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Intergranular fracture

Microcracks form by a mixture of local thinning and intergranular fracture in a 170-nm-thick Cu film that is well bonded to a polyimide substrate and is stretched to a strain of 30%. Details can be found in this paper. A related forum topic can be found

High ductility of a metal film adherent on a polymer substrate

In recent development of deformable electronics, it has been noticed that thin metal films often rupture at small tensile strains. Here we report experiments with Cu films deposited on polymeric substrates, and show that the rupture strains of the metal films are sensitive to their adhesion to the substrates. Well-bonded Cu films can sustain strains up to 10% without appreciable cracks, and up to 30% with discontinuous microcracks. By contrast, poorly bonded Cu films form channel cracks at strains about 2%. The cracks form by a mixture of strain localization and intergranular fracture.

Teng Li's picture

Mechanics of flexible macroelectronics

The following entry was first posted in on 8 May 2006.

Flat-panel displays are rapidly replacing cathode-ray tubes as the monitors of choice for computers and televisions, a commercial success that has opened the era of macroelectronics, in which transistors and other micro-components are integrated over large areas. In addition to the flat-panel displays, other macroelectronic products include x-ray imagers, thin-film solar cells, and thin-film antennas.
Like a microelectronic product, a macroelectronic product consists of many thin-film components of small features. While microelectronics advances by miniaturizing features, macroelectronics does so by enlarging systems. Macroelectronic products today are mostly fabricated on substrates of glass or silicon; they are expensive, fragile and not readily portable when their areas are large. To reduce cost and enhance portability, future innovation will come from new choice of materials and of manufacturing processes. For example, thin-film devices on thin polymer substrates lend themselves to roll-to-roll fabrication, resulting in lightweight, rugged and flexible products. These macroelectronic products will have diverse architectures, hybrid materials, and small features. Their mechanical behavior during manufacturing and use poses significant challenges to the creation of the new technologies.

A recent review paper by Suo et al. describes ongoing work in the emerging field of research – mechanics of flexible macroelectronics, with emphasis on the mechanical behavior at the scale of individual features, and over a long time. The following topics have been discussed in the paper:

Konstantin Volokh's picture

Griffith controversy

Using the Griffith energy method for analysis of cavitation under hydrostatic tension we conclude that the critical tension tends to infinity when the cavity radius approaches zero (IJSS, 2006, doi: 10.1016/j.ijsolstr.2006.12.022). The conclusion is physically meaningless, of course. Moreover, if we assume that the failure process occurs at the edge of the cavity then the critical tension should be length-independent for small but finite cavities while the Griffith analysis always exhibits length-dependence. The main Griffith idea - introduction of the surface energy - is controversial because it sets up the characteristic length, say, surface energy over volume energy. By no means is this approach in peace with the length-independent classical continuum mechanics.

The Ranking of Mechanics Related Journals (2004)

Based on a survey from Journal Citation Report (JCR), we listed below the 2004 Journal Impact Factors (IF) for some mechanics, material science, and solid state physics related scientific journals. Our list and information may not be complete. We welcome readers' input, comments, and information. We also caution readers that using IF as the sole criterion to rank scientific journals' academic reputation may not be objective nor true to a journal's actual scientific merits.

Which are the benchmark problems for a numerical method ?

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Hello mechanicians,

Please help me with some following questions.

Which are the benchmark problems must be tested for a new numerical method in 1D, 2D, and 3D ?

If there are two methods, with what criterions we can say one is better than other in such a particular problem? in all problems ?

And who supposed above rules ?

I look forward to your replies.

Happy new year to all !

Tienchong Chang's picture

Nonlinear stick-spiral model for predicting mechanical behavior of single-walled carbon nanotubes

(PRB,74,245428,2006)  Based on a molecular mechanics concept, a nonlinear stick-spiral model is developed to investigate the mechanical behavior of single walled carbon nanotubes (SWCNTs). The model is capable of predicting not only the initial elastic properties (e.g., Young’s modulus) but also the stress-strain relations of a SWCNT under axial, radial, and torsion conditions. The elastic properties, ultimate stress, and failure strain under various loading conditions are discussed and special attentions have been paid to the effects of the tube chirality and tube size. Some unique mechanical behaviors of chiral SWCNTs, such as axial strain-induced torsion, circumferential strain-induced torsion, and shear strain-induced extension are also studied. The predicted results from the present model are in good agreement with existing data, but very little computational cost is needed to yield them.

A "cool" way to remove hydrogen...and possibly a faster way to grow better crystals?

In growth of essentially every compound material such as GaN, one element always diffuses faster than the other(s) at the growth front. To grow good-quality materials, even the most sluggish element has to be sufficiently mobile, forcing materials growers to go to higher growth temperatures.

Multi-phase hyperelasticity with interface energy effect

Recently, J. Wang, L. Sun and I have formulated some ideas about the effective properties of heterogeneous materials with surface/interface energy effect, which are shown in the attached file.

Papers in the attached file can be viewed as a two-part paper, called “Multi-phase hyperelasticity with interface energy effect” if it is standalone. Part one of this topic is covered in “A theory of hyperelasticity of multi-phase media with surface/interface energy effect”, which provides theoretical background. Part two is covered in “Size-dependent effective properties of a heterogeneous material with interface energy effect: from finite deformation theory to infinitesimal strain analysis”, with more emphasis on application.

