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On Volterra Dislocations of Finitely Deforming Continua

In the context of finite deformations, a purely kinematical treatment of Volterra dislocations is presented. These dislocations correspond to deformations that have a jump discontinuity across a singular surface in a fixed reference configuration of the continuum, but whose right Cauchy-Green deformation tensor field is continuous and has second partial derivatives that are continuous. Analytical and geometrical proofs of Weingarten's theorem for finite deformations are given. Tune-dependent Volterra dislocations are also considered.