This paper revisits continua with microstructure from a geometric point of view. We model a structured continuum as a triplet of Riemannian manifolds: a material manifold, the ambient space manifold of material particles and a director field manifold. Green-Naghdi-Rivlin theorem and its extensions for structured continua are critically reviewed.

FACULTY POSITION
 
 
MECHANICAL ENGINEERING
COLLEGE OF ENGINEERING
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
 
 

The main idea is the following: a most natural mathematical setup for considering the motion of the void-solid interface of an expanding void is that of the traveling wave. Thus, a theory for macroscopic damage evolution may be suspected as being a homogenized version of basic theory that has such wave phenomena as an essential ingredient. This paper is a first step in probing such questions. 

A three-year
PhD studentship is available within the Glasgow Research Partnership in
Engineering (GRPE) as part of the Joint Research Institute in Mechanics of
Materials, Structures and Bioengineering at the University of Glasgow. 
The
specific goals of the PhD will be to manufacture MREs and determine the
influence of manufacture conditions on the micro-structure and magnetic-sensitivity
of the magnetorheological elastomers (smart material).

Full support is available for 2 PhD students in cellular mechanics group in Biomedical Engineering Department at Rensselaer Polytechnic Institute.  

The applicants should have mechanics, materials or soft matter physics background, with some experimental experience at micro-scales.  Experience with any of the following is considered a
plus: computational mechanics, cell/tissue culture, microscopy, image analysis, photonics.

Hi, all

Molecular dynamics (or MC) is a powerful tool in the protein research. There're lots of scientific works in this field, which deepen our understanding gradually. My question follows, "how about the continuum mechaics in protein research".

Any discussions and advices are appreciated.

Kong    5th Sep 2007

When you first start learning finite deformation plasticity, you will run into a plastic flow rate that can be derived from a flow potential such that 

(1)

whereis the Cauchy stress.  For an isotropic material with scalar internal variables, the plastic
flow potential can be assumed to have the form 

(2)

where is the pressure, are invariants of the deviatoric stress, is the temperature, and are the internal variables. The quantities , , and are defined as 

Using the chain rule you can write 

(4)

The first problem that you run into is how to find the derivatives of the
invariants. My first attempt was to express everything in terms of components
and do the differentiations. That works but can be tedious.

An experienced mechanician would just have gone and read Truesdell and Noll
[1] and picked out the formulas from page 26 of that book.
However, that book scared me with all its old German and Hebrew notation.
For those of you who find Truesdell and Noll difficult to read, here's the
way that book deals with the problem of finding the derivatives of invariants.
Hope you find it useful.

an interesting puzzle for fun:

Lame’s classical solution for an elastic 2D plate, with a hole of radius a and uniform tensile stress applied at the far field, gives a stress concentration factor (SCF) of two at the edge of the hole. This SCF=2 is independent of the hole radius.

Consider what happened to this concentration factor if the radius a approaches infinitely small. The SCF is independent of a, so it remains equal to two even when the hole disappears.

This is inconsistent with what one would expect physically, namely that the limit a->0 should be the same as when the plate is whole without a hole and has no stress concentration.

Henry.

In continuum mechanics, it is a common practice to view a body as a field of material particles, so that the continuum mechanics is phrased as an algorithm to determine the function x(X, t), where X is the name of a particle, and x is the place of the particle at time t.

It seems to me this practice is only sensible if you can identify material particles. For example, when a crystal lattice undergoes an elastic deformation, we can regard a collection of atoms as a material particle. By contrast, if the crystal creeps and atoms diffuse around, the notion of material particles becomes questionable. In such a case, any collection of atoms will not stay together for very long for you to identify them collectively as one material particle.

Let's say the world has only e-books, then someone introduces this technology called 'paper.' It's cheap, portable, lasts essentially forever, and requires no batteries. You can't write over it once it's been written on, but you buy more very cheaply. Wouldn't that technology come to dominate the market?

With this example, Andraw McAfee, of Harvard Business School, begins his discussion of the technology flip test. Such a test may let us see through hypes.