Foundations of the Theory of Elasticity, Plasticity, and Viscoelasticity details fundamental and practical skills and approaches for carrying out research in the field of modern problems in the mechanics of deformed solids, which involves the theories of elasticity, plasticity, and viscoelasticity. The book includes all modern methods of research as well as the results of the authors’ recent work and is presented with sufficient mathematical strictness and proof.
The first six chapters are devoted to the foundations of the theory of elasticity. Theory of stress-strain state, physical relations and problem statements, variation principles, contact and 2D problems, and the theory of plates are presented, and the theories are accompanied by examples of solving typical problems.
The last six chapters will be useful to postgraduates and scientists engaged in nonlinear mechanics of deformed inhomogeneous bodies. The foundations of the modern theory of plasticity (general, small elastoplastic deformations and the theory of flow), linear, and nonlinear viscoelasticity are set forth. Corresponding research of three-layered circular plates of various materials is included to illustrate methods of problem solving. Analytical solutions and numerical results for elastic, elastoplastic, lineaer viscoelastic and viscoelastoplastic plates are also given. Thermoviscoelastoplastic characteristics of certain materials needed for numerical account are presented in the eleventh chapter.
The informative book is intended for scientists, postgraduates and higher-level students of engineering spheres and will provide important practical skills and approaches.
“In this new book, the authors present contemporary approaches to the formulation and solution of problems in the theory of elasticity, plasticity, and viscoelasticity. The traditional sections of the course of the theory of elasticity and plasticity are presented in the modern interpretation, clearly and in an easy-to-understand manner. The tensor form of writing is used along with the coordinate form, which facilitates the student to understand the material. The analytical solutions and numerical results for elastic, elastic-plastic, linear viscoelastic and viscous elastoplastic three-layer circular plates under quasi-static and dynamic stresses are the results of the authors’ own work.”
--D. V. Tarlakovsky, DSc, Head, Department of Resistance of Materials, Dynamics and Strength of Machines, Moscow State Aviation Institute, Russia
“The book is devoted to the mechanics of deformable bodies. The authors present the results of many years of basic research. The book features a deep, comprehensive, and rigorous study of the issues covered. The authors have carefully and thoroughly studied the mechanics of deformable bodies and provide solutions. The methods will undoubtedly be useful to many researchers in this field. The methods illustrated in Chapter 8, on the theory of plasticity, and Chapter 11, which deals with the thermal effects on a number of specific materials, can be used to advance the construction of the theory of thermoviscoelastoplasticity, which is extremely important not only in theoretical terms, but also for the development of industrial production and processing of conductive material. The book will be of great benefit in the work of researchers and students in the field of solid mechanics.”
--Professor Mark Liberzon, Head, Department of Analytical Mechanics, and Vice President, Tsyolkovsky Moscow Aviation Technological University; Vice President, Russian Engineering Academy, Moscow, Russia
The Theory of Stress-Strain State
Physical Relations in the Elasticity Theory
Statement and Problem-Solving Procedures of Elasticity Theory
The Plane Elastic Problems
Deformation of a Half-Space and Contact Problems
Foundations of the Theory of Plasticity
Linear Viscoelastic Continua
Thermoviscoelastoplastic Characteristics of Materials
Dynamic Problems of the Elasticity Theory