English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This study presents a generalized multiscale nonlocal elasticity theory thatleverages distributed order fractional calculus to accurately capturecoexisting multiscale and nonlocal effects within a macroscopic continuum. Thenonlocal multiscale behavior is captured via distributed order fractionalconstitutive relations derived from a nonlocal thermodynamic formulation. Thegoverning equations of the inhomogeneous continuum are obtained via theHamilton principle. As a generalization of the constant order fractionalcontinuum theory, the distributed order theory can model complex mediacharacterized by inhomogeneous nonlocality and multiscale effects. In order tounderstand the correspondence between microscopic effects and the properties ofthe continuum, an equivalent mass-spring lattice model is also developed bydirect discretization of the distributed order elastic continuum. Detailedtheoretical arguments are provided to show the equivalence between the discreteand the continuum distributed order models in terms of internal nonlocalforces, potential energy distribution, and boundary conditions. Thesetheoretical arguments facilitate the physical interpretation of the role playedby the distributed order framework within nonlocal elasticity theories. Theyalso highlight the outstanding potential and opportunities offered by thismethodology to account for multiscale nonlocal effects. The capabilities of themethodology are also illustrated via a numerical study that highlights theexcellent agreement between the displacement profiles and the total potentialenergy predicted by the two models under various order distributions.Remarkably, multiscale effects such as displacement distortion, materialsoftening, and energy concentration are well captured at continuum level by thedistributed order theory.

Multiscale Nonlocal Elasticity: A Distributed Order Fractional Formulation