A finite element approach for nonhomogeneous nonlocal elastic problems

The paper deals with the implementation of a method, known in the relevant literature as Nonlocal Finite Element Method, for solving 2D boundary value problems in the context of nonhomogeneous nonlocal elasticity. The method, founded on a consistent thermodynamic formulation, is here improved making use of a phenomenological strain-differencebased nonhomogeneous nonlocal elasticity model. The latter assumes a two components local/nonlocal constitutive relation in which the stress is conceived as the sum of two contributions governed by the standard elastic moduli tensor and by a nonlocal stiffness tensor, respectively. Two numerical examples are presented and the obtained results are discussed both to verify the reliability of the method and to show its potential and limits for the analysis of nonhomogeneous nonlocal elastic problems.