arash_yavari's blog

We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold - where the body is stress free - is a Weitzenbock manifold, i.e. a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan's moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions.

In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem we consider the particular case of determining the residual stress field of a cylindrically-symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemaniann material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature.

In this paper we make a connection between covariant elasticity based on covariance of energy balance and Lagrangian field theory of elasticity with two background metrics. We use Kuchar's idea of reparametrization of field theories and make elasticity generally covariant by introducing a "covariance field", which is a time-independent spatial diffeomorphism. We define a modified action for parameterized elasticity and show that the Doyle-Ericksen formula and spatial homogeneity of the Lagrangian density are among its Euler-Lagrange (EL) equations.

Please see the attached ad.

Dear Friends:



I would like to encourage you to consider submitting papers to Mathematics and Mechanics of Solids. The focus of this journal is on applications of mathematical techniques to solid mechanics problems. You can find more information in the following link: http://mms.sagepub.com/



Please feel free to contact me (arash.yavari [at] ce.gatech.edu) if you have any questions regarding this journal.



Regards,

I am looking for a Ph.D. student to work on geometric mechanics of growing bodies (both surface and bulk growth). Candidates with strong math and mechanics backgrounds are encouraged to apply. Interested candidates should email me (arash.yavari [at] ce.gatech.edu) their CV along with the names of three references.

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.