Physico-chemical nanomaterials science

Effect of Local Mass Displacement on Coupled Fields 
in Dielectric Nano-Beam 
Hrytsyna O.O.
Department of Mechanics, Institute of Construction and Architecture, Slovak Academy of Sciences. Dúbravská cesta 9, 84503 Bratislava 45, Slovak Republic. 
Department for Mathematical Methods of Computing Experiment, Center of Mathematical Modeling of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine. Dudajev str. 15, 79005 Lviv, Ukraine
E-mail: hrytsyna.olha@gmail.com, usarolha@savba.sk

The electromechanical behavior of small-scale structures cannot be modeled accurately by the classical continuum theory. Surface and size effects can be considered by the modified theory of electroelastic media that alongside the mechanical and electromagnetic processes takes a non-diffusive and non-convective mass flux into account [1]. Such the mass flux might be caused by changes in the material microstructure of a body. This flux is linked with the process of the local mass displacement. The mentioned theory is called the local gradient theory of electroelasticity. In this study, the variational approach for the formulation of linear boundary-value problems of the local gradient electroelastisity is proposed. Using this approach, the fundamental equations and proper boundary conditions which describe the physical behavior of the local gradient continuum were derived. The obtained set of governing equations differs from the relations of the classical theory of electroelasticity and includes nonlocal effects. To verify the usefulness of the proposed variational approach, a generalized mathematical model of the Bernoulli-Euler electroelastic beam is formulated. The resulting local gradient beam model can capture the size depending behavior of the electroelastic beam at the nanoscale. To illustrate this effect, the solution to the static bending problem of the simply supported piezoelectric nano-beam is used. The beam is loaded by a constant distributed loading. It is shown that the beam deflection predicted by the local gradient theory is smaller than the one calculated within the classical Bernoulli-Euler beam theory if the beam thickness is comparable to the material length scale parameter. The results obtained in this study are general and can be useful for small scale devices utilizing the micro/nano-beam elements. 
1.	Hrytsyna, O, Kondrat, V. Local Gradient Theory for Dielectrics: Fundamentals and Applications. Singapore: Jenny Stanford Publishing Pte. Ltd., 2020.