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Foundations of Geometric Continuum Mechanics : Geometry and Duality in Continuum Mechanics by Reuven Segev is a nonfiction available to read on EtoBox.

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of fluxes through any r-dimensional simplex in an n-dimensional space. As an additional feature, the proof is completely combinatorial. Once flux mappings have been defined on simplices, they are extended in Chap. 5 by linearity to polyhedral chains-linear combinations of simplices. In addition, the major role played by antisymmetric tensors motivates the introduction of additional aspects of exterior algebra in Chap. 5. In Part II we consider the smooth theory of fluxes, forces, and stresses as formulated on general n-dimensional differentiable manifolds. With some necessary modifications, the analog of Cauchy's stress theory is formulated on manifolds. An important outcome of the theory should be mentioned. When the theory is formulated in Euclidean spaces, the stress tensor object plays two roles. On the one hand, it determines the traction fields on subbodies, and in addition, it acts on the gradient of a velocity field to produce power. In the generalized theory, these two roles are played by two distinct mathematical objects. The traction stress is the object determining the traction on a subbody, and the variational stress produces power when acting on the derivative-the jet

Who reads Foundations of Geometric Continuum Mechanics : Geometry and Duality in Continuum Mechanics?

Author

Reuven Segev

Publisher

Birkhäuser

Published

2023

Language

EN

ISBN

9783031356544

Category

nonfiction

Subjects

Science, Mathematics, Physics