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A solid shell finite element formulation to simulate the behaviour of thin dielectric elastomer structures
Author(s) -
Zwecker Sandro,
Klinkel Sven
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110241
Subject(s) - finite element method , shell (structure) , maxwell stress tensor , dielectric , elastomer , materials science , tensor (intrinsic definition) , electric field , stress (linguistics) , dielectric elastomers , constitutive equation , cauchy stress tensor , coupling (piping) , mechanics , classical mechanics , physics , composite material , structural engineering , geometry , engineering , mathematics , linguistics , philosophy , optoelectronics , quantum mechanics
To analyse the behaviour of thin structures of dielectric elastomer (DE) material a solid shell finite element is presented. The main characteristics of DEs are a non‐linear hyper elastic behaviour, the quasi‐incompressibility, and the ability to transform electric energy into mechanical work. Applying a voltage to thin DE structures may produce large elongation strains of 120‐380%. These large strains, the efficient electro‐mechanical coupling, and the light weight make DEs very attractive for the usage in actuators. Thus, there is a need for detailed research. With respect to the electro‐mechanical coupling a constitutive model is presented. An electric stress tensor and a total stress tensor are introduced by considering the electrical body force and couple in the balance of linear momentum and angular momentum, respectively. The governing equations are derived and embedded in the solid shell formulation. The element formulation is based on a Hu‐Washizu mixed variational principle using six independent fields: displacements, electric potential, strains, electric field, mechanical stresses, and dielectric displacements. It allows large deformations and accounts for physical nonlinearities to capture two of the main characteristics of DEs. The shell element could be applied for the modelling of arbitrary curved thin structures. The ability of the present element formulation is demonstrated in several examples. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)