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

TL;DR

This paper introduces a multiscale-multiphysics numerical modeling strategy for thin piezoelectric sheets made of polymeric nanofibers, enabling better understanding of microscale effects on macroscopic behavior in energy harvesting devices.

Contribution

It develops a multiscale, multiphysics finite element approach incorporating contact smoothing with Bézier patches for piezoelectric nanofiber arrays.

Findings

Enhanced accuracy in modeling microscale contact effects.

Effective scale transition from micro to macro behavior.

Improved computational framework for thin piezoelectric sheets.

Abstract

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.