iMechanica

In the attached paper, we have used Variational Analysis techniques (in particular, the theory of epi-convergence) to prove the continuity of maximum-entropy basis functions. In general, for non-smooth functionals, moving objectives and/or constraints, the tools of Newton-Leibniz calculus (gradient, point-convergence) prove to be insufficient; notions of set-valued mappings, set-convergence, etc., are required. Epi-convergence bears close affinity to Gamma- or Mosco-convergence (widely used in the mathematical treatment of martensitic phase transformations). The introductory material on convex analysis and epi-convergence had to be omitted in the revised version; hence the material is by no means self-contained. Here are a few more pointers that would prove to be helpful. Our main point of reference is Variational Analysis by RTR and RJBW; the Princeton Classic Convex Analysis by RTR provides the important tools in convex analysis. For convex optimization, the text Convex Optimization by SB and LV (available online) is excellent. The lecture slides provide a very nice (and gentle) introduction to some of the important concepts in convex analysis. The epigraphical landscape is very rich, and many of the applications would resonate with mechanicians.

On a different topic (non-planar crack growth), we have coupled the x-fem to a new fast marching algorithm. Here are couple of animations on growth of an inclined penny crack in tension (unstructured tetrahedral mesh with just over 12K nodes): larger `time' increment and smaller `time' increment. This is joint-work with Chopp, Bechet and Moes (NSF-OISE project). I will update this page as and when more relevant links are available.

From this Modern Mechanix scan of a 4 page article from the 1924 issue of Popular mechanics, we learn about Lincoln, the inventor!

Biasing reaction pathways with mechanical force, Charles R. Hickenboth, Jeffrey S. Moore, Scott R. White, Nancy R. Sottos, Jerome Baudry & Scott R. Wilson, Nature 446, 423-427 (22 March 2007).

The New York Times Magazine this weekend featured a Harvard undergraduate student from China, and her work to shake up education in China. The article is long, but if you grew up in China, it should be a quick read, and fun. If you grew up in US or Europe, perhaps this is a helpful read, just to learn how other people live.

Appl. Phys. Lett. 90, 133119 (2007)
Mechanics of Precisely Controlled Thin Film Buckling on Elastomeric Substrate

Laguna Beach, CA March 31, 2007 -- Kebaili Corporation a leading California based high-tech company announced today the release of the CPG-500 Series, the industry first compact current pulse generator, specifically designed for electrodeposition applications, such as (direct current) DC plating, pulse plating, and periodic reverse pulse plating for a variety of applications in MEMS and nanotechnology.

The molecular building blocks of a cell include:

What boundary conditions would allow failure to occur in the gauge length and not at or near the clamps? One is not allowed (in suggesting ways of overcoming stress concentation at the clamps) to create defects in the nanotube or nanowire, to configure the region where failure will occur.  Thus, it is not possible (or is it?)  to create an analog of dog-bone specimens by, e.g., milling away part of the nanowire with a focused ion beam, etc., because this creates defects in the nanowire.

Science 30 March 2007:
Vol. 315. no. 5820, pp. 1831 - 1834
DOI: 10.1126/science.1137580
Jagannathan Rajagopalan, Jong H. Han, M. Taher A. Saif*
In nanocrystalline metals, lack of intragranular dislocation sources leads to plastic deformation mechanisms that substantially differ from those in coarse-grained metals. However, irrespective of grain size, plastic deformation is considered irrecoverable. We show experimentally that plastically deformed nanocrystalline aluminum and gold films with grain sizes of 65 nanometers and 50 nanometers, respectively, recovered a substantial fraction (50 to 100%) of plastic strain after unloading. This recoverywas time dependent and was expedited at higher temperatures. Furthermore, the stress-strain characteristics during the next loading remained almost unchanged when strain recovery was complete.These observations in two dissimilar face-centered cubic metals suggest that strain recovery might be characteristic of other metals with similar grain sizes and crystalline packing.

Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.

I'm now working on the preparation and characterization of self-healing polymers, a promising branch in materials science. The following is a general conception of this kind of materials system. (Pasted from our group website http://www.autonomic.uiuc.edu.) I may introduce some of my current work later.