Young's modulus of single-walled carbon nanotubes

We report in detail that unlike other materials, carbon nanotubes are so small that changes in structure can affect the Young's modulus. The variation in modulus is attributed to differences in torsional strain, which is the dominant component of the total strain energy. Torsional strain, and correspondingly Young's modulus, increases significantly with decreasing tube diameter and increases slightly with decreasing tube helicity.  Journal of Applied Physics 84, 1939 (1998).

Force response and actin remodeling (agglomeration) in fibroblasts due to lateral indentation

We report the loading and unloading force response of single living adherent fibroblasts due to large lateral indentation obtained by a two-component microelectromechanical systems (MEMS) force sensor. Strong hysteretic force response is observed for all the tested cells. For the loading process, the force response is linear (often with small initial non-linearity) to a deformation scale comparable to the undeformed cell size, followed by plastic yielding. In situ visualization of actin fibers (GFP) reveals that during the indentation process, actin network depolymerizes irreversibly at discrete locations to form well-defined circular actin agglomerates all over the cell, which explains the irreversibility of the force response. Similar agglomeration is observed when the cell is compressed laterally by a micro plate. The distribution pattern of the agglomerates strongly correlates with the arrangement of the actin fibers of the pre-indented cell. The size of the agglomerates increases with time as ta  with a= 2~3 initially,   followed by a=.5~1. The higher growth rate suggests influx of actin into the agglomerates. The slower rate suggests a diffusive spreading, but the diffusion constant is two orders of magnitude lower than that of an actin monomer through the cytoplasm. Actin agglomeration has previously been observed due to biochemical treatment, gamma-radiation, and ischemic injury, and has been identified as a precursor to cell death. We believe, this is the first evidence of actin agglomeration due to mechanical stimuli. The study demonstrates that living cells may initiate similar functionalities in response to dissimilar mechanical and biochemical stimuli.

Axial-Strain-Induced Torsion in Single-Walled Carbon Nanotubes

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Using classical molecular dynamics and empirical potentials, we show that the axial deformation of single-walled carbon nanotubes is coupled to their torsion. The axial-strain-induced torsion is limited to chiral nanotubes—graphite sheets rolled around an axis that breaks its symmetry. Small strain behavior is consistent with chirality and curvature-induced elastic anisotropy (CCIEA)—carbon nanotube rotation is equal and opposite in tension and compression, and decreases with curvature and chirality. The largestrain compressive response is remarkably different.

Dhirendra Kubair's picture

Functionally Graded Materials

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Dear Fellow Mechanicians,

My group is looking into some aspects of fracture in "functionally graded materials". I was curious to know if there are groups (on imechanica) interested or actively pursuing research on functionally graded materials or nanocomposites.

Nanostructure Physics


I am Ph.D. student making semiconductor nano structure and studying the physics of them. I am also intersted to make common people aware of this branch of physics. For this I have just started making a web site on nanostructure phyiscs

Tienchong Chang's picture

Research cooperation wanted to develop a new type of nanoRAM

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Recently, we proposed a new concept to construct nano random access memory (nanoRAM) using carbon nanotubes. One of the most singnificant advantages of our design is that a RAM element is composed of only one single carbon nanotube. We are now looking for universities, companies and individuals who can perform experimental investigations on the electromechanical behavior of carbon nanotubes to realize this theoretical design.

Marino Arroyo's picture

Maximum-Entropy approximants Matlab routines

Dear iMechanica colleagues,

I would like to announce that Matlab routines implementing the maximum-entropy approximation schemes presented in

Marino Arroyo and Michael Ortiz, “Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods”, International Journal for Numerical Methods in Engineering, 65:2167–2202 (2006).

can be downloaded from

Xiaodong Li's picture

Experimental Nanomechanics

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Colleagues and friends,

sem graph

 a 175nm-thick cu films well bonded to polyimide substrate, and strained to 20% using the micro-force testing system( MTS tytron 250)

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phunguyen's picture

The eXtended Finite Element Method (XFEM)

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The aim of this writting is to give a brief introduction to the eXtended Finite Element Method (XFEM) and investigation of its practical applications.

Firstly introduced in 1999 by the work of Black and Belytschko, XFEM is a local partition of unity (PUM) enriched finite element method. By local, it means that only a region near the discontinuties such as cracks, holes, material interfaces are enriched. The most important concept in this method is "enrichment" which means that the displacement approximation is enriched (incorporated) by additional problem-specific functions. For example, for crack modelling, the Heaviside function is used to enrich nodes whose support cut by the crack face whereas the near tip asymptotic functions are used to model the crack tip singularity (nodes whose support containes the tip are enriched).

Non linear cell mechanics

Ex-vivo measure of stress-strain relationships in populations of living adherent cells by means of ligand-coated ferromagnetic microbeads (mean diameter: 4.5 µm) attached to the transmembrane mechanoreceptors which are linked to the cytoskeleton (CSK), reveal non linear cell mechanical behavior. However, this non linear cell mechanical behaviour is subjected to controversy for various reasons. First, it has not been systematically found. Results seem to depend on the micromanipulation method used and/or the cell type.


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