Deformation Theory of Plasticity
author: Robert M. Jones
640 p. cm.
Includes references and index.
ISBN: 978-0-9787223-1-9 (hardcover : alk. paper)
1. Plasticity. 2. Deformation Theory. 3. Structural Mechanics. I. Title
Library of Congress Control Number 2008905780
ISBN: 978-0-9787223-1-9 (hardcover)This book is an attempt to gather into one convenient semester-long
format the fundamental elements of an engineering approach to modeling
the nonlinear stress-strain behavior of some common engineering
materials. This topic is often called plasticity or the mathematical theory
of plasticity. However, we lim it ourselves to a fairly practical viewpoint
of the topic rather than the somewhat esoteric mathematical approach.
Chapter One is an introduction to the topic of nonlinear materials as
well as an outline of the approach used in this book. Chapter Two is an
overview of the various aspects of material stress-strain curve nonlinearity
that confront the material modeler.
Chapter Three is essentially a review of elasticity subjects such as
stress, strain, stress-strain relations, and strain energy that are central to
the study of plasticity. Those topics can be delved into in various depths
depending on the needs of the specific class.
Chapter Four is the real beginning of plasticity theory with an introduction
to the fundamentals characteristics of yielding and yield criteria
in multiaxial stress states. The deformation or total strain theory of
plasticity is addressed in Chapter Five with the incremental or flow theory
introduced in Chapter Six in order to contrast it with deformation theory.
The solution process for plasticity problems is begun in Chapter
Seven in general terms. Then, specific plasticity problems are addressed
in subsequent chapters. Deformation of thick-walled spherical shells
under internal pressure and separately under internal heating is studied
in Chapter Eight. Specifically, the load-deformation response is found for
shells made of elastic - perfectly plastic materials and for linear strainhardening
materials. Then, in Chapter Nine, plastic buckling of bars,
plates, and shells is examined, including thermal buckling of bars and
plates with temperature-dependent material properties.
The classical metals theory of plasticity is abandoned in Chapter Ten
so non-isotropic materials such as fiber-reinforced and particulate composite
materials can be treated realizing that the usual concepts of classical
plasticity are simply not applicable. A state-variable approach is
developed for an engineering model of orthotropic materials. Then, the
model is applied to laminae and laminates including buckling and to solid
bodies made of various orthotropic materials.
Finally, summary remarks and comments on advanced topics are
addressed in Chapter 11 along with additional history.
