A re-look into the modeling aspects of Eringen’s strain-driven nonlocal Euler-Bernoulli nanobeam bending problems

Abstract

There has long been debate on the applicability of Eringen’s strain-driven nonlocal model to the study of nanostructures. Previous studies based on Eringen’s differential and integral nonlocal models to simulate the static bending behavior of nanobeams have shown shortcomings in nanobeam elastostatics solutions. The solution methodologies employed to solve the differential and integro-differential equations arising from Eringen’s strain-driven nonlocal constitutive model have shown inconsistencies in ensuring the fulfillment of essential and natural boundary conditions. This study aims to conduct an in-depth investigation of the modeling aspects of Euler-Bernoulli nanobeams under different loading and boundary conditions. Dirac-delta identity and generalized functions-based approach shall be utilized for the same. A rigorous mathematical proof establishing the equivalence between Eringen’s differential and integral nonlocal models is presented here for the first time.