A fractional-order constitutive model for nonlocal piezoelectricity

This study proposes and develops a fractional-order constitutive model for nonlocal interactions over the electromechanical response of piezoelectric solids. More specifically, the integro-differential definition for fractional-order derivatives is employed to capture long-range interactions over the electrical and mechanical field variables at a point in the piezoelectric solid. This approach establishes a unique framework for modeling two-way multiphysics coupling, encompassing both direct and converse piezoelectric effects, following fractional-order constitutive relations. The potential of this model to develop metastructures with enhanced electromechanical coupling through manipulation of nonlocal interactions is explored. To illustrate this, an example of a smart beam composed of a nonlocal substrate and a piezoelectric layer/patch is considered. An analytical and numerical framework is developed based on variational principles, leading to the derivation of the governing equations. Detailed numerical studies are undertaken here on smart structures pointing toward a possible tuning of the multiphysics coupling via nonlocal interactions.