blogs

A free surface in a multi-layer can experience an undulation due to surface diffusion during fabrication or etching process. In order to analyze the undulation, the elasticity solution for the undulating film is needed. Considering the undulation as a perturbation of a flat surface, a boundary value problem for 2D elasticity is formulated. The solution procedure is straightforward, but very lengthy especially for a multi-layer.

Attached is the first announcement and call for papers for "nanomech 8", the 8th European Symposium on Nanomechanical Testing to be held in Huckelhoven, Germany, 3rd-5th September, 2007. Full details are also available at theconference website．今年的会议是“特别关注Across the scales: Size effects and scaling phenomena in micro- and nano-mechanics". Abstracts are due 5th May, 2007.

Update: February 2012

1) The lecture notes are on Wikiversity athttp://en.wikiversity.org/wiki/Waves_in_composites_and_metamaterials

2) The book on the topic can be bought from Amazon athttp://www.amazon.com/Introduction-Metamaterials-Waves-Composites/dp/1439841578

3) Solutions and errata can be found atnode/9727

In this blog entry, I'll maintain a list of books, essays and websites that have influenced me in developing iMechanica. I'll also list my notes on them whenever available. Because iMechanica shares many common problems with other online communities, it is natural that we find solutions discovered by other online communities helpful. At the same time, iMechanica is unique in some respects, and has its own unique problems, so that we cannot adopt any methods or viewpoints without adjustment.

猪年：身体健康, 家庭幸福,事业丰收!

As I promised, I start with some brief notes on themes loved by Ken Johnson to hopefully raise some interest for discussion on iMechanica. Regards, Mike

Are not as high as we expected althoughvery stiff and strong nanotubes or nanofibers (Young’s modulus E~1000GPa) are added into soft polymer matrices like epoxy (E~4GPa).In our early investigation on thesystematic mechanical property characterizations of nanocomposites (Xu et al.,Journal of Composite Materials, 2004--among top 5 in 2005;and top 10 in 2006 of the Most-Frequently-Read Articles in Journal of Composite Materials.)have shown that there was a very small increase (sometimes even decrease) of critical ultimate tensile/bending strengths, and mode-I fracture toughnesses in spite of complete chemical treatments of the interfacial bonding area, anduniform dispersions of nanofibers (click to view a TEM image).Similar experimental results were often reported in recent years. Therefore, mechanics analysis is extremely valuable before we make these “expensive” nanocomposite materials. Our goal is to provide in-depth mechanics insight, and future directions for nanocomposite development. Till now, nanocomposite materials are promising as multi-functional materials, rather than structural materials. Here we mainly focus on two critical parameters for structural materials: tensile strength and fracture toughness. We notice that other mechanical parameters such as compressive strengths and Young’s moduli of nanocomposite materials have slight increase over their matrices.

In December 2007 Elsevier will organise the 2nd International Conference on Mechanics of Biomaterials & Tissues (www.icmobt.elsevier.com). The aim of the conference is to provide a forum for the discussion of the modeling and measurement of deformation and fracture behavior in biological materials and in those materials which are used to replace them in the human body.

The response of low-dimensional solid objects combines geometry and physics in unusual ways, exemplified in structures of great utility such as a thin-walled tube that is ubiquitous in nature and technology.

当我还是一个研究生,我花了几个我的ths to measure interfacial toughness between metalic (Cu and Au) films and thick substrates(Si and Polycarbonate). My methods were bulge test (blistering test) and 4-point bending test. I had many problems such as making an initial crack(pre-cracking), changing load phase angle applied to specimens, preparing/patterning thin films, constructing my own test apparatus, etc. The biggest problem was to measure the interfacial toughness over a wide range of loading phase angle. For a bimaterial with a non-zero oscillatory index(epsilon), we don't know the phase angle for a minimum interfacial toughness beforehand. Therefore, we need to measure the interfacial toughness over a wide range of phage angle. For engineering purpose, we need a minimum interfacial toughness value for reliability design because this value will lead to a conservative design of systems.

Given link is for a stochastic micromechanical model developed for predicting probabilistic characteristics of elastic mechanical properties of an isotropic functionally graded material (FGM) subject to statistical uncertainties in material properties of constituents and their respective volume fractions.

Please find below the announcement for the NSF Summer Institute on Nano Mechanics and Materials:

Eric Mockensturmhas just posted a publication agreement proposed by provosts of several universities. In structuring iMechanica, we have tried to avoid the question of open access, and simply asked the questionwhat if all papers are already openly accessible．Many mechanicians have discovered iMechanica, and theregistered users have recently passed 1000．Recentdiscussions of copyrighton iMechanica have prompted Eric to post his entry, which has just led to this one.

Last year I spent three months modeling the compressive behavior of aluminum alloy foams. I had hoped to find some evidence of the banding instability that is often observed in elastomeric foams [1]. Lakes writes that this sort of banding instability provides indirect experimental evidence for negative shear modulus [2].

I wanted to share some our work on the deformation behavior of metal nanowires that was recently published in Advanced Functional Materials. In this work, we considered the tensile deformation of three experimentally observed silver nanowire geometries, including five-fold twinned, pentagonal nanowires. The manuscript abstract and urls to videos of the tensile deformation of the three nanowire geometries are below. A copy of the manuscript is attached.

Abstract.This letter addresses the dependence of homogeneous dislocation nucleation on the crystallographic orientation of pure copper under uniaxial tension and compression. Molecular dynamics simulation results with an embedded-atom method potential show that the stress required for homogeneous dislocation nucleation is highly dependent on the crystallographic orientation and the uniaxial loading conditions; certain orientations require a higher stress in compression (e.g., <110> and <111>) and other orientations require a higher stress in tension (<100>). Furthermore, the resolved shear stress in the slip direction is unable to completely capture the dependence of homogeneous dislocation nucleation on crystal orientation and uniaxial loading conditions.

Might also be useful for simulating dislocation motion in a finite body.

几套tw的边界积分方程o dimensional elasticity are derived from Cauchy integral theorem.These equations reveal the relations between displacements and resultant forces, between displacements and tractions, and between the tangential derivatives of displacements and tractions on solid boundary.Special attention is given to the formulation that is based on tractions and the tangential derivatives of displacements on boundary, because its integral kernels have the weakest singularities.The formulation is further extended to include singular points, such as dislocations and line forces, in a finite body, so that the singular stress field can be directly obtained from solving the integral equations on the external boundary without involving the linear superposition technique often used in the literature. Body forces and thermal effect are subsequently included. The general framework of setting up a boundary value problem is discussed and continuity conditions at a non-singular corner are derived.The general procedure in obtaining the elastic field around a circular hole is described, and the stress fields with first and second order singularities are obtained. Some other analytical solutions are also derived by using the formulation.