The concept of a material manifold was introduced into continuum mechanics. In order to describe, in the continuum limit, a crystalline solid which contained an arbitrary distribution of dislocations, the material manifold was endowed with a structure which was similar to that of a Lie group. Starting with a state function that was defined on the space of local thermodynamic equilibrium states, the dynamics of crystalline continua were formulated in accord with the least action principle of general relativity; with a mapping of the spacetime manifold into the material manifold. Electromagnetic effects were included in the formulation.

On the Geometry and Dynamics of Crystalline Continua. D.Christodoulou: Annales de l’Institut Henri Poincaré - Physique Theorique, 1998, 69[3], 335-58