On the geometry and dynamics of crystalline continua. (English) Zbl 0916.73013

Summary: We introduce the concept of a material manifold in continuum mechanics. To describe, in the continuum limit, a crystalline solid containing an arbitrary distribution of dislocations, we endow the material manifold with a structure similar to a Lie group. Starting with a state function defined on the space of local thermodynamic equilibrium states, we formulate the dynamics of crystalline continua in accordance with the least action principle, within the framework of general relativity, in terms of a mapping of the space-time manifold into the material manifold. Besides, we include in our formulation electromagnetic effects.


74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
82D25 Statistical mechanics of crystals
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