Vistas of nonlocal continuum physics

Abstract Solutions of several critical problems in nonlocal continuum physics are presented and discussed, in order to demonstrate the power and potential of this new field. These include dispersion of waves with high frquency and short wave-lengths, stress singularities in dislocations and cracks, a new physically realistic fracture criterion, viscosity and drainage of thin films of fluids in microscopic channels, nonlocal electromagnetic theory, Debye screening of electrons and superconductivity. Experimental verifications of nonlocal results are presented wherever they were available. In all cases nonlocal field theories are shown to predict macroscopic phenomena faithfully, in agreement with experimental observations and/or lattice dynamical calculations. Yet classical(local) theories either exclude microstructural effects on the response of bodies to external stimuli or give rise to unacceptable singular fields. The main purpose of this paper is to demonstrate the power and potential of nolocal continuum physics in the treatment of microstructural problems.