Civil Engineering Association

Elastoplasticity Theory

This book was written to serve as the standard textbook for instruction of elastoplasticity theory. It opens with an explanation of the mathematics and continuum mechanics which are necessary as a foundation of elastoplasticity theory. Subsequently, conventional and unconventional elastoplasticity theories are explained comprehensively for description of general loading behavior covering monotonic, nonproportional, and cyclic loading processes. Fundamental notions such as continuity and smoothness conditions, decomposition of deformation into elastic and plastic parts, the associated flow rule, the loading criterion and the anisotropy are defined, and then presented with their mechanical interpretations. Explicit constitutive equations of metals and soils, which are useful in engineering practice for the mechanical design of machinery and structures, are also introduced. Moreover, constitutive equations of friction with transition from static to kinetic friction and vice versa, and rotational and orthotropic anisotropy are provided. They are indispensable for analyses of boundary-value problems. A distinguishing feature of this book is that it is written to be understandable without difficulty even by beginners in the field of elastoplasticity, explaining physical backgrounds with illustrations and descriptions of detailed derivation processes without a jump. Furthermore, the history and the latest results related to elastoplasticity are explained thoroughly to the extent that the fundamentals of elastoplasticity theory can be understood and be applicable readily to analyses of engineering problems.

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Elastoplasticity Theory, 2nd Edition

This book was written to serve as the standard textbook of elastoplasticity for students, engineers and researchers in the field of applied mechanics. The present second edition is improved thoroughly from the first edition by selecting the standard theories from various formulations and models, which are required to study the essentials of elastoplasticity steadily and effectively and will remain universally in the history of elastoplasticity. It opens with an explanation of vector-tensor analysis and continuum mechanics as a foundation to study elastoplasticity theory, extending over various strain and stress tensors and their rates. Subsequently, constitutive equations of elastoplastic and viscoplastic deformations for monotonic, cyclic and non-proportional loading behavior in a general rate and their applications to metals and soils are described in detail, and constitutive equations of friction behavior between solids and its application to the prediction of stick-slip phenomena are delineated. In addition, the return-mapping algorithm, the consistent tangent operators and the objective time-integration algorithm of rate tensor are explained in order to enforce the FEM analyses. All the derivation processes and formulations of equations are described in detail without an abbreviation throughout the book.

The distinguishable features and importance of this book is the comprehensive description of fundamental concepts and formulations including the objectivity of tensor and constitutive equations, the objective time-derivative of tensor functions, the associated flow rule, the loading criterion, the continuity and smoothness conditions and their substantial physical interpretations in addition to the wide classes of reversible/irreversible constitutive equations of solids and friction behavior between solids.


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2nd edition

2nd edition