Elasticity, Fracture and Flow: with Engineering and Geological Applications
In: Springer eBook Collection
I Stress and Strain -- 1. Introductory -- 2. Stress. Definitions and notation -- 3. Stresses in two dimensions -- 4. Stresses in three dimensions -- 5. Mohr's representation of stress in three dimensions -- 6. Displacement and strain. Introduction -- 7. The geometry of finite homogeneous strain in two dimensions -- 8. Finite homogeneous strain in three dimensions -- 9. Mohr's representation of finite homogeneous strain without rotation -- 10. Infinitesimal strain in two dimensions -- 11. Infinitesimal strain in three dimensions -- II Behaviour of Actual Materials -- 12. Introductory -- 13. The stress-strain relations for a perfectly elastic isotropic solid -- 14. Special cases: biaxial stress and strain -- 15. Strain-energy -- 16. Anisotropic substances -- 17. Finite hydrostatic strain -- 18. Natural strain -- 19. The equations of viscosity -- 20. Fracture and yield -- 21. The maximum shear stress theory of fracture and its generalizations -- 22. Mohr's theory of fracture -- 23. Earth pressure -- 24. The Griffith theory of brittle strength -- 25. Strain theories of failure -- 26. The tensile test on ductile materials -- 27. Yield criteria -- 28. The yield surface -- 29. The equations of plasticity -- 30. Substances with composite properties -- III Equations of Motion and Equilibrium -- 31. Introductory -- 32. Simple problems illustrating the behaviour of elastic, viscous, plastic and Bingham substances -- 33. The elastic equations of motion -- 34. The elastic equations of equilibrium -- 35. Special cases of the equations of elasticity -- 36. Special problems in elasticity -- 37. Wave propagation -- 38. Elastic waves -- 39. The equations of motion of a viscous fluid -- 40. Special problems in viscosity -- 41. Plastic flow in two dimensions -- IV Applications -- 42. Introductory -- 43. Experimental results on the mechanical properties of rocks -- 44. Systems having one or more planes of weakness -- 45. Porous media -- 46. Further discussion of criteria for failure -- 47. Stresses and faulting in the crust -- 48. The Coulomb-Navier theory in terms of invariants -- 49. The representation of two-dimensional stress fields -- 50. Stresses around openings -- 51. The use of the complex variable -- 52. Displacements -- 53. Underground measurements and their results -- 54. Measurement of rock properties -- 55. Effects of flaws, size and stress gradient -- 56. The complete stress-strain curve -- V Applications to Structural Geology -- 57. Introductory -- 58. Combination of strains -- 59. Determination of finite strain from deformed objects -- 60. Progressive deformation -- 61. Analysis of strain in folding -- 62. Instability theory: folding and kinking -- 63. Development of preferred orientations of ellipsoidal particles -- Notation -- Author Index.