Titlebook: Geometric Continuum Mechanics; Reuven Segev,Marcelo Epstein Book 2020 The Editor(s) (if applicable) and The Author(s), under exclusive lic

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Care Supply in Its Structures and Processes,s the theory of Schwartz distributions plays with respect to ordinary functions. After a review of the main mathematical aspects, the theory is illustrated with a profusion of examples and applications.

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Learning, developing and planning,assumptions is necessary. Also, as motivation, we take the current effort in continuum mechanics to rationalize the connection between continuum and discrete models of materials, and so review results which elucidate the rigorous connection between continuous and discrete structures in the context of Davini’s model.

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Regular and Singular Dislocationss the theory of Schwartz distributions plays with respect to ordinary functions. After a review of the main mathematical aspects, the theory is illustrated with a profusion of examples and applications.

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1571-8689 analysis, algebraic topology, algebroids, groupoids, and geoThis contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topolog

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Robert Bor,Sheila Gill,Christine Parrott Whitney manifold germ is a smooth (in the interior) manifold with a very general boundary, but still admitting a continuous Whitney extension operator. This notion is developed here for the needs of geometric continuum mechanics.

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The Emergence of the Modern Prison,onals defined on tangent vectors, elements of the cotangent bundle. It is shown, in particular, that a natural choice of topology on the configuration space implies that force functionals may be represented by objects that generalize the stresses of traditional continuum mechanics.

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https://doi.org/10.1007/978-3-658-44640-6d edge-dislocations. We also define a notion of singular torsion current (associated with isolated dislocations), and prove that the torsion currents converge, in the homogenization limit, to the smooth torsion field which is the continuum measure of the dislocation density.

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