On the consistency of two-phase local/nonlocal piezoelectric integral model

Abstract In this paper, we propose general strain- and stress-driven two-phase local/nonlocal piezoelectric integral models, which can distinguish the difference of nonlocal effects on elastic behaviors nanostructures. The model is transformed from to an equivalent differential form with four constitutive boundary conditions due difficulty in solving intergro-differential equations directly. models are used static bending Euler-Bernoulli beam assumption that parameters coincident each other. governing as well standard deduced. It found purely ill-posed, because total number orders for less than conditions. Meanwhile, traditional would lead inconsistent response under different loading Several nominal variables introduced normalize conditions, quadrature method (GDQM) obtain numerical solutions. results current validated against literature. clearly established a consistent softening toughening be obtained based respectively.