iMechanica

I would like to share the research work I have been pursuing over the past four years. I believe, through this forum, I will be able to reach researchers with various backgrounds and expertise. Suggestions and comments from members will be very useful. I am also attaching links to preprints of manuscripts describing this work. Please follow these links:

http://www-personal.umich.edu/~vikramg/academic/Preprints/QC-OFDFT.pdf

The increasing use of fiber-reinforced composites accentuates the need for developing multi-axial fatigue failure models for these materials. In this article (attached), we proposed several multiaxial fatigue failure models for fiber-reinforced composites considering the contribution of mean and cyclic normal stress/strain and shear stress/strain at the plane of failure and examined their capability for predicting the fatigue life of the E-glass/epoxy composite materials.

A couple of years ago a colleague who wanted to simulate high-speed machining asked me: " Which is the best phenomenological flow stress model for metals?" I wasn't able to give an answer right away and decided to look in the literature.

What I found was, every ten years or so, a new model appears in the literature that tries to solve some of the problems of older models. However, a clear ranking of models has not been established yet.

I taught a short course some time ago on the eXtended Finite Element Method, and thought many people would find the notes useful.  

So I've posted them here, in .mov format (as exported with the Apple software keynote).  The advantage of this format is that, when you click on one of the .mov files, it should open a separate browser.  Clicking in the window will advance the slide. This way you see all the movies, etc, as well as the sequence as it appears when I gave the talk.  There is a way to add audio to this format as well - something I may pursue in the future.  

After the success of the course in 2005 (45 participants from 15 countries), the EPFL school of continuing education presents the second XFEM course.

I stumbled on this article in the NY Times "The Ultimate Distance Learning" (free registration required to view) about the establishment of University distance learning activities within the Second Life online community.

If you would like a copy of my lecture notes (on matrix algebra, indicial notation, vectors, tensors, vector calculus, groups, curvilinear coordinates and calculus of variations) they are available at

Using concepts of hierarchical multi-scale modeling, we report development of a mesoscopic model for single wall carbon nanotubes with parameters completely derived from full atomistic simulations. The parameters in the mesoscopic model are fit to reproduce elastic, fracture and adhesion properties of carbon nanotubes, in this article demonstrated for (5,5) carbon nanotubes. The mesoscale model enables one to model the dynamics of systems with hundreds of ultra-long carbon nanotubes over time scales approaching microseconds.

1. Introductory

Recently, there has been some active discussion on topics like:
-- Open-source textbooks
-- Comparing lecture notes
-- Unification of mechanics
-- Wikipedia and Citizendium

Most visitors/users of iMehanica will be aware of Wikipedia. Well, there is a new project of this kind underway. To quote from its "mission statement":

Since iMechanica went official on 9 September 2006, its growth has always been accelerating. As of 22 February 2007, the total number of hits on iMechanica reaches 1,000,000+, iMechanica has 1252 registered users, 908 posts and 1308 comments.

Lecture note of fracture mechanics of thin films and multilayers given at the Technical University of Denmark.

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Fracture in bone is a complex process that depends on the volume fraction (the relative fraction of bone tissue vs. void space), the architecture (the geometrical arrangement of the tissue), the mechanical properties of the bone tissue itself, and the applied loads. Theoretical approaches to the fracture of porous materials have been developed but their application to bone may be limited as they assume homogeneity of both the structure and the underlying material. The adaptation of the mechanical properties of bone to its loading history results in substantial heterogeneity of mechanical properties primarily due to the wide range of loads applied in the skeleton. Furthermore, bone diseases as well as pharmaceutical treatments for bone diseases can also affect the heterogeneity of material properties. All the above effects are intricately linked with bone micro-structure which incorporates collagen and mineral at the nanoscale in widely varying topological manners. With a wide ranging heterogeneity in length-scales of bone fracture it becomes imperative that fracture and failure analyses of bones are carried out at multiple lengthscales using a combination of modeling and experimental approaches. In this mini-symposium computational, experimental, and theoretical presentation of research on analyzing fracture of cortical as well as cancellous bone architectures are solicited. Presentations on computational and theoretical method development, experimental behavior characterization, and forming a link between theory and experiments are all strongly encouraged.

The six finalists for the 19th Annual Robert J. Melosh Medal Competition for the Best Student Paper in Finite Element Analysis were announced last Friday. They are

Baskar Ganapathysubramanian, Cornell University

A free surface in a multi-layer can experience an undulation due to surface diffusion during fabrication or etching process. In order to analyze the undulation, the elasticity solution for the undulating film is needed. Considering the undulation as a perturbation of a flat surface, a boundary value problem for 2D elasticity is formulated. The solution procedure is straightforward, but very lengthy especially for a multi-layer.

Attached is the first announcement and call for papers for "nanomech 8", the 8th European Symposium on Nanomechanical Testing to be held in Huckelhoven, Germany, 3rd-5th September, 2007. Full details are also available at the conference website. The special focus for this year's meeting is "Across the scales: Size effects and scaling phenomena in micro- and nano-mechanics". Abstracts are due 5th May, 2007.

Update: February 2012

1) The lecture notes are on Wikiversity at  http://en.wikiversity.org/wiki/Waves_in_composites_and_metamaterials

2) The book on the topic can be bought from Amazon at  http://www.amazon.com/Introduction-Metamaterials-Waves-Composites/dp/1439841578

3) Solutions and errata can be found at  node/9727

In this blog entry, I'll maintain a list of books, essays and websites that have influenced me in developing iMechanica. I'll also list my notes on them whenever available. Because iMechanica shares many common problems with other online communities, it is natural that we find solutions discovered by other online communities helpful. At the same time, iMechanica is unique in some respects, and has its own unique problems, so that we cannot adopt any methods or viewpoints without adjustment.

猪年：身体健康, 家庭幸福, 事业丰收!

As I promised, I start with some brief notes on themes loved by Ken Johnson to hopefully raise some interest for discussion on iMechanica. Regards, Mike