Deformation theory of Plasticity

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Deformation Theory of Plasticityauthor: Robert M. Jones640 p. cm.Includes references and index.ISBN: 978-0-9787223-1-9 (hardcover : alk. paper)1. Plasticity. 2. Deformation Theory. 3. Structural Mechanics. I. TitleLibrary of Congress Control Number 2008905780ISBN: 978-0-9787223-1-9 (hardcover)This book is an attempt to gather into one convenient semester-longformat the fundamental elements of an engineering approach to modelingthe nonlinear stress-strain behavior of some common engineeringmaterials. This topic is often called plasticity or the mathematical theoryof plasticity. However, we lim it ourselves to a fairly practical viewpointof the topic rather than the somewhat esoteric mathematical approach.Chapter One is an introduction to the topic of nonlinear materials aswell as an outline of the approach used in this book. Chapter Two is anoverview of the various aspects of material stress-strain curve nonlinearitythat confront the material modeler.Chapter Three is essentially a review of elasticity subjects such asstress, strain, stress-strain relations, and strain energy that are central tothe study of plasticity. Those topics can be delved into in various depthsdepending on the needs of the specific class.Chapter Four is the real beginning of plasticity theory with an introductionto the fundamentals characteristics of yielding and yield criteriain multiaxial stress states. The deformation or total strain theory ofplasticity is addressed in Chapter Five with the incremental or flow theoryintroduced in Chapter Six in order to contrast it with deformation theory.The solution process for plasticity problems is begun in ChapterSeven in general terms. Then, specific plasticity problems are addressedin subsequent chapters. Deformation of thick-walled spherical shellsunder internal pressure and separately under internal heating is studiedin Chapter Eight. Specifically, the load-deformation response is found forshells made of elastic - perfectly plastic materials and for linear strainhardeningmaterials. Then, in Chapter Nine, plastic buckling of bars,plates, and shells is examined, including thermal buckling of bars andplates with temperature-dependent material properties.The classical metals theory of plasticity is abandoned in Chapter Tenso non-isotropic materials such as fiber-reinforced and particulate compositematerials can be treated realizing that the usual concepts of classicalplasticity are simply not applicable. A state-variable approach isdeveloped for an engineering model of orthotropic materials. Then, themodel is applied to laminae and laminates including buckling and to solidbodies made of various orthotropic materials.Finally, summary remarks and comments on advanced topics areaddressed in Chapter 11 along with additional history.