Constitutive Equations of Nonlinear Electromagnetic-Elastic Crystals

ISBN-13: 9781461279631 / Angielski / Miękka / 2011 / 236 str.

E. Kiral; A. Cemal Eringen

Opis

Continuum physics is concemed with the predictions of deformations, stress, temperature, and electromagnetic fields in deformable and fluent bodies. To that extent, mathematical formulation requires the establishment of basic balance laws and constitutive equations. Balance laws are the union of those of continuum thermomechanics and MaxweIl's equations, as coIlected in Chapter 1. To dose the theory it is necessary to formulate equations for the material response to extemal stimuli. These equations bring into play the material properties of the media under consideration. In their simplest forms these are the constitutive laws, such as Hooke's law of dassical elasticity, Stokes' law of viscosity of viscous fluids, Fourier's law of heat conduction, Ohm's law of electric conduction, etc. For large deformations and fields in material media, the constitutive laws become very complicated, in vol ving all physical effects and material symmetry. The present work is concemed with the material symmetry regulations arising from the crystaIlographic symmetry of magnetic crystals. While there exist some works on the thirty-two conventional crystal dasses, exduding the linear case, there exists no study on the nonlinear constitutive equations for the ninty magnetic crystal dasses. Yet the interaction of strong electromagnetic fields with deformable solids cannot be explained without the material sym metry regulations relevant to magnetic crystals. In this monograph, we present a thorough discussion of magnetic symmetry by means of group theory. We consider onlyone scalar function which depends on one symmetric second-order tensor (e. g.

Spis treści

1 Electromagnetic Theory.- 1.1. Deformation and Motion.- 1.2. Balance Laws (in V — ?).- 1.3. Jump Conditions (on ?).- 1.4. Constitutive Equations of Electromagnetic Elastic Solids.- 1.5. Constitutive Equations of Electromagnetic Fluids.- 2 Conventional Crystallographic Point Groups.- 3 Crystallographic Magnetic Point Groups.- 4 Decomposition of Mechanical and Electromagnetic Quantities.- 4.1. Material Tensors and Physical Tensors.- 4.2. Transformation Properties of Tensors.- 4.3. Decomposition of Electromechanical Quantities.- 4.4. Basic Quantities of Electromechanical Tensors.- 5 Material Symmetry Restrictions.- 6 Linear Constitutive Equations.- 6.1. Higher-Order Effects.- 6.2. The Number of Independent Components.- 6.3. An Alternative Procedure for Finding Independent Components.- 7 Nonlinear Constitutive Equations for Electromagnetic Crystalline Solids.- 7.1. Magnetic Crystal Class $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\bar 1} $$ = {I, ?C}.- 7.2. Magnetic Crystal Class m = {I, ?R3}.- 7.3. Magnetic Crystal Class 2 = {I, ?D3}.- 7.4. Magnetic Crystal Class 2/m = {I, ?D3, R3, ?C}.- 7.5. Magnetic Crystal Class 2/m = {I, D3, ?R3, ?C}.- 7.6. Magnetic Crystal Class 2/m = {I, ?D3, ?R3, C}.- 7.7. Magnetic Crystal Class 2mm = {I, ?D3, ?R1, R2}.- 7.8. Magnetic Crystal Class 2mm = {I, D3, ?R1,?R2}.- 7.9. Magnetic Crystal Class 222 = {I, ?D1, ?D2, D3}.- 7.10. Magnetic Crystal Class mmm.- 7.11. Magnetic Crystal Class mmm.- 7.12. Magnetic Crystal Class mmm.- 7.13. Magnetic Crystal Class $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\bar 4} $$ = {I, D3, ?D1T3, ?D2T3}.- 7.14. Magnetic Crystal Class 4 = {I, D3, ?R1T3, ?R2T3}.- 7.15. Magnetic Crystal Class 4/m.- 7.16. Magnetic Crystal Class 4/m.- 7.17. Magnetic Crystal Class 4/m.- 7.18. Magnetic Crystal Class 4mm.- 7.19. Magnetic Crystal Class 4mm.- 7.20. Magnetic Crystal Class 422.- 7.21. Magnetic Crystal Class 422.- 7.22. Magnetic Crystal Class $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\bar 4} $$2m.- 7.23. Magnetic Crystal Class $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\bar 4} $$2m.- 7.24. Magnetic Crystal Class $$ \bar 4$$2m.- 7.25. Magnetic Crystal Class 4/mmm.- 7.26. Magnetic Crystal Class 4/mmm.- 7.27. Magnetic Crystal Class 4/mmm.- 7.28. Magnetic Crystal Class 4/mmm.- 7.29. Magnetic Crystal Class 4/mmm.- 7.30. Magnetic Crystal Class 3m = {I1, S1, S2, ?R1, ?R1S1, ?R1S2}.- 7.31. Magnetic Crystal Class 32 = {I, S1, S2, ?D1, ?D1S1, ?D1S2}.- 7.32. Magnetic Crystal Class $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\bar 3} $$ = {I, S1, S2, ?C,?CS1, ?CS2}.- 7.33. Magnetic Crystal Class $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\bar 6} $$ = {I, S1, S2, ?R3, ?R3S1, ?R3S2}.- 7.34. Magnetic Crystal Class 6 = {I, S1, S2, ?D3, ?D3S1, ?D3S2}.- 7.35. Magnetic Crystal Class $$ \bar 6$$m2.- 7.36. Magnetic Crystal Class $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\bar 6} $$m2.- 7.37. Magnetic Crystal Class $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\bar 6} $$m2.- 7.38. Magnetic Crystal Class $$ \bar 3$$m.- 7.39. Magnetic Crystal Class $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\bar 3} $$m.- 7.40. Magnetic Crystal Class $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\bar 3} $$m.- 7.41. Magnetic Crystal Class 622.- 7.42. Magnetic Crystal Class 622.- 7.43. Magnetic Crystal Class 6mm.- 7.44. Magnetic Crystal Class 6mm.- 7.45. Magnetic Crystal Class 6/m.- 7.46. Magnetic Crystal Class 6/m.- 7.47. Magnetic Crystal Class 6/m.- 7.48. Magnetic Crystal Class 6/mmm.- 7.49. Magnetic Crystal Class 6/mmm.- 7.50. Magnetic Crystal Class 6/mmm.- 7.51. Magnetic Crystal Class 6/mmm.- 7.52. Magnetic Crystal Class 6/mmm.- 7.53. Magnetic Crystal Class m3.- 7.54. Magnetic Crystal Class $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\bar 4} $$3m.- 7.55. Magnetic Crystal Class 432.- 7.56. Magnetic Crystal Class m3m.- 7.57. Magnetic Crystal Class m3m.- 7.58. Magnetic Crystal Class m3m.- 7.59. Composite Symbols of Chapter 7.- 8 Applications.- Appendices.- A. Review of Group Theory and Representation.- B. Integrity Bases of Crystallographic Groups.- C. Magnetic Point Symmetry of Certain Materials.- D. Basic Quantities for Second- and Third-Order Tensors.- References.