continuum mechanics

Amit Acharya         Marta Lewicka         Mohammad Reza Pakzad

In Nonlinearity, 29, 1769-1797

We study a class of design problems in solid mechanics, leading to a variation on the
classical question of equi-dimensional embeddability of Riemannian manifolds. In this general new
context, we derive a necessary and sufficient existence condition, given through a system of total
differential equations, and discuss its integrability. In the classical context, the same approach
yields conditions of immersibility of a given metric in terms of the Riemann curvature tensor.
In the present situation, the equations do not close in a straightforward manner, and successive
differentiation of the compatibility conditions leads to a more sophisticated algebraic description
of integrability. We also recast the problem in a variational setting and analyze the infimum value
of the appropriate incompatibility energy, resembling "non-Euclidean elasticity".  We then derive a
Γ-convergence result for the dimension reduction from 3d to 2d in the Kirchhoff energy scaling
regime. A practical implementation of the algebraic conditions of integrability is also discussed.

This paper presents a homogenization-based constitutive model for the mechanical behavior of particle-reinforced elastomers with random microstructures subjected to finite deformations. The model is based on a recently developed homogenization method (Avazmohammadi and Ponte Castaneda 2013; J. Elasticity 112, 1828–1850) for two-phase, hyperelastic composites, and is able to directly account for the shape, orientation, and concentration of the particles.

Dear friends of IMechanica:

Primary data mining through Web of Science
reveals that the number of papers containing “continuum mechanics ” increases
rapidly these years. This is a very exciting fact to our mechanicians. Thus, I
wrote a short paper titled “The Renaissance of Continuum Mechanics”, which was just
published online via:

Politecnico di Milano 

Department of Civil and Environmental Engineering

Postdoc position in Solid/Computational Mechanics

Fixed term position for up to 18 months

Salary: 25,000 Euro per annum

In armchair graphene sheets, crack propagates perpendicular to the applied strain, whereas crack propagation in zigzag sheets occurs at an angle to the straining direction. This occurs due to different bond structure along armchair and zigzag directions as shown in Fig. 1. Videos 1 and 2 show the fracture of armchair and zigzag sheets, respectively.

Fig. 1: Armchair and zigzag directions of graohene

I attach some class notes developed by the late Professor Donald Carlson from which many generations of students at the University of Illinois learnt Continuum Mechanics.

Linear algebra is significant to many aspects of mechanics.  For some years I have been using the book by Shilov.  But this book may or may not be a good one to recommend to a student, depending on his or her prior experience.  On StackExchange Mathematics, there are several excellent threads discussing textbooks of linear algebra.  A particular recommendation was made for

Amit Acharya         Claude Fressengeas

Springer Proceedings in Mathematics and Statistics on Differential Geometry and Continuum Mechanics, Vol. 137, pages 123-165. Ed: G. Q Chen, M. Grinfeld, R.J. Knops (Proceedings of  Workshop held at the Intl. Centre for Mathematical Sciences in Edinburgh, 2013.)

We cordially invite you to participate in at the 3rd African Conference on Computational Mechanics - An International Conference – AfriCOMP13 (July 30 – August 2, 2013, Livingston, Zambia) by giving a talk in our minisymposium "Computational modeling of nano- and microstructured materials". 

The Helmholtz-Institute of Materials Research in Geesthacht, Germany, invites applications for a Scientific researcher m/f.
The position is initially limited for one year with the possibility of an additional three-year-extension (starting as soon as possible).

Hossein Pourmatin     Amit Acharya       Kaushik Dayal

(to appear in Quarterly of Applied Mathematics)

After many publications and lecture notes, Prof. Ian Murdoch has finally organized much of that material in the form of a book.

I am very hopeful that like Prof. Murdoch's lectures, this monograph will also help the readers to develop a better understanding of the physical aspects of mechanics. It will be a valuable addition to the researchers' personal collection. 

Link:

http://www.cambridge.org/gb/knowledge/isbn/item6828574

more details in the flyer attached.

A new postdoctoral position in the mechanics of glassy/amorphous materials is
available at the Weizmann Institute of Science. The project will focus on
strongly non-linear phenomena such as cavitation, shear-banding and fracture,
with applications to Bulk Metallic Glasses, and will involve advanced

Dear Colleague:

An intensive 4-day short course on the fundamentals of continuum, atomistic and multiscale modeling of materials will be held at AICES in Aachen, Germany during August 14-17, 2012. The course will be taught by Profs. Ellad Tadmor and Ronald Miller. Please see the attached flyer for more information.

Enrollment is limited so early registration is recommended. To register, visit http://www.modelingmaterials.org/short-courses

There is an open position in the Advanced Tire Technology department in Bridgestone Americas Tire Operations (www.bridgestone-firestone.com). Please see the attached flyer for details and send resume, if interested, to bfpd@bfusa.com

Attached are some (hand-written) observations on wanting to do continuum mechanics when mass is not conserved for fixed sets of particles of the body (so, situations transcending the rocket-losing-mass type). I feel (un)comfortable with these observations, depending upon the day I think about such things.

Discover the NANOMOTION World as an Early Stage Researcher (PhD student) in an EU-wide program on “Nanoelectromechanical Motion in Functional Materials (NANOMOTION)”!

The individual project:

“Finite-element modelling of electromechanically coupled materials”

will be hosted at University of Duisburg-Essen (Germany), www.uni-due.de/mechanika, with secondment to the University College Dublin (Ireland).

Payam Soltani, J. Saberian, R. Bahramian, and A. Farshidianfar

http://fundamentaljournals.org/ijfps/archive.html#A14 

In this Paper, the nonlinear free and force vibration of a single-walled carbon nanotube (SWCNT) with simply supported ends is

investigated based on von Karman’s geometric nonlinearity. The SWCNT described as an individual shell and the Donnell’s

equations of cylindrical shells are used to obtain the governing equations. The Galerkin's procedure is used to discretized partial