Incompatibility-governed singularities in linear elasticity with dislocations

Incompatibility-governed Elasto-plasticity for Continua with Dislocations

In this paper, a novel model for elasto-plastic continua is presented and developed from the ground up. It is based on the interdependence between plasticity, dislocation motion and strain incompatibility. A generalized form of the equilibrium equations is provided, with as additional variables the strain incompatibility and an internal thermodynamic variable called compatibility modulus, that ...

Analysis of the Incompatibility Operator and Application in Intrinsic Elasticity with Dislocations

The incompatibility operator arises in the modeling of elastic materials with dislocations and in the intrinsic approach to elasticity, where it is related to the Riemannian curvature of the elastic metric. It consists of applying successively the curl to the rows and the columns of a 2nd-rank tensor, usually chosen symmetric and divergence free. This paper presents a systematic analysis of bou...

2 Minimizers with Topological Singularities in Two Dimensional Elasticity

For a class of 2-D elastic energies we show that a radial equilibrium solution is the unique global minimizer in a subclass of all admissible maps. The boundary constraint is a double cover of S; the minimizer u is C and is such that det∇u vanishes at one point. Mathematics Subject Classification. — Please, give AMS classification codes —. Received October 28, 2005. Revised March 31, 2006.

Discrete Crystal Elasticity and Discrete Dislocations in Crystals

This article is concerned with the development of a discrete theory of crystal elasticity and dislocations in crystals. The theory is founded upon suitable adaptations to crystal lattices of elements of algebraic topology and differential calculus such as chain complexes and homology groups, differential forms and operators, and a theory of integration of forms. In particular, we define the lat...

En224: Linear Elasticity