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This paper develops a theory of anharmonic lattice statics for the analysis of defective complex lattices. This theory differs from the classical treatments of defects in lattice statics in that it does not rely on harmonic and homogeneous force constants. Instead, it starts with an interatomic potential, possibly with in¯nite range as appropriate for situations with electrostatics, and calculates the equilibrium states of defects. In particular, the present theory accounts for the differences in the force constants near defects and in the bulk. The present formulation reduces the analysis of defective crystals to the solution of a system of nonlinear difference equations with appropriate boundary conditions. A harmonic problem is obtained by linearizing the nonlinear equations, and a method for obtaining analytical solutions is described in situations where one can exploit symmetry. It is then extended to the anharmonic problem using modified Newton-Raphson iteration. The method is demonstrated for model problems motivated by domain walls in ferroelectric materials.

J.R.Barber

The contact of rough surfaces

Surfaces are rough on the microscopic scale, so contact is restricted to a few `actual contact areas'. If a current flows between two contacting bodies, it has to pass through these areas, causing an electrical contact resistance. The problem can be seen as analogous to a large number of people trying to get out of a hall through a small number of doors.

Classical treatments of the problem are mostly based on the approximation of the surfaces as a set of `asperities' of idealized shape. The real surfaces are represented as a statistical distribution of such asperities with height above some datum surface. However, modern measurement techniques have shown surfaces have multiscale, quasi-fractal characteristics over a wide range of length scales. This makes it difficult to decide on what scale to define the asperities.

Comments and feedback of the following paper would be appreciated.

Abstract:

A new technique for the modelling of multiple dislocations based on introducing interior discontinuities is presented. In contrast to existing methods, the superposition of infinite domain solutions is avoided; interior discontinuities are specified on the dislocation slip surfaces and the resulting boundary value problem is solved by a finite element method. The accuracy of the proposed method is verified and its efficiency for multi-dislocation problems is illustrated. Bounded core energies are incorporated into the method through regularization of the discontinuities at their edges. Though the method is applied to edge dislocations here, its extension to other types of dislocations is straightforward.

We write to invite your participation in the symposium on New Directions in Large Deformation Solid Mechanics to be held at Texas A&M University campus in College Station as part of the 44th Annual Technical Meeting of the Society of Engineering Science, October 21–24, 2007. The purpose of this symposium is to address and outline new directions in large deformation solid mechanics and to furnish a forum for discussions on a wide range of research in all fields comprising modern mechanics.

Luis Dorfmann, Ray Ogden, Alan Wineman

There are 5 vacant PhD positions with good stipend in the field of solid mechanics, constitutive modelling and numerical simulations. We are looking for very competent, creative students all over the world. It is a rare opportunity for a young scientist to develop his versatile skills and this is your chance. As some people know, SIMLab (Structural Impact Laboratory) is internationally reputed group working on problems related to Crashworthiness and Structural Impact. Our group recently got a Centre for Research based Innovation (CRI). All these positions are filling under CRI. Please find the details in the links here:

The Division of Civil, Mechanical and Manufacturing Innovation (CMMI) of NSF and the DOE Office of Freedom CAR and Vehicle Technologies intend to co-sponsor proposals addressing fundamental research issues in advanced high strength steels (AHSS). Specifically, proposals focused on

1. AHSS materials development and characterization,
2. predictive modeling that integrates AHSS material structure and product performance, and
3. fundamental research in the area of processing and manufacturing of AHSS, are of interest. This collaborative effort is a direct outcome of the Advanced High Strength Steel Workshop.

Interested PIs should consider submitting an unsolicited proposal to the core programs of the CMMI Division namely, (1) Materials Processing & Manufacturing (MPM), (2) Materials Design & Surface Engineering (MDSE), (3) Applications & Structural Mechanics, or (4) Mechanics & Structures of Materials (MSM), during the January 15, 2007 to February 15, 2007 submission window. Unsolicited proposals in response to this letter should have titles beginning with "AHSS:".  Proposals from the March-April 2007 panel review will be eligible for co-funding, pending availability of funds.

Some time ago (12-19-06), Daniel Isabey posted an interesting comment on mechanical responses of cells obtained via magnetic twisting cytometry. While the comment was about the nonlinearity of the bead angular displacement, a broader question is how adequately the bead moment/angle relationship represents the complex cell mechanics. There are different patterns of actin bundles at the whole-cell level.

(A message from Dave Barnett) George Herrmann passed away yesterday in Switzerland -- quickly, quietly, and peacefully.

I just jointed iMechanica. Great blog site! I thought to bring to your attention another blog that I enjoy, run by a retired engineer, on renewable energy issues. Here is the link: http://thefraserdomain.typepad.com/