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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Homogenization of Edge-Dislocations as a Weak Limit of de-Rham Currentsd 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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Book 2020icular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics,

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Manifolds of Mappings for Continuum Mechanics 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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Manifolds of Mappings for Continuum Mechanicsracter is the smooth convenient manifold ..(., .) of all smooth mappings from a finite dimensional Whitney manifold germ . into a smooth manifold .. A Whitney manifold germ is a smooth (in the interior) manifold with a very general boundary, but still admitting a continuous Whitney extension operato

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Notes on Global Stress and Hyper-Stress Theoriessed framework is the infinite dimensional counterpart of the statics of a system having a finite number of degrees of freedom, as viewed in the geometric approach to analytical mechanics. For continuum mechanics, the configuration space is the manifold of embeddings of a body manifold into the space

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Applications of Algebraic Topology in Elasticityf nonlinear elasticity for non-simply-connected bodies when the ambient space is Euclidean. Algebraic topology is the natural tool to understand the topological obstructions to compatibility for both the deformation gradient . and the right Cauchy–Green strain .. We investigate the relevance of homo

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De Donder Construction for Higher Jetsresulting forms may depend on the coordinate system used. Nevertheless, it leads to many invariant conclusions. In some cases, like second order gravity, the construction leads to a unique De Donder form on the jet bundle that is independent of the choice of coordinates.

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