ON THE GEOMETRY AND DYNAMICS OF CRYSTALLINE CONTINUA

We introduce in continuum mechanics the concept of a material manifold . To describe, in the continuum limit, a crystalline solid containing an arbitrary distribution of dislocations, we endow the material manif old with a structure a k in to that of a Lie group. Starting with a st ate function defined on the space of local thermodynamic equilibrium s tates, we formulate the dynamics of crystalline continua in accordance with the least action principle, within the framework of general rela tivity, in terms of a mapping of the space time manifold into the mate rial manifold. We include in our formulation electromagnetic effects. (C) Elsevier, Paris.