arash_yavari's blog

This paper presents a stability analysis for fractal cracks. First, the Westergaard stress functions are proposed for semi-infinite and finite smooth cracks embedded in the stress fields associated with the corresponding self-affine fractal cracks. These new stress functions satisfy all the required boundary conditions and according to Wnuk and Yavari's embedded crack model they are used to derive the stress and displacement fields generated around a fractal crack.

In this paper, the coupled thermo-mechanical response of shape memory alloy (SMA) bars and wires in tension is studied.It is shown that the accuracy of assuming adiabatic or isothermal conditions in the tensile response of SMA bars strongly depends on the size and the ambient condition in addition to the rate-dependency that has been known in the literature.

Congratulations to Julian Rimoli (who's one of the moderators of iMechanica) for winning the 2010 James Clerk Maxwell Young Writers Prize!

http://www.tandf.co.uk/journals/authors/tphm-tphl-prize.asp

The School of Civil and Environmental Engineering invites applications for two tenure-track faculty positions in structural engineering/mechanics/materials (SEMM). Candidates at all ranks are sought with expertise in one or more of the following areas: (1) computational/solid mechanics; (2) infrastructure materials. The expected starting date is August, 2011.

A rigorous proof for convergence of the Wolf method for calculating electrostatic energy of a periodic lattice is presented. In particular, we show that for an arbitrary lattice of unit cells, the lattice sum obtained via Wolf method converges to the one obtained via Ewald method.

The session organizers would like to invite researchers to participate in a minisymposium titled "Multiscale constitutive modeling of materials" at the 11th US NATIONAL CONGRESS ON COMPUTATIONAL MECHANICS (USNCCM 11) to be held in Minneapolis, Minnesota from July 25-29, 2011.

We impose uniform electric fields both parallel and normal to 180^o ferroelectric domain walls in PbTiO3 and obtain the equilibrium structures using the method of anharmonic lattice statics. In addition to Ti-centered and Pb-centered perfect domain walls, we also consider Ti-centered domain walls with oxygen vacancies. We observe that electric field can increase the thickness of the domain wall considerably. We also observe that increasing the magnitude of electric field we reach a critical electric field E^c; for E > E^c there is no local equilibrium configuration.

It is with the deepest sadness that I inform you that Professor Jerrold E. Marsden passed away on September 21.

http://www.cds.caltech.edu/~marsden/

http://www.cds.caltech.edu/~marsden/remembrances/?p=1

Joint Postdoctoral Fellow Position at KAUST
and Georgia Institute of Technology — Accepting applications until the
position is filled

We have one more opening and have no U.S. visa waiver requirement anymore.

Using the method of anharmonic lattice statics, we calculate the equilibrium structure of steps on 180^o ferroelectric domain

                                     
Joint Postdoctoral Fellow Position at KAUST and Georgia Institute of Technology — Accepting applications until the position is filled

We have one more opening and have no U.S. visa waiver requirement anymore.

In this letter we obtain the finite-temperature structure
of 180^o domain walls in PbTiO_3 using a quasi-harmonic
lattice dynamics approach. We obtain the temperature dependence of
the atomic structure of domain walls from 0 K up to room
temperature. We also show that both Pb-centered and Ti-centered
180^o domain walls are thicker at room temperature; domain
wall thickness at T=300 K is about three times larger than that of
T=0 K. Our calculations show that Ti-centered domain walls have a

In this paper we first obtain the order of stress singularity for a dynamically propagating self-affine fractal crack. We then show that there is always an upper bound to roughness, i.e. a propagating fractal crack reaches a terminal roughness. We then study the phenomenon of reaching a terminal velocity. Assuming that propagation of a fractal crack is discrete, we predict its terminal velocity using an asymptotic energy balance argument. In particular, we show that the limiting crack speed is a material-dependent fraction of the corresponding Rayleigh wave speed.

In this paper we extend the classical method of lattice dynamics to defective crystals with partial symmetries. We start by a nominal defect configuration and first relax it statically. Having the static equilibrium configuration, we use a quasiharmonic lattice dynamics approach to approximate the free energy. Finally, the defect structure at a finite temperature is obtained by minimizing the approximate Helmholtz free energy. For higher temperatures we take the relaxed configuration at a lower temperature as the reference configuration.

In this paper, we study the effect of normal and shear strains and
oxygen vacancies on the structure of 180^o ferroelectric
domain walls in PbTiO_3.

This paper presents a geometric theory of the mechanics of growing bodies.

This paper is dedicated to the memory of Professor Jim Knowles.

http://lanl.arxiv.org/abs/0911.4671

In this paper we formulate a geometric theory of thermal stresses.
Given a temperature distribution, we associate a Riemannian
material manifold to the body, with a metric that explicitly
depends on the temperature distribution. A change of temperature
corresponds to a change of the material metric. In this sense, a
temperature change is a concrete example of the so-called
referential evolutions. We also make a concrete connection between
our geometric point of view and the multiplicative decomposition

http://arxiv.org/PS_cache/arxiv/pdf/0903/0903.5321v1.pdf

The above article is an April Fool's joke. It reminded me of the recent "discoveries" in the mechanics community regarding stress tensor.

Regards,
Arash

The fractal crack model described here incorporates the essential
features of the fractal view of fracture, the basic concepts of
the LEFM model, the concepts contained within the
Barenblatt-Dugdale cohesive crack model and the quantized
(discrete or finite) fracture mechanics assumptions. The
well-known entities such as the stress intensity factor and the
Barenblatt cohesion modulus, which is a measure of material
toughness, have been re-defined to accommodate the fractal view of
fracture.

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.

This paper studies the invariance of balance of
energy for a system of interacting particles under groups of
transformations. Balance of energy and its invariance is first
examined in Euclidean space. Unlike the case of continuous media,
it is shown that conservation and balance laws do not follow
from the assumption of invariance of balance of energy under
time-dependent isometries of the ambient space. However, the
postulate of invariance of balance of energy under arbitrary
diffeomorphisms of the ambient (Euclidean) space, does yield

This paper presents a geometric discretization of elasticity when
the ambient space is Euclidean. This theory is built on ideas from
algebraic topology, exterior calculus and the recent developments
of discrete exterior calculus. We first review some geometric
ideas in continuum mechanics and show how constitutive equations
of linearized elasticity, similar to those of electromagnetism,
can be written in terms of a material Hodge star operator. In the
discrete theory presented in this paper, instead of referring to

In this paper we covariantly obtain the governing equations of linearized elasticity. Our motivation is to see if one can make a connection between (global) balance of energy in nonlinear elasticity and its counterpart in linear elasticity. We start by proving a Green-Naghdi-Rivilin theorem for linearized elasticity. We do this by first linearizing energy balance about a given reference motion and then by postulating its invariance under isometries of the Euclidean ambient space.

This paper extends the recently developed theories of fracture
mechanics with finite growth (mainly the work of Pugno and Ruoff, 2004
on quantized fracture mechanics) to fractal cracks. One interesting
result is the prediction of crack roughening for fractal cracks.

This paper presents an anharmonic lattice statics analysis of 180 and 90 domain walls in tetragonal ferroelectric perovskites. We present all the calculations and numerical examples for the technologically important ferroelectric material PbTiO3. We use shell potentials that are fitted to quantum mechanics calculations. Our formulation places no restrictions on the range of the interactions. This formulation of lattice statics is inhomogeneous and accounts for the variation of the force constants near defects.