1. Motion and Deformation / 2. Stress / 3. Constitutive Axioms / 4. Nonlocal Electromagnetic Theory / 5. Constitutive Equations of Memory-Dependent Nonlocal E-M Elastic Solids / 6. Nonlocal Linear Elasticity / 7. Nonlocal Fluid Dynamics / 8. Nonlocal Linear Electromagnetic Theory / 9. Memory-Dependent Nonlocal Thermoelastic Solids / 10. Memory-Dependent Nonlocal Fluids / 11. Memory-Dependent Nonlocal Electromagnetic Elastic Solids / 12. Memory-Dependent Nonlocal Electromagnetic Thermofluids / 13. Nonlocal Microcontinua / 14. Memory-Dependent Nonlocal Micropolar E-M Elastic Solids / 15. Nonlocal Continuum Theory of Liquid Crystals
Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unified approach to field theories for elastic solids, viscous fluids, and heat-conducting electromagnetic solids and fluids that include nonlocal effects in both space and time (memory effects). The solutions to the field equations agree remarkably well with atomic theories and experimental observations.
Nonlocal continuum field theories are concerned with materials whose behavior at each interior point depends on the state of all other points in the body. This book presents a unified approach to field theories for elastic solids, viscous fluids, and heat-conducting electromagnetic solids and fluids that includes nonlocal effects in both space and time (memory effects).