The strain gradient elasticity via nonlocal considerations

Strain gradient elasticity and nonlocal are two enhanced elastic theories intensively used over the last fifty years to explain static dynamic phenomena that classical fails do. The theory has a clear differentiation from case by considering stresses at point of continuum as an integral defined in treated body. On other hand, strain is characterized non-classical because considers both potential kinetic energy densities not only functions strains velocities, respectively but also their gradients. Although considerations seem be completely different each other, it common belief lot with elasticity. goal present work derive all appearing so far literature via definitions Hamilton’s principle. Such consideration manifests nature SGE theories, correlates internal length scale parameters horizon material point, proposes nonlocality inertia behavior continuum. For sake simplicity brevity, one-dimensional wave propagation infinite domain considered. However, since principle employed, definition corresponding boundary conditions for finite domains accomplished simultaneously equation motion.