ABSTRACT
The nonlocal elasticity theory has received a considerable attention by the researchers intending to analyze the size-dependent structural materials. The key idea of the nonlocal theory is to use a continuum approach endowed with information regarding to the behavior of the material microstructure. Kröner (Kröner 1967) formulated a continuum theory for elastic materials with long range cohesive forces. A nonlocal elasticity theory for linear homogeneous isotropic continua was developed by Eringen and co-workers (Eringen et al. 1977, Eringen 1978, Eringen & Kim 1974). Polizzetto (Polizzotto 2001) proposed a FEM-based technique for the nonlocal elasticity of integral-type. Pisano et al. (Pisano et al. 2009, Pisano et al. 2009) developed a nonlocal FE model to study the homogeneous and non-homogeneous two-dimensional nonlocal elasticity problems. However, in the nonlocal integral elasticity the strain field solution exhibits high gradients in the thin boundary layer, these traditional FE approaches were usually linear approximation of the strain, which can lead to inaccuracies in the region close to the boundaries.
