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":

The Citizendium (sit-ih-ZEN-dee-um), a "citizens' compendium of everything," is an experimental new wiki project. The project, started by a founder of Wikipedia, aims to improve on that model by adding “gentle expert oversight” and requiring contributors to use their real names.

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.