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This book addresses the basic concepts of continuum mechanics, that is, the classical field theory of deformable bodies. The theory is systematically developed, from the kinematics to the balance equations, the material theory, and the entropy principles. In turn, the linear-elastic solids, the ideal liquid and the Newtonian liquid are presented in detail as concrete applications. The book concludes by covering the theory of small motions in a medium with a finite prestress. In general, the emphasis is on presenting the content in a clear and straightforward way that requires only an elementary grasp of calculus, linear algebra, and Newtonian mechanics. The book is intended for students of physics, mechanics, engineering and the geosciences, as well as applied mathematics, with a year or more of college calculus behind them.
List of contents
Geometry of Deformation.- Basic Kinematics.- Measures of Stress.- Fundamental Conservation Principles.- Moving Reference Frames.- Constitutive Equations.- Entropy Principles.- Classical Linear Elasticity.- Infinitesimal Deformation of a Body with a Finite Pre-Stress.
About the author
Zdenek Martinec, Dublin Institute for Advanced Studies, Dublin, IrelandandDepartment of Geophysics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Summary
This book addresses the basic concepts of continuum mechanics, that is, the classical field theory of deformable bodies. The theory is systematically developed, from the kinematics to the balance equations, the material theory, and the entropy principles. In turn, the linear-elastic solids, the ideal liquid and the Newtonian liquid are presented in detail as concrete applications. The book concludes by covering the theory of small motions in a medium with a finite prestress. In general, the emphasis is on presenting the content in a clear and straightforward way that requires only an elementary grasp of calculus, linear algebra, and Newtonian mechanics. The book is intended for students of physics, mechanics, engineering and the geosciences, as well as applied mathematics, with a year or more of college calculus behind them.
Additional text
“Principles of Continuum Mechanics can nevertheless serve as a useful quick-reference summary of major results and analysis methods in continuum mechanics.” (R. M. Brannon, Physics Today, April, 2020)
“The book will be a useful support for undergraduate students from different fields. It can also be useful to researchers who will find the bases of continuum mechanics with examples.” (Alain Brillard, zbMATH 1428.74001, 2020)
Report
"Principles of Continuum Mechanics can nevertheless serve as a useful quick-reference summary of major results and analysis methods in continuum mechanics." (R. M. Brannon, Physics Today, April, 2020)
"The book will be a useful support for undergraduate students from different fields. It can also be useful to researchers who will find the bases of continuum mechanics with examples." (Alain Brillard, zbMATH 1428.74001, 2020)
