A peridynamic approach to flexoelectricity

TL;DR

This paper introduces a novel peridynamic theory for flexoelectricity, enabling modeling of nanoscale electromechanical phenomena involving large strain gradients and discontinuities in solid dielectrics.

Contribution

It develops the first peridynamic formulation for flexoelectricity, capturing nanoscale coupling effects and non-uniform strains in centrosymmetric dielectrics.

Findings

Derived PD electromechanical equations satisfy global balance.

Analytical solution provided for static point forces in infinite dielectric.

Parametric study shows influence of length scales on response.

Abstract

A flexoelectric peridynamic (PD) theory is proposed. Using the PD framework, the formulation introduces, perhaps for the first time, a nanoscale flexoelectric coupling that entails non-uniform strain in centrosymmetric dielectrics. This potentially enables PD modeling of a large class of phenomena in solid dielectrics involving cracks, discontinuities etc. wherein large strain gradients are present and the classical electromechanical theory based on partial differential equations do not directly apply. Derived from Hamilton's principle, PD electromechanical equations are shown to satisfy the global balance requirements. Linear PD constitutive equations reflect the electromechanical coupling effect, with the mechanical force state affected by the polarization state and the electrical force state in turn by the displacement state. An analytical solution of the PD electromechanical equations in the integral form is presented for the static case when a point mechanical force and a point electric force act in a three dimensional infinite solid dielectric. A parametric study on how the different length scales influence the response is also undertaken.