What can we do in this discovery and creation?
By Xudong Wang, Jinhui Song, Jin Liu, Zhong Lin Wang*
Professor Dr. Liviu Librescu was murdered while teaching a solid mechanics course at Virginia Tech on April 16, 2007.
The great works he left behind are, including, but not limited to, the following books (which are the ones in English):
Scale bridging mechanics: Nanoscale planar field projection of atomic decohesion and slip in crystalline solidsSubmitted by Seungtae Choi on Tue, 2007-04-17 10:06.
I would like to introduce my recent paper on field projection method with Prof. K.-S. Kim at Brown University. When atomistic simulations or atomic resolution experiments are carried out to analyze deformation energetics of atomic lattices near a crack tip, the results of the atomic positions and the total energy of the system have not been systematically converted to field quantities such as stresses or tractions near the crack tip. In this study, we introduce a mathematically consistent way of defining and measuring the cohesive tractions, separations and surface stresses in an atomic decohesion process zone using the atomic displacement data at some distance away from the crack tip. The method is called “nano-scale planar field projection method.” This is a generalization of the method developed for isotropic homogeneous solids by Hong and Kim (2003). The formulation introduced here is applicable to interface cracks between anisotropic solids as well as to cracks in homogeneous solids whether they are anisotropic or isotropic. The field projection method is then applied to a crack tip field in gold, simulated atomistically. The atomistic simulation is made with an embedded atom method (EAM) potential for a crystal decohesion along  direction in a (111) plane. Then, the details of energy partition in various modes of nano-scale separation processes are analyzed with the field projection method.
During the shootings occurred on the campus of Virginia Tech, the department of engineering science and mechanics lost two fine professors. Dr. Liviu Librescu was teaching solid mechanics class when the gunman initiated a two-minute massacre next door. Most of the students in his class escaped from the windows while Dr. Librescu held the door and did not survive when the gunman broke in. Another professor is Dr. Kevin Granata.
With a great many ties to VT, I have been following the tragic shootings there closely. While my former student (Nakhiah Goulbourne) and my former department head (Dick Benson) are both safe, I am afraid we may have lost one of our own this morning. From an AP report, a student stated that the instructor teaching a 9:05am mechanics class in 204 Norris Hall was killed. According to the timetable of classes at VT, this instructor would have been Liviu Librescu. I certainly hope the AP's report is wrong. As someone very interested in shell theories, I have spoken with Prof. Librescu many times and followed his work. His loss would be a great loss to our community.
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This paper has been published in Journal of the Mechanics and Physics of Solids 56 (2008), pp. 1609-1623 (doi:10.1016/j.jmps.2007.07.013).
Head traumatic injury due to the impact of a flying golf ball is one of the severest injuries sustained on a golf course. This paper presents numerical simulation results based on the finite element (FE) method to investigate head injuries in children due to impacts by flying golf balls.
Terence Tao (one of the Fields Medal winners this year) has started blogging. He has a detailed discussion on the Navier-Stokes equations here. It's long but definitely worth reading - particularly because of the wide range of ideas that he talks about.
As many of you know, last year we had a lively debate prior to the launch of the j-club regarding the rules and regulations governing the functioning of the j-club. This continued in a more low-key fashion this year. One of the more important topics under discussion has been the selection of the future editors (which is to be done each year). I, and perhaps a few other people, had reasoned that the editor should be elected by popular vote. It was proposed that candidates will either self-nominate themselves or be nominated by other mechanicians.
Just a reminder that this Sunday, April 15 will be exactly 300 years since Leonhard Euler was born.
I am sure many mechanicians will toast this weekend on this extraordinnary anniversary to the person who laid down much of the foundations in mathematics and mechanics.
Some of the related links on the web are:
From the Call for Papers:
Microelectromechanical Systems (MEMS) represent the integration of miniaturized mechanical, chemical, fluidic, and optical devices with microelectronics. MEMS have a broad range of applications in optical- and radio-frequency communications, physical/chemical/biosensing, display technology, drug delivery, and the manipulation and isolation of cells.
First announcement and call for papers.
The symposium "Fundamentals of Nanoindentation and Nanotribology" will run for the fourth time at the Fall, 2007, Materials Research Society Meeting, Boston, MA, USA.
