Multiscale nonlocal elasticity: A distributed order fractional formulation

This study presents a generalized multiscale nonlocal elasticity theory that leverages distributed order fractional calculus to accurately capture coexisting and effects within macroscopic continuum. The behavior is captured via constitutive relations derived from thermodynamic formulation. governing equations of the inhomogeneous continuum are obtained Hamilton principle. As generalization constant theory, can model complex media characterized by nonlocality effects. In understand correspondence between microscopic properties continuum, an equivalent mass–spring lattice also developed direct discretization elastic Detailed theoretical arguments provided show equivalence discrete models in terms internal forces, potential energy distribution, boundary conditions. These facilitate physical interpretation role played framework theories. They highlight outstanding opportunities offered this methodology account for capabilities illustrated numerical highlights excellent agreement displacement profiles total predicted two under various distributions. Remarkably, such as distortion, material softening, concentration well at level theory.