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Foundations of Geometric Continuum Mechanics [2023]

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