The attached tutorial paper is yet unpublished but I am posting a pre-print since several students I know have found it to be a useful pedagogical resource. You may also access the document on arXiv.

Here is the abstract.

Soft materials, such as liquids, polymers, foams, gels, colloids, granular materials, and most soft biological materials, play an important role in our daily lives. From a mechanical viewpoint, soft materials can easily achieve large deformations due to their low elastic moduli; meanwhile, surface instabilities, including wrinkles, creases, folds, and ridges, among others, are often observed. In particular, soft dielectrics when subjected to electrical stimuli can achieve signicantly large deformations that are often accompanied by instabilities. While instabilities are conventionally thought to cause failures in the engineering context and carry a negative connotation, they can also
be harnessed for various applications such as surface patterning, giant actuation strain, and energy harvesting. In the biological world, instability and bifurcation phenomena often precede important events such as endocytosis, cell fusion, among others. Stability and bifurcation analysis (especially for soft materials) is challenging and often presents a formidable barrier to entry in this important field. A multidisciplinary audience may lack the background in one or more areas that are needed to carry out the requisite modeling or even understand papers in the literature. Furthermore, combining electrostatics together with large deformations brings its own challenges. In this article, we provide a tutorial on the basics of stability and bifurcation analysis in the context of soft electromechanical materials. The aim of the article is to use simple examples and to gently lead a reader, unfamiliar with either stability analysis or electrostatics of deformable media, to develop the ability to understand the pertinent literature that already exists and position them to embark on the state-of-the-art research on this topic.

The NNIN/C at the University of Michigan will be hosting a presentation on “Solving for Micro and Macro-scale Electrostatic Configurations using Robin Hood Solver.”, which will be broadcast live as a web based seminar.

Topic: Solving for Micro and Macro-scale Electrostatic Configurations using Robin Hood Solver.
Date: March 14th, 2013
Time: 11:00 am – 12:00 pm EDT.

Presenters:
Toni Drabik, Sales Director at Artes Calculi Ltd.
Hrvoje Abraham, CEO, Artes Calculi Ltd.

Abstract:

In this webinar you will learn how you can use Robin Hood Solver to create and solve electrostatic models – from simple to the more complex ones. We will demonstrate how Robin Hood Solver can be used to quickly and easily set-up and solve electrostatic problems with various boundary conditions, precise calculation and attractive visualization of electric field and potential, estimation of Faraday cage shielding capabilities, capacitance and capacitance matrix of arbitrary electrode configuration which is of special importance in capacitive sensor development. We will also show how the results of the calculation can be post-processed and visualized in order to quickly grasp the meaning of the obtained numbers. Advanced features such as Lua scripting, export/import of data to/from other tools will be also discussed and we will show Robin Hood Solver advanced task-based concept which enables the user to easily go back to any previously performed operation and change it, thus also changing all subsequent operations. At the end, we will briefly touch on more complex examples and applications of use and we will dedicate time for questions and answers.

Registration is free.

To Register, please visit

http://lnf.umich.edu/nnin-at-michigan/index.php/robin-hood/

In this manuscript (available at http://arxiv.org/abs/1004.1765), we present a systematically improvable, linear scaling formulation for the solution of the all-electron Coulomb problem in crystalline solids. In an infinite crystal, the electrostatic (Coulomb) potential is a sum of nuclear and electronic contributions, and each of these terms diverges and the sum is only conditionally convergent due to the long-range 1/r nature of the Coulomb interaction. In the all-electron quantum-mechanical problem in solids, there are three distinct divergences that must be addressed simultaneously: (1) the 1/r divergence of the electrostatic potential at the nuclei; (2) the divergence of both potential and energy lattice sums due to the long-range Coulomb interaction; and (3) the infinite self energies of the nuclei.

We achieve linear scaling by introducing smooth, strictly local neutralizing densities to render nuclear interactions strictly local, and solving the remaining neutral Poisson problem for the electrons in real space. In so doing, the all-electron problem is decomposed into analytic strictly-local nuclear, and numerical long-range electronic parts; with required numerical solution in the Sobolev space , so that convergence is assured and approximation is optimal in the energy norm. Expressions for the Coulomb energy per unit cell, analytically excluding the divergent nuclear self-energy, are derived. Rapid variations in the required neutral electronic potential in the vicinity of the nuclei are efficiently treated by an enriched finite element solution, using local radial solutions as enrichments (see this paper). We demonstrate the accuracy and convergence of the approach by direct comparison to standard Ewald sums for a lattice of point charges, and demonstrate the accuracy in quantum-mechanical calculations with an application to crystalline diamond.

For some background material on density-functional theory and all-electron calculations, the discussions in the September 2008 and February 2009 journal club issues are pertinent.

Update: The position has been filled; thanks to all who responded.

A post-doctoral position is immediately available at UC Davis. The individual will work on a joint project led by myself and John Pask at LLNL on the development and application of a new finite-element based approach for large-scale quantum mechanical materials calculations.

The research is aimed at getting beyond standard planewave based methods for large-scale quantum molecular dynamics, and addressing a range of problems that have been inaccessible so far by such accurate, quantum-mechanical means. The key ingredient of the new finite-element based approach, as currently formulated, is the partition-of-unity basis which allows known physics to be built into the basis set without sacrificing locality or systematic improvability; thus allowing for a substantial reduction in basis size while retaining natural and efficient parallelization.

The candidate should possess a strong background in finite elements and computational mathematics, with excellent programming skills. Knowledge and research experience in quantum mechanics, electronic-structure calculations, and/or nanomechanics will be advantageous. Interested individuals should send a copy of their curriculum vitae, a list of three references, and a short statement of research interests (upto a page) to me via e-mail. Please send a single PDF file to me at nsukumar@ucdavis.edu

Electro-sensitive (ES) elastomers form a class of smart materials whose mechanical properties can be changed rapidly by the application of an electric field. These materials have attracted considerable interest recently because of their potential for providing relatively cheap and light replacements for mechanical devices, such as actuators, and also for the development of artificial muscles. In this paper we are concerned with a theoretical framework for the analysis of boundary-value problems that underpin the applications of the associated electromechanical interactions. We confine attention to the static situation and first summarize the governing equations for a solid material capable of large electroelastic deformations. The general constitutive laws for the Cauchy stress tensor and the electric field vectors for an isotropic electroelastic material are developed in a compact form following recent work by the authors. The equations are then applied, in the case of an incompressible material, to the solution of a number of representative boundary-value problems. Specifically, we consider the influence of a radial electric field on the azimuthal shear response of a thick-walled circular cylindrical tube, the extension and inflation characteristics of the same tube under either a radial or an axial electric field (or both fields combined), and the effect of a radial field on the deformation of an internally pressurized spherical shell.

A. Dorfmann and R. W. Ogden, DOI: 10.1007/s10659-005-9028-y

T. Zhu, Z. Suo, A. Winkleman, G. M. Whitesides, Applied Physics Letters, 88, 144101, (2006)

A process has been demonstrated recently to assemble microspheres on a patterned electrode under the influence of an applied voltage. Here we examine the mechanics of this process, and describe both the conditions under which excess microspheres jump off the electrode when the voltage is applied, and the forces that attract the remaining microspheres to the desired positions. A quantitative mechanistic understanding of this process rationalizes experimental observations, provides scaling relations, and suggests modifications of the process.