Channeling cracks in low-k dielectrics have been observed to be a key reliability issue for advanced interconnects. The constraint effect of surrounding materials including stacked buffer layers has been studied. This paper analyzes the effect of interfacial delamination on the fracture condition of brittle thin films on elastic substrates. It is found that stable delamination along with the growth of a channel crack is possible only for a specific range of elastic mismatch and interface toughness. An effective energy release rate is defined to account for the influence of interfacial delamination on both the driving force and the fracture resistance, which can be significantly higher than the case assuming no delamination.
Indentation is widely used to measure material mechanical properties such as hardness, elastic modulus, and fracture toughness (for brittle materials). Can one use indentation to extract material elastoplastic properties directly from the measured force-displacement curves? Or simply, is it possible to obtain material stress-strain curves from the corresponding indentation load-displacement curves? In an upcoming paper in JMPS titled "On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials," Xi Chen and colleagues at Columbia University and National Defense Academy, Japan show the existence of "mystical materials", which have distinct elastoplastic properties yet they yield almost identical indentation behaviors, even when the indenter angle is varied in a large range. These mystical materials are, therefore, indistinguishable by many existing indentation analyses unless extreme (and often impractical) indenter angles are used. The authors have established explicit procedures of deriving these mystical materials. In many cases, for a given indenter angle range, a material would have infinite numbers of mystical siblings, and the existence maps of the mystical materials are also obtained. Furthermore, they propose two alternative techniques to effectively distinguish these mystical materials. The study in this paper addresses the important question of the uniqueness of indentation test, as well as providing useful guidelines to properly use the indentation technique to measure material elastoplastic properties.
In nature, several species use flexible probes to actively explore their environment, and acquire important sensory information, such as surface topology and texture, water/air flow velocity, etc. For example, rats and other rodents have an array of facial vibrissae (or whiskers) with which they gather tactile information about the external world. The complex mechanisms, by which mechanical deformations of the probe lead to neuronal activity in the animal’s nervous system are still far from being understood. This is due to the intricacy of the deformation mechanics of the flexible sensors, the processes responsible for transforming the deformation to electrical activity, and the subsequent representation of the sensory information by the nervous system. Understanding how these mechanosensory signals are transduced and extracted by the nervous system promises great insight into biological function, and has novel technological applications. To understand the mechanical aspect of sensory transduction, here we monitored the deformation of a rat’s vibrissa as it strikes rigid objects with different topologies (surface features) during locomotion, using high-speed videography. Motivated by our observations, we developed detailed numerical models to study the mechanics of such flexible probes. Our findings elucidate how active sensation with vibrissae might provide sensory information and in addition have direct implications in several technological areas. To put this in perspective, we propose strategies in which flexible probes can be used to characterize surface topology at high speeds, which is a desirable feature in several technological applications such as memory storage and retrieval. (The full article is attached)
Attached is a paper outlining ideas for averaging autonomous dynamics, based on a dynamical systems point of view.
People interested in computational multiscale modeling, especially of the sequential kind, as well as nonequilibrium statistical mechanics may find these ideas useful.
Does the word "randomness" have antonym? If yes, what is it? Why? What view of randomness does that imply?
The notion of randomness is, of course, basic to both statistical mechanics (or kinetic theory) and quantum mechanics. But these are not the only fields where it is relevant. The notion also appears virtually in any field where probabilities are used. For example, we speak of random loads and vibrations (in structures and machine design), random noise (say, in acoustics), etc. But what does the term "randomness" really mean? Any idea? What would you say? Here, I am here looking for brain storming, so half-baked ideas, side comments, etc. etc. are welcome.
We demonstrate, by theoretical analysis and molecular dynamics simulation, a mechanism for fabricating nanotubes by self-bending of nanofilms under intrinsic surface stress imbalance due to surface reconstruction. A freestanding Si nanofilm may spontaneously bend itself into a nanotube without external stress load, and a bilayer SiGe nanofilm may bend into a nanotube with Ge as the inner layer, opposite of the normal bending configuration defined by misfit strain. Such rolled-up nanotubes can accommodate a high level of strain, even beyond the magnitude of lattice mismatch, greatly modifying the tube electronic and optoelectronic properties.
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.
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!.
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.