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Konstantin Volokh's picture

Why fingerprints are different

A possible explanation of the variety of fingerprints comes from the consideration of the mechanics of tissue growth. Formation of fingerprints can be a result of the surface buckling of the growing skin. Remarkably, the surface bifurcation enjoys infinite multiplicity. The latter can be a reason for the variety of fingerprints. Tissue morphogenesis with the surface buckling mechanism and the growth theory underlying this mechanism are presented in the attached notes.

Jun He's picture

Materials Impact on Interconnects Process Technology and Reliability

M.A. Hussein and Jun He (Intel Corporation)

IEEE Transactions on Semiconductor Manufacturing, vol. 18, No. 1, p.69-85, 2005

In this work, we explain how the manufacturing technology and reliability for advanced interconnects is impacted by the choice of metallization and interlayer dielectric (ILD) materials. The replacement of aluminum alloys by copper, as the metal of choice at the 130nm technology node, mandated notable changes in integration, metallization, and patterning technologies. Those changes directly impacted the reliability performance of the interconnect system. Although further improvement in interconnect performance is being pursued through utilizing progressively lower dielectric constant (low-k) ILD materials from one technology node to another, the inherent weak mechanical strength of low-k ILDs and the potential for degradation in the dielectric constant during processing, pose serious challenges to the implementation of such materials in high volume manufacturing. We will consider the cases of two ILD materials; carbon-doped silicon dioxide (CDO) and low-k spin-on-polymer to illustrate the impact of ILD choice on the process technology and reliability of copper interconnects. preprint pdf 2.49 MB

Jie-Hua Zhao's picture


Flip-chip plastic ball grid array (FC-PBGA) packages are widely used in high performance components. However, its die back is normally under tensile stress at low temperatures. This paper presents a probabilistic mechanics approach to predict the die failure rate in the FC-PBGA qualification process. The methodology consists of three parts:

Jie-Hua Zhao's picture

Microstructure-based Stress Modeling of Tin Whisker Growth

Jie-Hua Zhao, Peng Su, Min Ding, Sheila Chopin, and Paul S. Ho

A 3-dimensional finite element method (FEM) model considering the elasticity anisotropy, thermal expansion anisotropy and plasticity of β-Sn is established. The Voronoi diagrams are used to generate the geometric patterns of grains of the Sn coating on Cu leadframes. The crystal orientations are assigned to the Sn grains in the model using the x-ray diffraction (XRD) measurement data of the samples. The model is applied to the Sn-plated package leads under thermal cycling tests. The strain energy density (SED) is calculated for each grain. It is observed that the samples with higher calculated SED are more likely to have longer Sn whiskers and higher whisker density. The FEM model, combined with the XRD measurement of the Sn finish, can be used as an effective indicator of the Sn whisker propensity. This may expedite the qualification process significantly.

Zhigang Suo's picture

Solid Mechanics Homework 1-5

Due 26 September 2008 in class

  1. Nothing Is Continuum, but...
  2. Hooke's law in various forms
  3. Compatibility: the strain-displacement relations
  4. Traction vector on a plane
  5. Turbine blade: centrifugal force and creep

Return to the outline of the course.

Indentation: A widely used technique for measuring mechanical properties

Indentation is one of the most widely used techniques of measuring mechanical properties of materials, especially for materials of small volume. In micro- or nano- scales, performing traditional tests such as the tension test and bending test becomes less feasible because of the nontrivial task of sample preparation. In contrast, by using the indentation technique, the difficulty of sample preparation may be dramatically reduced. On the other hand, indentation test is not a direct measurement and advanced mechanics analysis is needed to correlate the material properties with the indentation response. 

In an indentation test, a hard tip is pressed into a sample. The tip can be sharp or spherical. After the tip is removed, an impression is left. The hardness is defined as the indentation load divided by the projected area of impression. Moreover, by means of instrumental indentation testers, the indentation load and indentation depth can be continuously and simultaneously measured. Many models have been developed to extract the material properties from the recorded indentation load-depth curve, including the elastic modulus, yield stress, strain hardening coefficient, residual stress, fracture toughness, etc. 

