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Exact relations in the micromechanics of composites

There are several exact relations from the theory of composites that can be used to determine whether a new numerical or analytical approach gives reasonable answers. Here's a paper on some exact relations that I wrote up a long time ago and just recently posted on Scribd. 

PDF icon iutam.pdf169.78 KB
PDF icon icm98.pdf160.12 KB


Thanks for posting this for us.

I suppose I should offer an apology now: first, I did not read your paper; second, I'm going to talk about your medium rather than your message. (Third, I might apologise for complaining at all!)

I am curious why you chose Scribd to show us your paper. Did you want to keep some control over your work, or did you just wish to use it for convinience or some reason like that? I had intended to at least skim your paper, but I found it difficult to see and navigate.

I hope you don't mind my hijacking your thread a bit, but I'd be interested in hearing if others have anything to say about Scribd.

Hi Mike,

Thanks for the feedback.  I've gone and changed the fonts and the size of the window.  Let me know whether the paper is readable now - it looks OK on my Firefox/Ubuntu and downloads reasonable fast given my slow internet connection.   Some of the equations look strange .. but the pdf version of the paper can be downloaded from Scribd if needed.

The idea behind using Scribd was to have a version of the paper that people could take a glance at without having to download a pdf file.  And hopefully get people to re-examine some exact relations for composites which are not well known outside the applied mathematics community.


Thanks for changing that—it made it a lot more readable for me (also on Ubuntu/Firefox). The document was easier to see and to navigate. I had went to Scribd to try to find a downloadable pdf, but I did not see one. The print function also does not seem to work for the whole document, but that might be a problem with Flash being quirky.

Incidentally, that did let me  read the paper some. I might come back with a few remarks.


Many thanks. Smile

For Mike and others who may be interested, here's the direct link to the paper on Scribd: 

For more on exact relations I'd like to point you to Graeme Milton's page , particularly the papers titled

Composites: A myriad of microstructure independent relations

Exact relations for composites: Towards a complete solution
.  And of course Graeme's excellent text called "The Theory of Composites".   The papers are in postscript form.  I've taken the liberty of converting them to pdf and attaching them to the original post (though I'm not sure whether that's kosher).

-- Biswajit 



Thank you for the link to the pdf directly. I kept looking on Scribd to find such a link, but I could not find it until I just looked again. I feel even more silly having seen it.

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