Eulerian theory of deformable media

Dislocation and disclination charges in solids

One proposes here a theory which lays methodically the foundations of an original approach of the solid lattices deformation using the Euler coordinates, and which introduces in details the concept of tensor dislocation charges and tensor disclination charges within a lattice. This new concept allows one to quantify the topological singularities which can appear at the microscopic scale of a solid lattice. On the basis of this original approach of the solid lattices and their topological singularities, one can deduce a set of fundamental and phenomenological equations allowing to treat rigorously the macroscopic spatiotemporal evolution of a newtonian solid lattice which deforms in the absolute space of an external observer laboratory.