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Rui Huang's picture

Surface effects on thin film wrinkling

A recent discussion here about the effect of surface stress on vibrations of microcantilever has gained some interest from our members. A few years ago, Zhigang and I looked at surface effect on buckling of a thin elastic film on a viscous layer (Huang and Suo, Thin Solid Films 429, 273-281, 2003). Although the physical phenomena (buckling vs vibrations) are different, the conclusion is quite consistent with Wei Hong and Pradeep's comments toward the end of the discussion. That is, surface stress only contributes as a residual stress and thus does not affect the buckling wavelength (frequency in space in analogy to frequency in time for vibrations).

Yaoyu Pang's picture

Nonlinear effect of stress and wetting on surface evolution of epitaxial thin films

Y. Pang and R. Huang, Physical Review B 74, 075413 (2006).

An epitaxial thin film can undergo surface instability and break up into discrete islands. The stress field and the interface interaction have profound effects on the dynamics of surface evolution. In this work, we develop a nonlinear evolution equation with a second-order approximation for the stress field and a nonlinear wetting potential for the interface. The equation is solved numerically in both two-dimensional (2D) and three-dimensional (3D) configurations using a spectral method. The effects of stress and wetting are examined. It is found that the nonlinear stress field alone induces "blow-up" instability, leading to crack-like grooving in 2D and circular pit-like morphology in 3D. For thin films, the blow-up is suppressed by the wetting effect, leading to a thin wetting layer and an array of discrete islands. The dynamics of island formation and coarsening over a large area is well captured by the interplay of the nonlinear stress field and the wetting effect.

Jeffrey Kysar's picture

Analytical solutions for plastic deformation around voids in anisotropic single crystals

It is well established that the growth of microscopic voids near a crack tip plays a fundamental role in establishing the fracture behavior of ductile metals. Mechanics analyses of plastic void growth have typically assumed the plastic properties of the surrounding metal to be isotropic. However voids are typically of the order of magnitude of one micron so that they exist within individual grains of the metal, or along grain boundaries, at least at the initial growth stage. For that reason, the plastic properties of the material surrounding the void are most properly treated as being anisotropic, rather than isotropic.

In the uploaded preprint, the stress state and deformation state are derived around a cylindrical void in a hexagonal close packed single crystal. The orientation of the cylindrical void and the loading state relative to the crystal are chosen so that the deformation state is one of plane strain. The active slip systems reduce to a total of three slip systems which act within the plane of plane strain. The solution shows that the deformation state consists of angular sectors around the void within which only one slip system is active. Further, it is shown that the stress state and deformation state exhibit self-similarity both radially and circumferentially, as well as periodicity along certain logarithmic spirals which emanate from the void surface.

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.

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. 

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.

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].

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.

Ting Zhu's picture

Handbook of Materials Modeling

by S. Yip (Editor), 2005

Book Review
"A new guide to materials modeling largely succeeds in its aim to be the defining reference for the field of computational materials science and represents a huge undertaking..." -- by James Elliott | University of Cambridge, Materials Today, Volume 9, Issues 7-8, July-Aug 2006, Pages 51-52.

Book Description
The first reference of its kind in the rapidly emerging field of computational approachs to materials research, this is a compendium of perspective-providing and topical articles written to inform students and non-specialists of the current status and capabilities of modelling and simulation. From the standpoint of methodology, the development follows a multiscale approach with emphasis on electronic-structure, atomistic, and mesoscale methods, as well as mathematical analysis and rate processes. Basic models are treated across traditional disciplines, not only in the discussion of methods but also in chapters on crystal defects, microstructure, fluids, polymers and soft matter. Written by authors who are actively participating in the current development, this collection of 150 articles has the breadth and depth to be a major contributor toward defining the field of computational materials. In addition, there are 40 commentaries by highly respected researchers, presenting various views that should interest the future generations of the community. Subject Editors: Martin Bazant, MIT; Bruce Boghosian, Tufts University; Richard Catlow, Royal Institution; Long-Qing Chen, Pennsylvania State University; William Curtin, Brown University; Tomas Diaz de la Rubia, Lawrence Livermore National Laboratory; Nicolas Hadjiconstantinou, MIT; Mark F. Horstemeyer, Mississippi State University; Efthimios Kaxiras, Harvard University; L. Mahadevan, Harvard University; Dimitrios Maroudas, University of Massachusetts; Nicola Marzari, MIT; Horia Metiu, University of California Santa Barbara; Gregory C. Rutledge, MIT; David J. Srolovitz, Princeton University; Bernhardt L. Trout, MIT; Dieter Wolf, Argonne National Laboratory.

