On Some Aspects in the Special Theory of Gradient Elasticity

In this paper a special form of gradient-dependent elasticity is considered. The motivation for considering higher-order gradients of strains in elasticity is discussed. Equilibrium equations and boundary conditions are discussed. The relationship between the special form of gradient elasticity adopted in this study and mixture or nonlocal theories is considered. Solutions to certain problems including the propagation of harmonic waves, the longitudinal vibrations of a beam, and the displacement field in an infinite medium weakened by a line crack are given.