  This study presents a physically consistent displacement-driven reformulation
of the concept of action-at-a-distance, which is at the foundation of nonlocal
elasticity. In contrast to existing approaches that adopts an integral
stress-strain constitutive relation, the displacement-driven approach is
predicated on an integral strain-displacement relation. The most remarkable
consequence of this reformulation is that the (total) strain energy is
guaranteed to be convex and positive-definite without imposing any constraint
on the symmetry of the kernels. This feature is critical to enable the
application of nonlocal formulations to general continua exhibiting asymmetric
interactions; ultimately a manifestation of material heterogeneity. Remarkably,
the proposed approach also enables a strong satisfaction of the locality
recovery condition and of the laws of thermodynamics, which are not foregone
conclusions in most classical nonlocal elasticity theories. Additionally, the
formulation is frame-invariant and the nonlocal operator remains physically
consistent at boundaries. The study is complemented by a detailed analysis of
the dynamic response of the nonlocal continuum and of its intrinsic dispersion
leading to the consideration that the choice of nonlocal kernels should depend
on the specific material. Examples of exponential or power-law kernels are
presented in order to demonstrate the applicability of the method to different
classes of nonlocal media. The ability to admit generalized kernels reinforces
the generalized nature of the displacement-driven approach over existing
integral methodologies, which typically lead to simplified differential models
based on exponential kernels. The theoretical formulation is also leveraged to
simulate the static response of nonlocal beams and plates illustrating the
intrinsic consistency of the approach, which is free from unwanted boundary
effects.