I found very interesting web site (at least for me). That is World Universities’ ranking on the Web (WR).

Our current ability to accurately measure ventricular global contractile behavior remains unsatisfactory due to the lack of quantitative diagnostic indexes that can assess the mechanical properties of myocardial tissue.

A systematic characterization of the motion and friction of a linear bearing with rolling elements used for nanopositioning reveals an explicit distinction of static and rolling friction. The effects

For the polymer-supported metal thin films that are finding increasing applications, the critical strain to nucleate microcracks ( εc ) should be more meaningful than the generally measured rupture strain. In this paper, we develop both electrical resistance method and microcrack analyzing method to determine εc of polymer-supported Cu films simply but precisely. Significant thickness dependence has been clearly revealed for εc of the polymer-supported Cu films, i.e., thinner is the film lower is εc . This dependence is suggested to cause by the constraint effect of refining grain size on the dislocation movability.

I’m delighted that mechanicians now have this platform to discuss our work as well as share ideas and perspectives. While we advance knowledge in our field and come up with innovative solutions for engineering and materials problems, I believe that we also have a responsibility to speak on issues of global significance, especially where the power of science and technology can be harnessed to address challenges and issues impacting the world.

Rubber or rubber-like materials, or generally elastomers, sustain large elastic deformations. The problems of such cases are non-linear, the non-linearity came from two sources, the first one due to materials, and the second is geomertrical non-linearity. Elastomers are, also, viscoelastic, i.e. time and temperature dependent.

Recently I received a message from the Cambridge University Press regarding a coming text on biomechanics entitled Introductory Biomechanics, From Cells to Organisms. by C. Ross Ethier and Craig A. Simmonds. I ordered an exam copy, went through, and found it very interesting. It covers cellular biomechanics, hemodynamics, circulatory system, ocular biomechanics, muscles and movement, and skeletal biomechanics. Each section has a significant number of problems. I examined closely the part on cellular biomechanics which is one of the main areas of my research and teaching interests, and enjoyed reading it. The cellular mechanics is presented in its interrelation to cell structure and biology (there are nice images of cells and their components to use for teaching). The main techniques of probing the cell, such as micropipette aspiration, AFM, optical tweezers, and magnetic cytometry, are considered. Models of the cytoskeleton (tensergity, foams) are also introduced. The math is limited to linear equations, one-dimensional or axisymmetric problems, but it seems appropriate for the introductory level. In addition, some results of computational (finite element) modeling are also included. I certainly expect that this textbook will be quite useful in my teaching. The web site http://www.cambridge.org/us/catalogue/catalogue.asp?isbn=9780521841122 has more details on the book.

As another celebration of March Journal Club of Mechanics of Flexible Electronics, this paper has just been submitted.

Abstract 

In one design of flexible electronics, thin-film islands of a stiff material are fabricated on a polymeric substrate, and functional materials are grown on these islands. When the substrate is stretched, the deformation is mainly accommodated by the substrate, and the islands and functional materials experience relatively small strains. Experiments have shown that, however, for a given amount of stretch, the islands exceeding a certain size may delaminate from the substrate. We calculate the energy release rate using a combination of finite element method and complex variable method. Our results show that the energy release rate diminishes as the island size or substrate stiffness decreases. Consequently, the critical island size is large when the substrate is compliant. We also obtain an analytical expression for the energy release rate of debonding islands from a very compliant substrate.

A typical two phase microstructure consists of a topologically continuous `matrix' phase in which islands of `precipitate' phase are embedded. Usually, the matrix phase is also the majority phase in terms of volume fraction. However, sometimes this relationship between the volume fraction and topology is reversed, and this reversal is known as phase inversion. Such a phase inversion can be driven by an elastic moduli mismatch in two-phase solid systems. In this paper (submitted to Philosophical magazine), we show phase inversion, and the effect of the elastic moduli mismatch and elastic anisotropy on such inversion.

During solid-solid phase transformations elastic stresses arise due to a difference in lattice parameters between the constituent phases. These stresses have a strong influence on the resultant microstructure and its evolution; more specifically, if there be externally applied stresses, the interaction between the applied and the transformation stresses can lead to rafting.