Geometric Continuum Mechanics - by Reuven Segev & Marcelo Epstein (Paperback)

Number of Pages: 416
Genre: Mathematics
Sub-Genre: Geometry
Format: Paperback
Publisher: Birkhauser
Age Range: Adult
Book theme: Differential
Author: Reuven Segev & Marcelo Epstein
Language: English

Book Synopsis

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.

From the Back Cover

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.