LAUSR

Abstract In this paper, we compare direct and energy based homogenization schemes in the framework of the second gradient electroelasticity theory. We consider a special type of the model with simplified constitutive equations that allow to derive an exact analytical solution for the effective properties of fiber-reinforced piezoelectric composite under anti-plane loading. To find the solution we use an approach that was proposed by Benveniste for similar problem in classical electroelasticity. Based on the transformations of the field variables, we construct a solutions for the coupled anti-plane problem of gradient electroelasticity by using known solutions for the uncoupled problem of the strain gradient elasticity and similar problem of gradient electrostatics. Based on the derived solution, we demonstrate the main effects that arise in the composite armed with thin piezoelectric fibers, which diameter is of the order of the characteristic length of material’s microstructure. We show that such composites may demonstrate an unusual behavior: With the decrease of the fiber diameter its effective properties increase and its apparent behavior becomes similar to the homogeneous material. We carry out a comparison between predictions for effective properties, which were provided by the Mori–Tanaka scheme (MTS) and generalized self-consistent scheme (GSCS). We show that these methods give significantly different predictions, which can deviate from each other by hundreds of percent, especially for the effective piezoelectric constants.