Physical Basis Of Plasticity In Solids

This book introduces the physical mechanism of the plastic deformation of solids, which relies essentially on the occurrence and motion of dislocations. These are linear defects, specific of crystalline solids whose motion under external stresses explains the relative ease by which solids (metals in particular) can be deformed in order to give them desired shapes. The objective is to introduce the topic to undergraduate students, restricting to the main ideas and showing their relevance in interpreting phenomena well known to everyone (e.g. why are certain metals harder than others?), and finally training the students in the practice of calculating the simplest properties of dislocations.

This book is about geoplasticity, solid mechanics of rock, jointed rock and soil beyond the domain of a purely elastic deformation. Plastic deformation is irreversible and begins at the limit to elasticity with any attempt at further loading. Stress at the limit to elasticity is "strength" which is described by a functional relationship amongst stresses, that is, by a yield function or failure criterion. Mohr-Coulomb, Drucker-Prager and Hoek-Brown criteria are well-known examples in geomechanics. Beyond the elastic limit, but still within the realm of small strain increments, a total strain increment is the sum of an elastic increment and a plastic increment. The elastic increment is computed through an incremental form of Hooke’s law, isotropic or anisotropic as the case may be. Computation of the plastic part is at the core of any plasticity theory and is approached through the concept of a plastic potential. The plastic potential is a function of stresses and perhaps other material parameters such as plastic strain and temperature. Derivatives of the plastic potential with respect to stress lead to the plastic part of the total strain increment. If the yield criterion and plastic potential are the same, then the plastic stress-strain relationships are "associated rules of flow" and follow a "normality" principle. Normality is in reference to a graphical portrayal in principal stress space where the plastic strain increment is perpendicular to the yield surface. If the plastic potential and yield criterion are different, as is often the case in geoplasticity, then the rules of flow are "non-associated". Drucker’s famous stability postulate implies normality at a smooth point on the yield surface, convexity of the yield function and other important features of plasticity theory in geomechanics. However, there is no point to proceeding to theoretical analyses without physical justification. Hence, the physical foundations for application of plasticity theory to rock, jointed rock and soil are examined in Chapter 2 of this book. A brief review of continuum mechanics principles is given in Chapter 3. Chapter 4 focuses on plane plastic strain and "sliplines". The technical literature is replete with numerous diagrams of sliplines, especially in discussions of foundations on soils, but the relevant mathematics is often lacking and with it genuine understanding. Examples illustrate application of theory to traditional geomechanics problems such as computation of retaining wall forces in soils, foundation bearing capacity of soil and rock, wedge penetration of rock under confining pressure and others. Brief discussions of anisotropy, visco-plasticity and poro-plasticity are presented in Chapters 6, 7 and 8. This book will be of interest to civil, geological and mining engineers, particularly those involved in reliable design of excavations and foundations beyond elasticity, especially in jointed rock.

Primarily aiming to give undergraduate students an introduction to solid state physics, Physics of Electrons in Solids explains the properties of solids through the study of non-interacting electrons in solids. While each chapter contains a qualitative introduction to the main ideas behind solid state physics, it also provides detailed calculations of utmost importance to graduate students.The introductory chapters contain crystallographic and quantum prerequisites. The central chapters are devoted to the quantum states of an independent electron in a crystal and to the equilibrium properties of conductors, insulators, and semiconductors. The final chapters contain insights into the assumptions made throughout, briefly describing the origin of ferromagnetism and superconductivity. The book ends with exercises and solutions based on a physics course taught by the author at École Polytechnique.

Inelastic Analysis of Solids and Structures presents in a unified manner the physical and theoretical background of inelastic material models and computational methods, and illustrates the behavior of the models in typical engineering conditions. The book describes experimental observations and principles of mechanics, and efficient computational algorithms for stress calculations as typically performed in finite element analysis. The theoretical background is given to an extent necessary to describe the commonly employed material models in metal isotropic and orthotropic plasticity, thermoplasticity and viscoplasticity, and the plasticity of geological materials. The computational algorithms are developed in a unified manner with some detailed derivations of the algorithmic relations. Many solved examples are presented, which are designed to give insight into the material behavior in various engineering conditions, and to demonstrate the application of the computational algorithms.

Introduction to Mechanics of Solid Materials is concerned with the deformation, flow, and fracture of solid materials. This textbook offers a unified presentation of the major concepts in Solid Mechanics for junior/senior-level undergraduate students in the many branches of engineering - mechanical, materials, civil, and aeronautical engineering among others. The book begins by covering the basics of kinematics and strain, and stress and equilibrium, followed by a coverage of the small deformation theories for different types of material response: (i) Elasticity; (ii) Plasticity and Creep; (iii) Fracture and Fatigue; and (iv) Viscoelasticity. The book has additional chapters covering the important material classes of: (v) Rubber Elasticity, and (vi) Continuous-fiber laminated composites. The text includes numerous examples to aid the student. A substantial companion volume with example problems is available free of charge on the book's companion website.