Classical Continuum Mechanics

This book provides a comprehensive foundation in mathematics and physics for understanding the deformation of solid and fluent continua, including compressible and incompressible materials. It covers Lagrangian and Eulerian descriptions, co- and contra-variant bases, and introduces tensor calculus. It discusses Galilean and non-Galilean coordinate transformations, convected time derivatives, and entropy inequality. The book also demonstrates the use of energy methods and the principle of virtual work in deriving constitutive theories. It is suitable for graduate students and researchers in engineering and sciences.

Format: Hardback
Length: 510 pages
Publication date: 23 December 2021
Publisher: Taylor & Francis Ltd

This comprehensive text offers a solid foundation in both physical and mathematical principles, providing a thorough derivation of the mathematical descriptions and constitutive theories related to the deformation of solid and fluent continua, encompassing both compressible and incompressible materials. It distinguishes clearly between Lagrangian and Eulerian descriptions, as well as co- and contra-variant bases, and introduces definitions of co- and contra-variant tensors and tensor calculus within a curvilinear frame, which can then be specialized for the Cartesian frame. The book covers both Galilean and non-Galilean coordinate transformations, emphasizing their application in establishing objective tensors and objective rates. It derives convected time derivatives using conventional approaches as well as non-Galilean transformations, highlighting their significance in finite deformation of solid continua and in the context of fluent continua.

Constitutive theories are derived using entropy inequality and representation theorem, providing a robust framework for deriving these theories. The decomposition of total deformation into volumetric and distortional deformation is crucial in establishing a sound, general, and rigorous approach to constitutive theory development. Energy methods and the principle of virtual work are showcased as a subset of the calculus of variations, while differential forms of mathematical models and the calculus of variations preclude the use of these methods.

The material in this book is carefully structured to cater to students with varying levels of expertise, gradually progressing from fundamental concepts to advanced topics. It serves as a valuable resource for graduate students seeking to delve into the realm of mathematical concepts and theories related to deforming continuous matter, equipping them with the necessary knowledge for fundamental and basic research in engineering and sciences.

Weight: 950g
Dimension: 162 x 243 x 37 (mm)
ISBN-13: 9780367612962
Edition number: 2 New edition