The Article demonstrates the spontaneous symmetry breaking of isotropic homogeneous elastic medium in form of transition from Euclidean to Riemann-Cartan internal geometry of medium. The deformation of elastic medium without defects is based on Euclidean geometry in three dimensional space. The deformation of elastic medium with defects is based on Riemann-Cartan geometry and is interpreted in this Article, as different phase state. In this article, the expression for the free energy leading is… Expand

The elasticity of continuous media with topological defects is described naturally by differential geometry, since it relates metric to strain. We construct a geometrical field theory, identifying… Expand

Dislocations are the elementary carriers in many situations of plastic flow. Since they can be seen, counted and typified, e.g. in the electron microscope, and since their presence changes the state… Expand

Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences

1998

This work presents a study of the formal structure of the theory of finite–strain polar elasticity and thermoelasticity with special attention to the construction of canonical balance laws that… Expand

IN THIS PAPER, we shall review earlier work on canonical forms in linear elasticity, and applications to the classification of conservation laws (path-independent integrals).

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… Expand