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Flexible piezoelectric devices made of polymeric materials are widely usedfor micro- and nano-electro-mechanical systems. In particular, numerous recentapplications concern energy harvesting. Due to the importance of computationalmodeling to understand the influence that microscale geometry and constitutivevariables exert on the macroscopic behavior, a numerical approach is developedhere for multiscale and multiphysics modeling of piezoelectric materials madeof aligned arrays of polymeric nanofibers. At the microscale, therepresentative volume element consists in piezoelectric polymeric nanofibers,assumed to feature a linear piezoelastic constitutive behavior and subjected toelectromechanical contact constraints using the penalty method. To avoid thedrawbacks associated with the non-smooth discretization of the master surface,a contact smoothing approach based on B\'ezier patches is extended to themultiphysics framework providing an improved continuity of theparameterization. The contact element contributions to the virtual workequations are included through suitable electric, mechanical and couplingpotentials. From the solution of the micro-scale boundary value problem, asuitable scale transition procedure leads to the formulation of a macroscopicthin piezoelectric shell element.

A multiscale-multiphysics strategy for numerical modeling of thin piezoelectric sheets