Blog posts

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

Eric Mockensturm has 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 question what if all papers are already openly accessible. Many mechanicians have discovered iMechanica, and the registered users have recently passed 1000. Recent discussions of copyright on 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.

Several sets of boundary integral equations for two 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. 

Myfeeling is that what we're trying to find are elastic constants of a continuum structure whose response in several (ideally all) deformations is the same as that of the carbon nanotube subjected to the same boundary conditions as the continuum structure.  We (A. Sears and R. C. Batra, Macroscopic Properties of Carbon Nanotubes from Molecular-Mechanics Simulations, Physical Reviews B, 69, 235406, 2004) have simulated simple tension and torsional deformations of a SWNT and its equivalent continuum structure defined as the one whose strain energy density is the same as that of the SWNT.  For an isotropic structure, the thickness of the equivalent structure was found to be~0.21 and it depends upon the MM potential used.  This has been validated by performing bending, buckling and combined loading tests on the SWNT and the equivalent continuum structure.

Here is a link to a 1996 book by C.H. Wang on Fracture Mechanics from the DSTO Aeronautical and Maritime Research Laboratory in Melbourne.

http://www.dsto.defence.gov.au/publications/1880/DSTO-GD-0103.pdf