Reuven Segev

Title: Some Geometric Aspects of Stress Theory

Stress tensors are used in strength analysis of structures, fluid dynamics, electromagnetism, and general relativity. Yet, from the theoretical point of view, the stress tensor object is not a primitive one. It is derived on the basis of some physically motivated mathematical assumptions which one would like to weaken. A formulation of stress theory that applies to the geometry of differentiable manifolds, devoid of any particular Riemannian metric or a connection, will be presented. The properties of stresses emerge naturally from the structure of the configuration space, a manifold of mappings, of a material body in the physical space.

 

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