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Cosserat Continuum Mechanics [electronic resource] : With Applications to Granular Media / by Ioannis Vardoulakis (Deceased).

By: Vardoulakis (Deceased), Ioannis [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Applied and Computational Mechanics: 87Publisher: Cham : Springer International Publishing : Imprint: Springer, 2019Edition: 1st ed. 2019.Description: IX, 179 p. 68 illus., 43 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319951560.Subject(s): Mechanics, Applied | Solids | Engineering geology | Soft condensed matter | Solid Mechanics | Geoengineering | Soft and Granular MatterAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 620.105 Online resources: Click here to access online
Contents:
Introduction -- Rigid-body mechanics and motors -- Cosserat continuum kinematics -- Cosserat continuum statics -- Cosserat continuum dynamics -- Cosserat continuum energetics -- Cosserat-elastic bodies -- Cosserat fluids -- Mechanics of discrete granular media.
In: Springer Nature eBookSummary: This textbook explores the theory of Cosserat continuum mechanics, and covers fundamental tools, general laws and major models, as well as applications to the mechanics of granular media. While classical continuum mechanics is based on the axiom that the stress tensor is symmetric, theories such as that expressed in the seminal work of the brothers Eugène and François Cosserat are characterized by a non-symmetric stress tensor. The use of von Mises motor mechanics is introduced, for the compact mathematical description of the mechanics and statics of Cosserat continua, as the Cosserat continuum is a manifold of oriented “rigid particles” with 3 dofs of displacement and 3 dofs of rotation, rather than a manifold of points with 3 dofs of displacement. Here, the analysis is restricted to infinitesimal particle displacements and rotations. This book is intended as a valuable supplement to standard Continuum Mechanics courses, and graduate students as well as researchers in mechanics and applied mathematics will benefit from its self-contained text, which is enriched by numerous examples and exercises. .
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Introduction -- Rigid-body mechanics and motors -- Cosserat continuum kinematics -- Cosserat continuum statics -- Cosserat continuum dynamics -- Cosserat continuum energetics -- Cosserat-elastic bodies -- Cosserat fluids -- Mechanics of discrete granular media.

This textbook explores the theory of Cosserat continuum mechanics, and covers fundamental tools, general laws and major models, as well as applications to the mechanics of granular media. While classical continuum mechanics is based on the axiom that the stress tensor is symmetric, theories such as that expressed in the seminal work of the brothers Eugène and François Cosserat are characterized by a non-symmetric stress tensor. The use of von Mises motor mechanics is introduced, for the compact mathematical description of the mechanics and statics of Cosserat continua, as the Cosserat continuum is a manifold of oriented “rigid particles” with 3 dofs of displacement and 3 dofs of rotation, rather than a manifold of points with 3 dofs of displacement. Here, the analysis is restricted to infinitesimal particle displacements and rotations. This book is intended as a valuable supplement to standard Continuum Mechanics courses, and graduate students as well as researchers in mechanics and applied mathematics will benefit from its self-contained text, which is enriched by numerous examples and exercises. .

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