The TDNNS method in ferroelectric material modeling

Astrid Pechstein (JKU, Linz)

May 18. 2026, 10:45 — 11:30

A main motivation for using the tangential-displacement normal-normal-stress (TDNNS) method in engineering applications is its insensitivity to shear locking, and thus the feasability of using flat elements of high aspect ratio. This treat is of importance especially when thin or layered structures are concerned. In this talk, we explore the possibilities of using the method for modeling piezoceramic patches, as are commercially available and used in sensing and actuation applications, both applied to and immersed within so-called smart structures. Starting from the standard variational formulation for linear piezoelasticity based on displacement and electric potential, we explore several mixed formulations. Here, strain and electric field as well as the dual quantities stress and dielectric displacement are considered independently, and by providing a thermodynamic potential representing an energy or enthalpy, reversible electromechanically coupled behavior can be described. Piezoceramics are often modeled in this framework of linear piezoelectric materials, reproducing direct and converse piezoelectric effect. However, these characteristics are obtained only after electric polarization, which is not a reversible process. We speak of ferroelectric material models if they capture irreversible or hysteretic effects, such as remanent electric polarization or mechanic strain. These models become relevant not only when considering the polarization process itself, but also when high electric or mechanic loads lead to a depolarization of the piezoceramic. Internal polarization and/or internal strains are introduced as additional, independent unknowns, and dissipation leads to hysteretic behavior. The benefits of choosing a discretization following the TDNNS idea for ferroelectric materials are highlighted through computational examples.

 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Differential Complexes: Theory, Discretization, and Applications (Thematic Programme)
Organizer(s):
Andreas Cap (U of Vienna)
Ralf Hiptmair (ETH Zurich)
Kaibo Hu (U of Oxford)
Joachim Schöberl (TU Wien)