain curve obtained in the above step for this purpose. (This could be interesting out of the non-linear stress strain curve for rubber.)

(v) Now, think of putting a hole in the sheet. Take one shape at a time, e.g. circle, square, etc. Again experimentally draw the regularly spaced grid and photograph the deformed shape. (Ensure the grid is finer near the hole.) Find out stress concentration. Compare it with the theoretically predicted value.

(vi) Observe if you find any other effect such as wrinkles in the sheet, striations due to thinning, any other visible effect--its nature, orientation, effect on your measurements, etc. That is to say, learn to find any systematic spurious effect present in your measurements and to record it straight-forwardly, with as much precision as is possible to you in your circumstances.

(vii) If you make a poster presentation out of this, make sure to include Mohr's circle representations for the state of stress at a few well selected points.

(viii) Think about this whole series of measurements and correlate it to the concepts you are being taught in your solid mechanics course. For example, ask yourself that if the material is, unlike rubber, very stiff, and so the relative displacements almost zero, why would you still use displacements as the primary unknown? Would there be any advantages doing that?

(II) A Coarse Approximation to 2D Stress Field

Here I am deliberately deleting the experimental details to let you have all the fun. The idea is to use that piece of foam which is meant for washing dishes at home. The piece of foam deforms easily and comes in the right, brick-like shape.

Keep it on a desk, constrain it from deforming over the vertical three sides, and press horizontally from the remaining side using a punch. The punch should have a bulge in the center so that the middle portion gets pushed to a greater extent. Think of getting a punch in a shape of known curve such as parabola.

Overall, in the language of BV problems and solid mechanics, you are imposing displacement constraints.

Then, the idea is to find the non-uniform deformation of the foam under the above boundary conditions.

How would you experimentally measure that? I will leave the matter to your creativity, but note just one point. If you insert a pin (i.e. pin and not a safety pin) all the way into the foam, it won’t distort the foam a lot. Yet, its head will come out prominently in the photograph because it will be quite shiny. But also feel free to think of alternatives—including not marking the foam with anything at all, but just using a high resolution photograph. (The coarse foam walls could show up like an irregular but neatly drawn grid!)

Now, repeat the steps from point no. (iv) in (I) above, and, after making suitable assumptions, infer the state of stress at different points in the foam.

(III) Fracture Studies of a "Composite Material"

We want to study failure criteria and fracture behavior. This experiment is going to be sweet. Literally!

Get a box of "chikki" or "gud-dani" i.e. the Indian sweet consisting of peanut pieces embedded in a matrix of jaggery. The chikki is a great candidate for composites study.

Take suitable sized pieces. (Find creative solutions to the problem of getting pieces of a specified size.) Experimentally break these pieces using known weights under various arrangements or configurations. For example, you may find the 3-point bend arrangement to be suitable. Other possibilities are: cantilever loading; out-of-plane point loading in the center of a square plate clamped on all its four sides; etc.

Digitally photograph the piece of “chikki” both before and after the experiment. This will be your "micrograph” of sorts. Actually, it will be a macrograph, so let’s call it by that name. Also photograph the fracture surface.

Discuss with some teacher from your Metallurgy department to find out how you can use stereological methods to estimate various surface areas starting from your macrographs.

Conduct experiments to find out if the cracking preferentially occurs within peanuts, within jaggery, or if the matter is uncertain (i.e. if there is no preference for the crack path to go through one of the two constituents). If the cracking is preferential, report it using suitable quantitative measures: e.g. percentage number of cracked peanuts, the fraction of peanuts found in the fracture-exposed surface vs. their overall volume fraction, the area-fraction of cracked peanuts, etc.

You may want to report on the interfacial strength. Find if these measurements differ under various kinds of loadings (e.g. slow vs. impact--as delivered by a hammer swinging from a known height as in impact testing.)

Correlate these measurements with volume fraction of the second phase i.e. peanuts. Finally, find out which one of the failure theories from mechanics of solids suits best to your experimental findings.

Compare the strength and fracture behavior of "chikki" composite with plain jaggery of the same batch and lot.

In any case:

If you take any of this up for your actual project, do send me your experimental raw data and also the final report. (I may find other uses for that material.)

If the observational material obtained by you is large enough, and if it looks good enough (say, if you obtain it with the help of some experienced person like a PhD student and/or a faculty member), then, go ahead and publish a paper!

In any case, never forget--you read it here first, and from me!

Other Matters

Other routine project ideas would be: (i) assisting PhD student/faculty member in conducting photo-elasticity experiments; (ii) assisting some PhD student/faculty member in computerized data acquisition, say of strain-gauge outputs; etc.

Yet, I think, nothing would beat the excitement of doing the above home-grown variety of projects. Of course, refinements or alternatives to the above ideas are possible, and should be pursued.

Feel free to contact me by email for further discussion--but only after you have seriously decided to pursue the above ideas.

Finally, yet another (minor) matter. This is not a C/Unix programming forum. I suppose many people (perhaps a majority here) expect to see messages or posts written using mixed cases (i.e. as in plain English). So, I guess, you should take care to type in the uppercase letters too--especially if it's you who is making the request. (It would be a different story if you were replying!)

The reason on avoiding all lowercase messages is simple. Normal English (i.e. mixed case writing) is easier on the eyes because it does break down the monotony of reading. Anything that helps one "take in" larger blocks of material, i.e., facilitates speed-reading, is better. You can't do that with the all lowercase messages. Take that care in future.

Best wishes for your project!