Mixed Finite Elements for large-strain electro-mechanics suitable for high aspect ratios

Dipl.-Ing.in Dr.in Astrid Pechstein

Nov. 8, 2018, 1:45 p.m. S2 346

So-called smart materials are state of the art in realizing noise and vibration control, high-precision actuation or sensing and energy harvesting applications. Among the most popular smart materials are piezoceramics, which offer fast and accurate response when used as actuators or sensors in the small deformation regime, while they are cheap in production. More recently, electro-active polymers (EAP) have been developed that can undergo very large deformations under electric loading. In this talk, we are concerned with the efficient electro-mechanically coupled simulation of piezoceramics as well as EAPs in a common variational framework.
The problems that arise in these simulations are of different nature. On the one hand, piezoelectric actuators and sensors are mostly flat patches of thickness less than one millimeter, that are applied to an underlying "unintelligent structure". When resolving such a patch with standard finite elements as realized in ABAQUS, one easily arrives at 100.000s of unknowns even for small model problems. On the other hand, electro-active polymers are often (almost) incompressible, which also leads to locking or numerical instabilities.
In this talk, we describe how to use the "Tangential Displacement Normal Normal Stress" mixed finite elements in the electromechanically coupled problem. Originally, these elements were introduced for small deformation linear elasticity. From there, we progress to small deformation linear piezoelasticity, as is of interest in the simulation of piezoelectric patch actors and sensors. Then, we extend the elements to the large deformation case in an "Updated Lagrangian" setting. We show numerical results that were procured in the open-source FE software package Netgen/NGSolve (see ngsolve.org), and compare them to results from ABAQUS.

Martin Meindlhumer acknowledges support of Johannes Kepler University Linz, Linz Institute of Technology (LIT).