ON THE NONLINEAR MECHANICS OF BRAVAIS CRYSTALS WITH CONTINUOUS DISTRIBUTIONS OF DEFECTS

Basic ideas in the mechanics of Bravais crystals with continuous distr ibutions of point and line defects are revisited from a perspective th at emphasizes the role of configurational forces. In addition, the cre ation, destruction, and transport of defects are presented in detail. The formulation of the balance laws is given over time-dependent spati al control volumes; furthermore, independent configurational and defor mational force balances are postulated. Such a formulation is more ver satile than one with standard fixed control volumes and provides the c orrect Eshelby relation from simple invariance arguments independent o f 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 f ormulations of continuous distributions of dislocations and vacancies are discussed.