Computational homogenization of fibrous piezoelectric materials

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 thin piezoelectric sheets made of aligned arrays of polymeric nanofibers, manufactured by electrospinning. At the microscale, the representative volume element consists in piezoelectric polymeric nanofibers, assumed to feature a piezoelastic behavior and subjected to electromechanical contact constraints. The latter are incorporated into the virtual work equations by formulating suitable electric, mechanical and coupling potentials and the constraints are enforced by using the penalty method. From the solution of the micro-scale boundary value problem, a suitable scale transition procedure leads to identifying the performance of a macroscopic thin piezoelectric shell element.