Saturated voids in interconnect lines due to thermal strains and electromigration

Zhen Zhang, Zhigang Suo, Jun He

Thermal strains and electromigration can cause voids to grow in conductor lines on semiconductor chips. This long-standing failure mode is exacerbated by the recent introduction of low-permittivity dielectrics. We describe a method to calculate the volume of a saturated void (VSV), attained in a steady state when each point in a conductor line is in a state of hydrostatic pressure, and the gradient of the pressure along the conductor line balances the electron wind. We show that the VSV will either increase or decrease when the coefficient of thermal expansion of the dielectric increases, and will increase when the elastic modulus of the dielectric decreases. The VSV will also increase when porous dielectrics and ultrathin liners are used. At operation conditions, both thermal strains and electromigration make significant contributions to the VSV. We discuss these results in the context of interconnect design.

This has been published and the related references are listed here:

  • Z. Zhang, Z. Suo, and J. He, J. Appl. Physics, 98, 074501 (2005). link
  • J. He, Z. Suo, T.N. Marieb, and J.A. Maiz, Appl. Phys. Lett. 85, 4639 (2004). link


Electric Field May Promote Exfoliation of Clay Nanoplates

Nanocomposite performance fundamentally relies on reproducible dispersion and arrangement of nanoparticles, such that the dominate morphology across macroscopic dimensions is also nanoscopic. To facilitate dispersion, chemical approaches, including surfactant or macromolecular stabilization are usually employed to modify the surface of nanoparticles. However, the approach depends on the material system and usually involves trial-and-error to identify the best practice. Much less quantitative information is available on the coupling between the surface modification and external processing factors, including shear, electric or magnetic fields. In a recent work, we considered electric field on the interaction of nano-plates. For ideal dielectrics an electric field may assist (or retard) exfoliation depending on the angle between a collection of plates and the field. A critical electric field strength to promote exfoliation is predicted when the field is parallel to the surface of the plates. Structural refinement is predicted to occur by cleavage through the center of the stack. For lossy dielectrics, frequency can be tuned to cause exfoliation in all plate orientations.

Nanshu Lu's picture

Critical Size of Stiff Islands on Stretchable Substrates due to Interface Delamination

One possible design of stretchable integrated circuits consists of functional islands of stiff thin films on a polymer substrate. When such a structure is stretched, the substrate carries most of the deformation while the islands experience little strain. However, in practice, the island/substrate interface can never cohere perfectly. Existing experiments suggest that, interface debonding occurs if the island is larger than a certain size. I am now studying the critical size of stiff islands on stretchable polymer substrates due to thin film delamination, using finite element simulations. We show that the maximum energy release rate of interfacial cracking goes down as island size or substrate stiffness decreases. As a result, the critical island size can be enhanced if the substrate is chosen to be more compliant. An approximate formula is given to predict the energy release rate for the configuration of stiff islands on very compliant substrate.

Xiaodong Li's picture

A New Class of Composite Materials - Graphene-based Composite Materials

Professor Rodney Ruoff and colleagues at Northwestern University and Purdue University have developed a process that promises to lead to the creation of a new class of composite materials - graphene-based materials. They reported the results of their research in Nature, 442 (2006) 282-286. This team has overcome the difficulties of yielding a uniform distribution of graphene-based sheets in a polymer matrix. Such composites can be readily processed using standard industrial technologies such as moulding and hot-pressing. The technique should be applicable to a wide variety of polymers. The graphene composites may compete with carbon nanotube-based materials in terms of mechanical properties. This new class of composites may stimulate the applied mechanics community to study the fundamental reinforcing mechanisms of graphene sheets from both experimental and theoretical approaches.

Wei Hong's picture

Interplay between elastic interactions and kinetic processes in stepped Si (001) homoepitaxy

A vicinal Si (001) surface may form stripes of terraces, separated by monatomic-layer-high steps of two kinds, SA and SB. As adatoms diffuse on the terraces and attach to or detach from the steps, the steps move. In equilibrium, the steps are equally spaced due to elastic interaction. During deposition, however, SA is less mobile than SB. We model the interplay between the elastic and kinetic effects that drives step motion, and show that during homoepitaxy all the steps may move in a steady state, such that alternating terraces have time-independent, but unequal, widths. The ratio between the widths of neighboring terraces is tunable by the deposition flux and substrate temperature. We study the stability of the steady state mode of growth using both linear perturbation analysis and numerical simulations. We elucidate the delicate roles played by the standard Ehrlich-Schwoebel (ES) barriers and inverse ES barriers in influencing growth stability in the complex system containing (SA+SB) step pairs.

