Abstract
The fundamental postulate of continuum mechanics states that a body is a three-dimensional differentiable manifold and its motions are diffeomorphisms. Simple thought experiments with cyclic motions of dislocations show that they do not preserve topology (set of neighborhoods). The same is valid for chaotic and turbulent motions with coarse-graining. To describe such motions, kinematics of a generalized continuum mechanics is suggested. Observables are defined operationally in the laboratory system which is not anymore equivalent to the Lagrangian picture. The body is a submanifold of a higher-dimensional space and generalized motions are its diffeomorphisms. In a gauge-theoretic interpretation, the motion is a translational connection with the curvature identified as a “dislocation” density-flux.
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Kunin, I.A. Kinematics of media with continuously changing topology. Int J Theor Phys 29, 1167–1176 (1990). https://doi.org/10.1007/BF00672929
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DOI: https://doi.org/10.1007/BF00672929