John Lee Bogdanoff

Bio: John Lee Bogdanoff is an academic researcher. The author has contributed to research in topics: Discontinuity (geotechnical engineering) & Classification of discontinuities. The author has an hindex of 1, co-authored 1 publications receiving 1056 citations.

On the Theory of Dislocations

Abstract: If, in a multiply‐connected elastic solid, discontinuities are permitted across a stationary barrier in either the strain or its first derivatives or both, dislocations of a more general type than encountered in classical theory are possible. A number of these more general dislocations have been obtained for states of plane and anti‐plane strain in a hollow right circular cylinder when the surface of discontinuity is a single stationary plane barrier. Some of the dislocations found possess the characteristic that although the strain is continuous across the barrier the displacement discontinuity is not one which would be possible in a rigid body. Examination of the conditions for the uniqueness of solution of the boundary value problems of elasticity reveals that when dislocations of the more general type are admitted appropriate data must be given at each point on the specified barrier in addition to the usual information.

Mechanical behavior of materials

Abstract: Chapter 1. Introduction.1.1 Strain1.2 Stress.1.3 Mechanical Testing.1.4 Mechanical Responses to Deformation.1.5 How Bonding Influences Mechanical Properties.1.6 Further Reading and References.1.7 Problems.Chapter 2. Tensors and Elasticity.2.1 What Is a Tensor?2.2 Transformation of Tensors.2.3 The Second Rank Tensors of Strain and Stress.2.4 Directional Properties.2.5 Elasticity.2.6 Effective Properties of Materials: Oriented Polycrystals and Composites.2.7 Matrix Methods for Elasticity Tensors.2.8 Appendix: The Stereographic Projection.2.9 References.2.10 Problems.Chapter 3. Plasticity.3.1 Continuum Models for Shear Deformation of Isotropic Ductile Materials.3.2 Shear Deformation of Crystalline Materials.3.3 Necking and Instability.3.4 Shear Deformation of Non Crystalline materials.3.5 Dilatant Deformation of Materials.3.6 Appendix: Independent Slip Systems.3.7 References.3.8 Problems.Chapter 4. Dislocations in Crystals.4.1 Dislocation Theory.4.2 Specification of Dislocation Character.4.3 Dislocation Motion.4.4 Dislocation Content in Crystals and Polycrystals.4.5 Dislocations and Dislocation Motion in Specific Crystal Structures.4.6 References.4.7 Problems.Chapter 5. Strengthening Mechanisms.5.1 Constraint Based Strengthening.5.2 Strengthening Mechanisms in Crystalline Materials.5.3 Orientation Strengthening.5.4 References.5.5 Problems.Chapter 6. High Temperature and Rate Dependent Deformation.6.1 Creep.6.2 Extrapolation Approaches for Failure and Creep.6.3 Stress Relaxation.6.4 Creep and Relaxation Mechanisms in Crystalline Materials.6.5 References.6.6 Problems.Chapter 7. Fracture of Materials.7.1 Stress Distributions Near Crack Tips.7.2 Fracture Toughness Testing.7.3 Failure Probability and Weibull Statistics.7.4 Mechanisms for Toughness Enhancement of Brittle Materials.7.5 Appendix A: Derivation of the Stress Concentration at a Through Hole.7.6 Appendix B: Stress Volume Integral Approach for Weibull Statistics.7.7 References.7.8 Problems.Chapter 8. Mapping Strategies for Understanding Mechanical Properties.8.1 Deformation Mechanism Maps.8.2 Fracture Mechanism Maps.8.3 Mechanical Design Maps.8.4 References.8.5 Problems.Chapter 9. Degradation Processes: Fatigue and Wear.9.1 Cystic Fatigue of materials.9.2 Engineering Fatigue Analysis.9.3 Wear, Friction, and Lubrication.9.4 References.9.5 Problems.Chapter 10. Deformation Processing.10.1 Ideal Energy Approach for Modeling of a Forming Process.10.2 Inclusion of Friction and Die Geometry in Deformation Processes: Slab Analysis.10.3 Upper Bound Analysis.10.4 Slip Line Field Analysis.10.5 Formation of Aluminum Beverage Cans: Deep Drawing, Ironing, and Shaping.10.6 Forming and Rheology of Glasses and Polymers.10.7 Tape Casting of Ceramic Slurries.10.8 References.10.9 Problems.Index.

Thin Film Materials: Stress, Defect Formation and Surface Evolution

Abstract: 1. Introduction and overview 2. Film stress and substrate curvature 3. Stress in anisotropic and patterned films 4. Delamination and fracture 5. Film buckling, bulging and peeling 6. Dislocation formation in epitaxial systems 7. Dislocation interactions and strain relaxation 8. Equilibrium and stability of surfaces 9. The role of stress in mass transport.

The force on an elastic singularity

Abstract: The parallel between the classical theory of elasticity and the modern physical theory of the solid state is incomplete; the former has nothing analogous to the concept of the force acting on an imperfection (dislocation, foreign atom, etc.) in a stressed crystal lattice. To remedy this a general theory of the forces on singularities in a Hookean elastic continuum is developed. The singularity is taken to be any state of internal stress satisfying the equilibrium equations but not the compatibility conditions. The force on a singularity can be given as an integral over a surface enclosing it. The integral contains the elastic field quantities which would surround the singularity in an infinite medium, multiplied by the difference between these quantities and those actually present. The expression for the force is thus of essentially the same form whether the force is due to applied surface tractions, other singularities or the presence of the free surface of the body (‘image force’). A region of inhomogeneity in the elastic constants modifies the stress field; if it is mobile one can define and calculate the force on it. The total force on the singularities and inhomogeneities inside a surface can be expressed in terms of the integral of a ‘ Maxwell tensor of elasticity’ taken over the surface. Possible extensions to the dynamical case are discussed,

Peridynamic Theory of Solid Mechanics

Abstract: Publisher Summary The classical theory of solid mechanics is based on the assumption of a continuous distribution of mass within a body and all internal forces are contact forces that act across zero distance. The mathematical description of a solid that follows from these assumptions relies on PDEs that additionally assume sufficient smoothness of the deformation for the PDEs to make sense in their either strong or weak forms. The classical theory has been demonstrated to provide a good approximation to the response of real materials down to small length scales, particularly in single crystals, provided these assumptions are met. Nevertheless, technology increasingly involves the design and fabrication of devices at smaller and smaller length scales, even interatomic dimensions.