Flexible piezoelectric devices made of polymeric materials are widely used
for micro- and nano-electro-mechanical systems. In particular, numerous recent
applications concern energy harvesting. Due to the importance of computational
modeling to understand the influence that microscale geometry and constitutive
variables exert on the macroscopic behavior, a numerical approach is developed
here for multiscale and multiphysics modeling of piezoelectric materials made
of aligned arrays of polymeric nanofibers. At the microscale, the
representative volume element consists in piezoelectric polymeric nanofibers,
assumed to feature a linear piezoelastic constitutive behavior and subjected to
electromechanical contact constraints using the penalty method. To avoid the
drawbacks associated with the non-smooth discretization of the master surface,
a contact smoothing approach based on B\'ezier patches is extended to the
multiphysics framework providing an improved continuity of the
parameterization. The contact element contributions to the virtual work
equations are included through suitable electric, mechanical and coupling
potentials. From the solution of the micro-scale boundary value problem, a
suitable scale transition procedure leads to the formulation of a macroscopic
thin piezoelectric shell element.Comment: 11 pages, 6 pages, 21 reference