Joost Vlassak's picture

The Effect of Water Diffusion on the Adhesion of Organosilicate Glass Film Stacks

Ting Y. Tsui, Andrew J. McKerrow, and Joost J. Vlassak

Published in the Journal of The Mechanics and Physics of Solids, 54 (5), 887-903 (2006)

Abstract – Organosilicate glass (OSG) is a material that is used as a dielectric in advanced integrated circuits. It has a network structure similar to that of amorphous silica where a fraction of the Si-O bonds has been replaced by organic groups. It is well known from prior work that OSG is sensitive to subcritical crack growth as water molecules in the environment are transported to the crack tip and assist in rupturing Si-O bonds at the crack tip. In this study, we demonstrate that exposure of an OSG containing film stack to water prior to fracture results in degradation of the adhesion of the film stack. This degradation is the result of the diffusion of water into the film stack. We propose a quantitative model to predict adhesion degradation as a function of exposure time by coupling the results of independent subcritical crack growth measurements with diffusion concentration profiles. The model agrees well with experimental data and provides a novel method for measuring the water diffusion coefficient in film stacks that contain OSG. This study has important implications for the reliability of advanced integrated circuits.

Ashkan Vaziri's picture

Deformation of the cell nucleus under indentation: Mechanics and Mechanisms

Computational models of the cell nucleus, along with experimental observations, can help in understanding the biomechanics of force-induced nuclear deformation and mechanisms of stress transition throughout the nucleus. Here, we develop a computational model for an isolated nucleus undergoing indentation, which includes separate components representing the nucleoplasm and the nuclear envelope. The nuclear envelope itself is composed of three separate layers: two thin elastic layers representing the inner and outer nuclear membranes and one thicker layer representing the nuclear lamina. The proposed model is capable of separating the structural role of major nuclear components in the force-induced biological response of the nucleus (and ultimately the cell). A systematic analysis is carried out to explore the role of major individual nuclear elements, namely inner and outer membranes, nuclear lamina, and nucleoplasm, as well as the loading and experimental factors such as indentation rate and probe angle, on the biomechanical response of an isolated nucleus in atomic force microscopy indentation experiment.

Ashkan Vaziri's picture

Mini-symposium on “Computational Methods in Impact Engineering” in Ninth U.S. National Congress on Computational Mechanics

The aim of the “Computational Methods in Impact Engineering” mini-symposium is to recognize the increasing role of the computation methods in Impact Engineering. It is now established that computational tools are indispensable to augment experimental techniques for the analysis of complex systems under dynamic loading. Many new computational techniques are currently being developed and new applications in the fields of impact and shock loadings are emerging. This mini-symposium will bring together engineers and scientists working in the area of Computational Impact Engineering.

Topics of interest include (but are not restricted to) the following:

Microcantilever for biomolecular detections

Microcantilevers have taken much attention as devices for label-free detection of molecules and/or their conformations in solutions and air. Recently, microcantilevers have allowed the nanomechanical mass detection of thin film [1-3], small molecules [4, 5], and biological components such as viruses [6] and vesicles [7] in the order of a pico-gram to a zepto-gram. The great potential of microcantilevers is the sensitive, reliable, fast label-free detection of proteins and/or protein conformations. Specifically, microcantilevers are capable of label-free detection of marker proteins related to diseases, even at a low concentration in solution [8-17]. Microcantilevers, operated in a viscous fluid, have also enabled the real-time monitoring of protein-protein interactions [8, 12-15]. Furthermore, microcantilevers are able to recognize the specific protein conformations [18] and/or reversible conformation changes of proteins/polymers [19, 20].

Demitris Kouris's picture

Associate or Assistant Professor -- Experimental Mechanics of Materials

The Department of Mechanical Engineering at the University of Wyoming invites applications for a tenure-track faculty position. Applicants are sought at the Associate or Assistant Professor level with expertise in experimental mechanics and particularly in emerging areas of science and technology. Such areas include but are not limited to the study of biomaterials, tissue engineering, nanomechanics of engineering materials, as well as thin films and multilayers, fracture, fatigue and damage.

