Elastoplasticity Theory

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However, conventional plasticity models are applicable to the prediction of monotonic loading behavior, but are inapplicable to prediction of deformation behavior of machinery subjected to cyclic loading and civil or architectural str- tures subjected to earthquakes.

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.

Contents Recent advancements in the performance of industrial products and structures are quite intense. Consequently, mechanical design of high accuracy is necessary to enhance their mechanical performance, strength and durability. The basis for their mechanical design can be provided through elastoplastic deformation analyses. For that reason, industrial engineers in the fields of mechanical, civil, architec- ral, aerospace engineering, etc. must learn pertinent knowledge relevant to elas- plasticity. Numerous books about elastoplasticity have been published since “Mathema- cal Theory of Plasticity”, the notable book of R. Hill (1950), was written in the middle of the last century. That and similar books mainly address conventional plasticity models on the premise that the interior of a yield surface is an elastic domain. However, conventional plasticity models are applicable to the prediction of monotonic loading behavior, but are inapplicable to prediction of deformation behavior of machinery subjected to cyclic loading and civil or architectural str- tures subjected to earthquakes. Elastoplasticity has developed to predict defor- tion behavior under cyclic loading and non-proportional loading and to describe nonlocal, finite and rate-dependent deformation behavior.

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