  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.