The successful applicant will be expected to establish a strong, funded research program, as well as teach at the graduate and undergraduate levels. She/He will be expected to participate in interdisciplinary research efforts both within and outside the College of Engineering. Minimum qualifications include an earned doctorate in mechanical engineering, materials science/engineering, or a closely related field.

Interesting Conference: "micro-TAS 2006"

The conference "micro-TAS" may be interesting to researchers in engineering and science, especially involving Bio-MEMS/NEMS, biophysics, and biochemistry. See details of this conference.

Cellular and Molecular Mechanics

Cellular and Molecular Mechanics I was invited by Dr. Zhigang Suo to write a short piece on “Cellular and Molecular Mechanics”. I am writing this informally to introduce this subject matter rather than talk in vernacular such as mechanotransduction, phosphorylation, etc. I have more formal papers if someone is interested in more detailed discussions on this subject area. This is a field in which I have been working for over a decade now and I find it more exciting every day. The question always is how does mechanics affect biological processes. This is a very interdisciplinary subject matter as mechanists, engineers, physicists, chemists, and biologists have been investigating this process from various perspectives. I am obviously not the first to study this process. For most of us, it is realized from an empirical perspective that mechanics matters to biology, but exactly how mechanics specifically alters biochemistry continues to be highly debated today. Mechanics of course matters in many physiological areas. Your blood flows, your heart pumps, your bone and muscle feel mechanics. Not only does the body experience mechanical stimulation, but it reacts biochemically to it. A wonderful example is when people go into space (NASA) for long periods of time. The bone in one’s body begins to resorb in a similar response mode to what one experiences in aging (osteoporosis). This is primarily due to just the change in the gravity (mechanics). Other diseases are related to these issues including the two biggest killers: heart disease and cancer. While biomechanics on this scale has been studied for awhile (Leonardo Da Vinci, who was interested in mechanics, also wrote one of the first texts on anatomy), the movement to the cellular and molecular scales has brought a tremendous amount of excitement. I consider the cell as one of the ultimate smart materials exhibiting these characteristics. The cell has evolved over millions of years and is designed better than almost any system that we can personally build. Just as the biological eye provides a beautiful template for optics based lenses, much can be learned about building technology (“nanotechnology” and “microtechnology”) through examining the behavior of cells and molecules.

Zhigang Suo's picture

A Fresh Look at a Beautiful Subject

This is a review on Thermal Physics by Charles Kittle and Herbert Kroemer. I posted the review on Amazon on 2 December 2001.

This is by far THE BEST textbook on the subject. As many people say, thermodynamics is a subject that one has to learn at least three times. I can easily understand the very negative review from the undergraduate student at Berkely. The subject itself is hard, and simply is not for everyone, not for the first run at least. I say this from experience. I earned a Ph.D. degree over ten years ago, and took courses on thermodynamics at both undergraduate and graduate levels. I didn't understand the subject at all, and didn't find much use in my thesis work. However, something about the subject has kept me going back to it ever since. I now own about 40 books on the subject, and use the ideas almost daily in my research.

the FFT based algorithm to solve the continuum electrostatic field

In the paper[1], the continuum electrostatic simulation in the ion transport through membrane-spanning nanopores is realized by the implicit-solvent method. To solve the problem, the governing equation (Poisson equation for systems with heterogeneous permittivity) is expressed and the electric field is calculated in its reciprocal space by applying 3D-FFT[2]. The system is considered periodic, and a modified vacuum field outside is defined. The rectangular unit cell is discredited into grid points. By iteratively revise this modified vacuum field, the residual of the electric field at the grid points reach its minimum in the real space. After getting the predefined threshold, the iteration is terminated and the reaction potential is calculated. The potential at any point in the domain is interpolate by its eight surrounding grid points. The accuracy and convergence properties of this proposed algorithm are very well, with an overall speed comparable to a typical finite-difference solver.

Zhigang Suo's picture

Elements of linear elasticity

Update on 26 September 2008: An updated file on elements of linear elasticity is posted. You can still access the older version by clicking "revisions".

Return to the outline of the course.

The Fourth China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems

The Fourth China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems will be held in Kunming, China, November 6–9, 2006.

