KIT | KIT-Bibliothek | Impressum | Datenschutz

A Novel Energy and Momentum Consistent Mixed Formulation for Coupled Nonlinear Electro‐Thermo‐Elastodynamics

Zähringer, Felix; Franke, Marlon 1; Betsch, Peter
1 Institut für Mechanik (IFM), Karlsruher Institut für Technologie (KIT)

Abstract:

In the present contribution, a novel mixed formulation aimed at the energy-momentum consistent simulation of coupled nonlinear electro-thermo-elastodynamic systems, in particular dielectric elastomer actuators, is proposed. It is essentially based on a mixed framework for elastodynamics in the case of polyconvex stored energy functions. In accordance with this framework, the properties of the rediscovered tensor cross product are exploited in a first step to derive a mixed formulation via a Hu-Washizu type extension of the stored energy function. Afterwards, the corresponding strong form is derived and supplemented with the (initial) boundary value problems of thermodynamics and electrostatics. By additionally choosing an appropriate polyconvexity-inspired energy density function, this procedure leads to a fully coupled electro-thermo-elastodynamic formulation that benefits from the properties of the underlying mixed framework.

Furthermore, an energy-momentum consistent time integration scheme is proposed for the novel framework, where discrete derivatives in the sense of Gonzalez are employed. The formulation is second-order accurate and stable even for large time step sizes. ... mehr


Verlagsausgabe §
DOI: 10.5445/IR/1000159874
Veröffentlicht am 27.06.2023
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Mechanik (IFM)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 05.2023
Sprache Englisch
Identifikator ISSN: 1617-7061
KITopen-ID: 1000159874
Erschienen in PAMM
Verlag Wiley-VCH Verlag
Band 23
Heft 1
Seiten Art.-Nr.: e202200037
Bemerkung zur Veröffentlichung Special Issue: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)
Nachgewiesen in Dimensions
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page