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N. Sukumar's picture

Epi-convergence (max-ent bases), crack growth

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.

Amit Pandey's picture

2007 Karl Terzaghi Award

C. S. Desai Is Recipient of the 2007 Karl Terzaghi Award

The recipient of the 2007 Karl Terzaghi Award, to be presented at GeoDenver, is Regent's Professor Chandrakant S. Desai. Besides countless achievements, Prof. Desai was the founding General Editor of the International Journal for Numerical and Analytical Methods in Geomechanics from 1977-2000. Prof. Desai is President of the International Association for Computer Methods and Advances in Geomechanics (IACMAG). Congratulations for a well-deserved honor!.

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Zhigang Suo's picture

Education in China and in America

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.

The Industry First Compact Reverse Pulse Plating Controller for R&D Applications in MEMS and Nanotechnology

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.

iMechanica get together at McMat 2007

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Time: 5:45 pm - 7:00 pm, Wednesday, 6 June 2007.

Place: TCC 2.120 , UT Austin. (The room is reserved form 5:45 pm to 10:00 pm.)

Session moderators: Rui Huang and K. Ravi-Chander

Audience: Anyone interested in iMechanica. See a thread of discussion initiated by Pradeep Sharma. The event is free for all. So if you are local but are not attending McMat, you are still welcome to drop by.

Is it possible to obtain (without modeling) the fracture strength of defect-free nanotubes or nanowires by tensile loading?

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.

Plastic Deformation Recovery in Freestanding Nanocrystalline Aluminum and Gold Thin Films

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.

Self-healing polymers - an introduction

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 I may introduce some of my current work later.

Arash_Kheradvar's picture

Characterization of myocardial viscoelastic behavior based on ventricular harmonic motion

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 posteriori error estimation (indication) for extended finite element methods (XFEM)

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Extended finite element methods (XFEM) have been employed in computational fracture mechanics contexts since their inception in 1999. Although some work has been performed, leading to the first adaptive strategies for the generalised finite element method (GFEM), little or no work has been published on error estimation and adaptive approximations for XFEM. A first attempt at this challenging problem is published here: 

A book on mechanics that would pique your curiosity

I am happy to recommend the following book for your general reading.

Ranganath, G.S., ``Mysterious Motions and other Intriguing Phenomena in Physics," Hyderabad, India: Universities Press (2001)

Liu's picture

Motion of precision linear bearings on nanometre scale

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

Thickness dependent critical strain in Cu films adherent to polymer substrate

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.

SHIH Choon Fong's picture

Innovation and Integration in the Changing Global Higher Education Landscape

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.

Zhigang Suo's picture

Self-assembled structures in a viscoelastic liquid

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About a year ago, Zak Stone introduced me to YouTube with this video titled amazing liquid. I wonder how much of this behavior is understood. There must be a lot of fantastic videos of mechanical phenomena on YouTube. Perhaps we can embed them in iMechanica, and comment on them. Teng Li has provided an instruction of how to embed videos. You can check out a few other interesting videos in iMechanica video channel.

Mohsin Hamzah's picture

Constitutive Modelling of Elastomers

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.

Alexander A. Spector's picture


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 has more details on the book.

Nanshu Lu's picture

Delamination of stiff islands patterned on stretchable substrates

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


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.

Mogadalai Gururajan's picture

Elastic stress driven phase inversion

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.

Mogadalai Gururajan's picture

Elastic stress driven rafting

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.


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