This 1980 monograph develops from first principles the description of finite deformations of solids under stress and the forces acting, and also the expression of internal forces in terms of stress tensors. The important feature of the book is that elastic properties are discussed and developed consistently from classical thermodynamics. In other books, this point of view is acknowledged only by assuming the existence of an elastic energy function, thus restricting their range mainly to the problem of the spatial distribution of stresses and strains. Topics discussed as applications of the…mehr
This 1980 monograph develops from first principles the description of finite deformations of solids under stress and the forces acting, and also the expression of internal forces in terms of stress tensors. The important feature of the book is that elastic properties are discussed and developed consistently from classical thermodynamics. In other books, this point of view is acknowledged only by assuming the existence of an elastic energy function, thus restricting their range mainly to the problem of the spatial distribution of stresses and strains. Topics discussed as applications of the theory include thermal expansion, specific heats, stiffness and complicances, the effects of symmetry on thermodynamic properties, diffusion in a stressed solid, equilibrium in contact with a solution of the solid, phase stability, solid state phase transitions and twinning.
Part I. The Mathematical Foundations of Finite Strain Theory: 1. Introduction 2. Mathematical description of homogeneous deformations 3. Infinitesimal deformation 4. Transformations describing deformations of a material medium 5. Forces 6. Boundary conditions and work 7. Another unique factorisation of D 8. Virtual work 9. Transformation of cartesian tensors Part II. Non-Hydrostatic Thermodynamics: 10. The thermodynamic basis 11. Thermodynamic relations 12. Thermodynamic functions, equations of state 13. Thermodynamic quantities, definitions, and geometrical situation 14. Thermal expansion coefficients 15. Specific heats 16. Elastic stiffness and compliances 17. Tensorial forms for the elastic stiffness and compliance matrices 18. The effects of symmetry on the thermodynamic properties of crystals 19. Equilibrium and stability conditions for thermodynamic systems 20. Equilibrium conditions for diffusion in phases under non-hydrostatic stresses 21. The equilibrium of a stressed solid in contact with a solution of the solid 22. The thermodynamic stability of a phase 23. Discussion of the elastic stability conditions 24. Phase transitions and instability 25. An example of a phase transition involving a simple shear 26. Limiting the values of thermodynamic quantities at an instability 27. The a-ß quartz transition 28. The thermodynamic theory of the growth of Dauphiné twinning in quartz under stress 29. The tetragonal/cubic ferroelectric transition of barium titanate References Index.
Part I. The Mathematical Foundations of Finite Strain Theory: 1. Introduction 2. Mathematical description of homogeneous deformations 3. Infinitesimal deformation 4. Transformations describing deformations of a material medium 5. Forces 6. Boundary conditions and work 7. Another unique factorisation of D 8. Virtual work 9. Transformation of cartesian tensors Part II. Non-Hydrostatic Thermodynamics: 10. The thermodynamic basis 11. Thermodynamic relations 12. Thermodynamic functions, equations of state 13. Thermodynamic quantities, definitions, and geometrical situation 14. Thermal expansion coefficients 15. Specific heats 16. Elastic stiffness and compliances 17. Tensorial forms for the elastic stiffness and compliance matrices 18. The effects of symmetry on the thermodynamic properties of crystals 19. Equilibrium and stability conditions for thermodynamic systems 20. Equilibrium conditions for diffusion in phases under non-hydrostatic stresses 21. The equilibrium of a stressed solid in contact with a solution of the solid 22. The thermodynamic stability of a phase 23. Discussion of the elastic stability conditions 24. Phase transitions and instability 25. An example of a phase transition involving a simple shear 26. Limiting the values of thermodynamic quantities at an instability 27. The a-ß quartz transition 28. The thermodynamic theory of the growth of Dauphiné twinning in quartz under stress 29. The tetragonal/cubic ferroelectric transition of barium titanate References Index.
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