Foundations of the Theory of Plasticity

Abstract

Based on the author's series of lectures at the Mechanics-Mathematics Faculty of the University of Leningrad, this text is primarily concerned with the plastic deformation of metals at normal temperatures, as applied to the strength of machines and structures. Its focus on delivering a simple presentation of the basic equations of plasticity theory encompasses the best-developed methods for solving the equations; it also considers problems associated with the special nature of plastic state and the most important engineering applications of plasticity theory. This volume traces the main trends in the theory's development, assuming readers' familiarity with the fundamentals of strength of materials and elasticity theory. Advanced topics are marked with an asterisk and can be omitted on a first reading. Intended as a text for advanced engineering students, as well as a reference book for practicing engineers, it features problems at the end of each chapter that enable readers to test their grasp of the material. Contents include the fundamentals of continuum mechanics, equations of plastic state and elastic-plastic equilibrium, torsion, plane strain and stress, and axially symmetric strain. Additional topics range from extremum principles and energy methods of solution to theory of shakedown, stability of elastic-plastic equilibrium, dynamic problems, complex media, and viscoplasticity. An extensive bibliography appears at the end of the book. 1971 edition.