On the Nonlinear Mechanics of Bravais Crystals with Continuous Distributions of Defects

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Abstract
Basic ideas in the mechanics of Bravais crystals with continuous distributions of point and line defects are revisited from a perspective that emphasizes the role of configurational forces. In addition, the creation, destruction, and transport of defects are presented in detail. The formulation of the balance laws is given over time-dependent spatial control volumes; furthermore, independent configurational and deformational force balances are postulated. Such a formulation is more versatile than one with standard fixed control volumes and provides the correct Eshelby relation from simple invariance arguments independent of constitutive relations. Two alternative but equivalent constitutive models are proposed, and the corresponding restrictions following from a dissipation inequality are determined. Relations to some previous formulations of continuous distributions of dislocations and vacancies are discussed.

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