Table of Contents

The Classical Theory of Elasticity.- A. General theory.- I. The analysis of strain.- II. The analysis of stress.- III. The relation between stress and strain.- B. Torsion and flexure.- I. The torsion problem.- II. Bending of beams.- C. Two-dimensional problems in elasto-statics.- I. General theory.- II. Airy stress function.- III. Complex potentials.- IV. Cauchy integral methods.- V. Fourier transform methods.- VI. Real potential methods.- D. Three-dimensional problems in elasto-statics.- I. General theory.- II. Betti's method.- III. The method of integral transforms.- IV. Applications of curvilinear coordinates..- E. Dynamical problems.- I. Elastic waves.- II. Boundary value problems of dynamic elasticity.- F. Thermoelasticity.- Photoelasticity.- A. Theory.- I. History.- II. The optical basis of photoelasticity.- III. The mechanical basis of photoelasticity.- IV. Theory of photoelasticity.- B. Exploration of two-dimensional stress systems.- I. Photoelastic equipment.- II. Photoelastic materials.- III. Exploration of two-dimensional stresses.- C. Exploration of three-dimensional stress systems.- I. Frozen stress materials and techniques.- II. The determination of the stresses.- III. The tilting stage method of exploration of three-dimensional stresses...- IV. The scattered light method of observation.- D. Practical applications.- I. Two-dimensional examples.- II. Three-dimensional examples.- III. Present state and possible future developments.- The Mathematical Theories of the Inelastic Continuum.- First part. The inelastic continuum.- A. Mechanics and thermodynamics of the inelastic continuum.- I. The inelastic behavior of solids.- II. Mechanics of deformable media.- III. Thermodynamic considerations.- B. Stress-strain relations.- I. General formulation.- II. Anelastic relations.- III. Visco-elastic relations.- IV. Plastic relations.- V. Combined quasi-linear relations.- C. The visco-elastic and the visco-plastic medium.- I. The visco-elastic continuum.- II. The visco-plastic medium.- D. Problems of structural mechanics.- I. Visco-elastic structures.- II. Elastic-plastic structures.- Second part. The ideal plastic body.- E. The basic equations.- I. The three-dimensional problem.- II. Discontinuous solutions.- a) Characteristics. Application to the three-dimensional problem of the perfectly plastic body.- b) General consideration of discontinuous solutions.- c) Hadamard's theory.- d) Shock conditions. Stress discontinuities.- F. The problem of plane strain.- I. Plane strain, plane stress, and generalizations.- II. The theory of plane strain.- a) Differential relations.- b) Integration. Particular solutions.- G. The general plane problem.- I. Basic theory.- a) The equations.- b) Characteristics of the complete plane problem.- c) Remarks on integration. Examples.- II. Singular solutions and various remarks.- a) Limit line singularities and branch line singularities.- b) Simple waves.- c) Various remarks.- H. Boundary-value problems.- I. Some elastic-plastic problems.- a) The torsion problem.- b) The thick walled tube.- c) Flat ring and flat sheet in plane stress. Further elastic-plastic problems.- II. Some plastic-rigid problems.- a) Introductory remarks.- b) Wedge with pressure on one face.- c) Plastic mass between rough rigid plates.- Reference Books.- Rheology.- A. Preliminaries.- I. Introduction.- II. The classical bodies.- B. Macrorheology.- I. First-order phenomena.- II. Higher order phenomena.- III. Strength.- C. Microrheology.- D. Rheometry.- E. Addenda.- Symbols.- Fracture.- I. Tensile strength of liquids.- II. Stress and force relations in fracture.- III. Forming and spreading of cracks.- IV. Stress field, velocity, and division of a running crack.- V. Effects of size upon fracturing.- Bibliography references.- Fatigue.- I. The fatigue phenomenon.- II. Micromechanics of progressive damage.- III. Fatigue theories.- IV. Cumulative damage.- References.- Sachverzeichnis (Deutsch-Englisch).- Subject Index (English-German).