Elastic and plastic deformations

Abstract The decomposition of deformation into elastic and plastic parts is introduced in terms of transformations of the material symmetry group, due to plastic evolution, pertaining to a local undistorted state of the material. This leads naturally to the notion of dislocation density, interpreted as the torsion of the underlying material manifold. Torsion, in turn, implies that the elastic strain is incompatible, and hence that the material is residually stressed when unloaded.