Discussion of “Derivation of Mindlin's first and second strain gradient elastic theory via simple lattice and continuum models” by Polyzos and Fotiadis
Document Type
Article
Publication Date
5-15-2020
Department
Department of Mechanical Engineering-Engineering Mechanics
Abstract
We discuss “Derivation of Mindlin's first and second strain gradient elastic theory via simple lattice and continuum models” by Polyzos and Fotiadis in [Int. J. Solids Struct. 49 (2012), pp. 470-480]. Polyzos and Fotiadis derived the equations of motion of Mindlin's first and second strain gradient elasticity theory by continualizing the response of simple mass-and-spring chains with one-neighbor and two-neighbor interactions in addition to the inclusion of distributed mass alongside lumped mass. When passing from the finite difference equations of the discrete lattice to the continualized equations of the corresponding higher-order continuum model, certain inconsistencies in truncating the various Taylor series are noted. By including the missing terms, corrected potential and kinetic energy densities are presented here, after which corrected governing equations are derived by the application of Hamilton's variational principle.
Publication Title
International Journal of Solids and Structures
Recommended Citation
De Domenic, D.,
Askes, H.,
&
Aifantis, E. C.
(2020).
Discussion of “Derivation of Mindlin's first and second strain gradient elastic theory via simple lattice and continuum models” by Polyzos and Fotiadis.
International Journal of Solids and Structures,
191-192, 646-651.
http://doi.org/10.1016/j.ijsolstr.2019.11.016
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/1502