Displacement-driven approach to nonlocal elasticity

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