Preprint available in the attachment.

Teng Li's picture

Organic LED could replace light bulb?

Lighting accounts for about 22% of the electricity consumed in buildings in the United States, and 40% of that amount is eaten up by inefficient incandescent light bulbs. The search for economical light sources has been a hot topic.

Recently, scientists have made important progress towards making white organic light-emitting diodes (OLEDs) commercially viable as light source. As reported in a latest Nature article, even at an early stage of development this new source is up to 75% more fficient than today's incandescent sources at similar brightnesses. The traditional light bulb's days could be numbered.

Read media report here.


Rui Huang's picture

EPN - E-print Network

I was notified today that my Web site ( has been included in the E-print Network (EPN). EPN is a fast-growing searchable scientific network of over 20,000 Web sites containing research conducted by researchers - from Nobel Laureates to post-doctoral students - who are offering e-prints of their work via the Internet.

Developed by the Office of Scientific and Technical Information (OSTI) to facilitate the needs of the Department of Energy (DOE) research community, E-print Network enhances dissemination of important research and helps to create opportunities for productive professional contacts.

E-print Network indexes over 900,000 e-prints. Most documents included in the network are recent scientific literature. Functions available to users include conducting full-text searches, searching for documents by contributing author, establishing a personalized alert service to keep abreast of new e-prints, and exploring laboratory Web sites for further details about selected research programs.

Once users find a paper of interest, they can download it from the site hosting the paper. This way you control distribution of your e-prints and can more readily track Web interest in your papers.

My page is listed under both Engineering and Materials Science.

Rui Huang's picture

Modeling Place

Starting from January 2006, my group has been posting in Modeling Place as a blogspot to share research experience and ideas. We will gradually migrate to iMechanica for better publicity and more web functions.

Xi Chen's picture

A molecular dynamics-decorated finite element framework for simulating the mechanical behaviors of biomolecules

Cover of Biophysical JournalOur first paper in biomechanics is featured as the cover of the Biophysical Journal. The paper is attached. Several freelance writers in biophysics have reported this paper in magazines and websites/blogs. This framework is very versatile and powerful, and we are now implementing more details/atomistic features into this phenomenological approach, and the follow-up paper will be submitted soon.

Abstract: The gating pathways of mechanosensitive channels of large conductance (MscL) in two bacteria (Mycobacterium tuberculosis and Escherichia coli) are studied using the finite element method. The phenomenological model treats transmembrane helices as elastic rods and the lipid membrane as an elastic sheet of finite thickness; the model is inspired by the crystal structure of MscL. The interactions between various continuum components are derived from molecular-mechanics energy calculations using the CHARMM all-atom force field. Both bacterial MscLs open fully upon in-plane tension in the membrane and the variation of pore diameter with membrane tension is found to be essentially linear. The estimated gating tension is close to the experimental value. The structural variations along the gating pathway are consistent with previous analyses based on structural models with experimental constraints and biased atomistic molecular-dynamics simulations. Upon membrane bending, neither MscL opens substantially, although there is notable and nonmonotonic variation in the pore radius. This emphasizes that the gating behavior of MscL depends critically on the form of the mechanical perturbation and reinforces the idea that the crucial gating parameter is lateral tension in the membrane rather than the curvature of the

Split singularities and the competition between crack penetration and debond at a bimaterial interface

Zhen Zhang and Zhigang Suo

For a crack impinging upon a bimaterial interface at an angle, the singular stress field is a linear superposition of two modes, usually of unequal exponents, either a pair of complex conjugates, or two unequal real numbers. In the latter case, a stronger and a weaker singularity coexist (known as split singularities). We define a dimensionless parameter, called the local mode mixity, to characterize the proportion of the two modes at the length scale where the processes of fracture occur. We show that the weaker singularity can readily affect whether the crack will penetrate, or debond, the interface.

Teng Li's picture

Review Articles on Flexible Electronics

[img_assist|nid=46|title=|desc=|link=url,|align=right|width=75|height=100]The cover story of the April 2006 issue of Materials Today features Flexible Electronics. This issue also includes two review articles in this emerging field of research. Access to full text articles is free of charge at

Review Article:

Material challenge for flexible organic devices, by Jay Lewis

Review Article:

Organic and polymer transistors for electronics, by Ananth Dodabalapur

Cover Story:

Jet printing flexible displays, by R.A. Street et al.


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