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Foundations of Geometric Continuum Mechanics [2023]
- 1
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Introduction
- 2
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Prelude: Finite-Dimensional Systems
- 3
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Simplices in Affine Spaces and Their Boundaries
- 4
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Uniform Fluxes in Affine Spaces
- 5
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From Uniform Fluxes to Exterior Algebra
- 6
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Smooth Analysis on Manifolds: A Short Review
- 7
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Interlude: Smooth Distributions of Defects
- 8
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Smooth Fluxes
- 9
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Frames, Body Points, and Spacetime Structure
- 10
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Stresses
- 11
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Smooth Electromagnetism on Manifolds
- 12
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The Elasticity Problem
- 13
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Symmetry and Dynamics
- 14
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Banachable Spaces of Sections of Vector Bundles over Compact Manifolds
- 15
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Manifolds of Sections and Embeddings
- 16
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The General Framework for Global Analytic Stress Theory
- 17
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Dual Spaces Corresponding to Spaces of Differentiable Sections of a Vector Bundle: Localization of Sections and Functionals
- 18
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de Rham Currents
- 19
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Interlude: Singular Distributions of Defects in Bodies
- 20
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Vector-Valued Currents
- 21
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The Representation of Forces by Stresses and Hyperstresses
- 22
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Simple Forces and Stresses
- 23
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Whitney’s Geometric Integration Theory and Non-smooth Bodies
- 24
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Optimal Fields and Load Capacity of Bodies