Variational approach in dislocation theory

Variational approach in dislocation theory

A variational approach is presented to calculate the stress field generated by a system of dislocations. It is shown that in the simplest case, when the material containing the dislocations obeys Hooke’s law the variational framework gives the same field equations as Kröner’s theory. However, the variational method proposed allows to study many other problems like dislocation core regularisatio...

Variational Approach to Retinex Theory

The Cosserat Vector In Membrane Theory : A Variational Approach

In a previous article (see [BFM]) the authors studied a model of nonlinear membrane where the external surface loading induces a density of bending moment. Due to the special form of the applied surface forces, the emerging Cosserat vector, result of the 3D-2D dimension reduction, was restricted to a class of two dimensional functions. In this paper we analyze the more general case where the Co...

Thermal effects in dislocation theory.

The mechanical behaviors of polycrystalline solids are determined by the interplay between phenomena governed by two different thermodynamic temperatures: the configurational effective temperature that controls the density of dislocations, and the ordinary kinetic-vibrational temperature that controls activated depinning mechanisms and thus deformation rates. This paper contains a review of the...

Generalized Sampling: A Variational Approach. Part I: Theory

We consider the problem of reconstructing a multidimensional vector function f in : R → R from a finite set of linear measures. These can be irregularly sampled responses of several linear filters. Traditional approaches reconstruct in an a priori given space; e.g., the space of bandlimited functions. Instead, we have chosen to specify a reconstruction that is optimal in the sense of a quadrati...