Generalized wave equation in nonlocal elasticity

Fractional calculus for continuum mechanics – anisotropic non-locality

“…that we describe the deformation in terms of dX and dx, classical deformation appears as (one of possible) 'intermediate' one. Therefore, it is clear that stre should be postulated dependently on chosen description of deformation in a result is analogous to the one presented in [40] Eqs 2.7,2.17, and 2.18).…”

“…The this area were released in the 1960s, and dates back to the scientists, such as Toupin [2 Eringen [4], Dillon [5], Dafalias [6], Bažant [7], Maugin [8], Aifantis [9], Fleck and Hu Regardless of the details of specific formulation, it is common that non-local model intro 2 ) appears as (one of possible) 'intermediate' one. Therefore, it is clear that stresses and balance laws should be postulated dependently on chosen description of deformation in a standard manner (such result is analogous to the one presented in [40], Eqs 2.7,2.17, and 2.18).…”

“…Later a closely related proposition was stated by Atanackovic and Stankovic [40], namely erators [51], and many different ways how to introduce them into the specific formulation, days several fractional continuum mechanics concepts. In general, one can distinguish troducing spatial non-local effects through fractional calculus into continuum mechanics nition of kinematics; (ii) redefinition of constitutive law.…”

“…(1) but with physical unit [m − Later a closely related proposition was stated by Atanackovic and Stankovic [40], namely…”

Diffusion problems on fractional nonlocal media

“…Only recently, by implementing a power-law decaying relationship, a few models based on fractional calculus have been proposed. They are applied both to statics [3,4], studying the stress field of a nonlocal bar under tensile load, and to dynamics [5][6][7][8][9][10], investigating anomalous wave propagation. Accord-ing to these works, mainly related to the unidimensional case, fractional space derivatives replace the standard ones or represent an adding term in the governing equations.…”