Recent advances of computer technology have given powerful practical tools to structural and mechanical designs. Optimal design is one of such area where various theories and methodologies are well developed. It is, however, lacking general interests among field designers and engineers. Innovative optimal design techniques and new applications are yet to be developed. Following the successful first CJK-OSM1 in Xian, China in 1999, second (CJK-OSM2) in Busan, Korea in 2002 and the third (CJK-OSM3) in Kanazawa, Japan in 2004, as agreed among participants in the symposium, the fourth CJK-OSM symposium will be held in Kunming, China during Nov. 6th -Nov. 9th, 2006. As before this will be a forum for exchange of recent research ideas and fostering new developments and new applications. Reflecting current interests from various fields, several new topics are included. The scope is, however, not limited to those listed.

Symposium on Mechanics in Biology and Medicine

This symposium will be part of the 2007 ASME Applied Mechanics and Materials Conference, to be held in the University of Texas in Austin, in June 3-6, 2007.

Nanotube 'forest' makes super slippery surface

A material less sticky than Teflon has been created by covering a surface with a "forest" of carbon nanotubes. has a very interesting report. Read more...

Student Presentation Competition at USNCCM IX

The 9th US National Congress on Computational Mechanics will feature a student presentation competition. This competition continues in the format pursued at the recent World Congress in Los Angeles. It is open to students who have an abstract accepted for presentation at the Congress.

19th Annual Melosh Competition at ETH Zurich

The 19th Annual Melosh Competition for the Best Student Paper on Finite Element Analysis will be held at ETH Zurich, on April 27, 2007.    The competition has become one of the premier graduate student events in the broad area of mechanics.   We have held the competition at a variety of locations over the past several years, but this is the first time it will be held outside the US.  We are presently seeking funds to provide travel fellowships for those students selected as finalists, as this represents an excellent opportunity for students to visit a world-class institution.  

Details on the competition and submission procedure can be found here.   The extended abstracts are due on January 8, 2007. I want to emphasize that the competition is really one on computational science.   As a result, papers on meshfree methods, molecular dynamics methods, their coupling with the FEM, etc., are welcome.   Please encourage your colleagues working in computational science to consider applying.  

Pradeep Sharma's picture

Journal Club: Response/Feedback requested

Hello everyone,

I had previously posted this entry on the AMD blog and perhaps it worthwhile to post it again on this forum. I would like to solicit feedback and comments on an idea to further enhance the role and utility of iMechanica.

This inspiration comes from Bell labs and the physics community.....

They started a journal club (year 2003). Each month ONLY 2-3 already published recent journal papers are reviewed and commentary posted in the form of a newsletter. Since only 2-3 papers are reviewed, the selection is much more stringent and careful. The contribution is regular and periodic (monthly). Hence, this newsletter is taken seriously by physicists.

In our case, this can be done within iMechanica. I suspect we could achieve the same kind of interest if we restrict "notable" papers to 1-3 per month and make it a regular monthly feature. In principle anyone could submit a commentary but the blog moderators will select the top 2-3.

The operational rules are open for discussion. Briefly though, I am thinking on the lines of rotating 1-2 moderators with a term of say 2 months. The moderator will receive commentaries on recently published papers RELATED to mechanics area. The moderator will highlight 1-3 notable commentaries in the journal club newsletter. A key requirement must be that the commentaries/paper highlighted are related to mechanics in some form or the other. The concept of rotating moderator is to provide breadth and prevent bias of any one individual. Rotation of journal club moderators will also keep the "work-load" well distributed.

Pradeep Sharma's picture

Collected Works of J.D. Eshelby

Perhaps a post has already been made in this regard; A book containing all the papers by J.D. Eshelby was recently released by Springer. This book is compiled by Markenscoff and Gupta. Congratulations to both of them for such a great idea!

I bought this book last week and it is fascinating to read all of Eshelby's papers in chronological order. Furthermore, I found a few papers that I had not even been aware of. The price, at roughly $195 on Amazon is a bit steep but (in my opinion) well worth it. The book also contains forewords by several researcher who knew Eshelby personally.

Here is the amazon link to this book


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