Geometric Continuum Mechanics

This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics.

Geometric Continuum Mechanics

This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.

More Books:

Geometric Continuum Mechanics
Language: en
Pages: 416
Authors: Reuven Segev, Marcelo Epstein
Categories: Mathematics
Type: BOOK - Published: 2020-05-13 - Publisher: Springer Nature

This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from
Geometric Continuum Mechanics and Induced Beam Theories
Language: en
Pages: 146
Authors: Simon R. Eugster
Categories: Science
Type: BOOK - Published: 2015-03-19 - Publisher: Springer

This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the
Differential Geometry and Continuum Mechanics
Language: en
Pages: 387
Authors: Gui-Qiang G. Chen, Michael Grinfeld, R. J. Knops
Categories: Mathematics
Type: BOOK - Published: 2015-08-11 - Publisher: Springer

This book examines the exciting interface between differential geometry and continuum mechanics, now recognised as being of increasing technological significance. Topics discussed include isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, the use of manifolds in the description of microstructure in continuum mechanics, experimental measurement
Geometrical Foundations of Continuum Mechanics
Language: en
Pages: 517
Authors: Paul Steinmann
Categories: Technology & Engineering
Type: BOOK - Published: 2015-04-07 - Publisher: Springer

This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity. After a motivation that arises
The Geometrical Language of Continuum Mechanics
Language: en
Pages: 312
Authors: Paul Steinmann
Categories: SCIENCE
Type: BOOK - Published: 2010 - Publisher:

"Epstein presents the fundamental concepts of modern differential geometry within the framework of continuum mechanics. Divided into three parts of roughly equal length, the book opens with a motivational chapter to impress upon the reader that differential geometry is indeed the natural language of continuum mechanics or, better still, that