Electrodynamic-mechanical boundary value problems and gauge transformations in rigid dielectrics with constitutive magnetoelectric coupling

Ricoeur, Andreas; Merkel, Eugen

doi:10.1016/j.apm.2016.09.015

Cited by 3 publications

(1 citation statement)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…( 1) and (3). A boundary value problem is then formulated in terms of the eight independent variables φ, A i , u i and T. A set of mechanical-electrodynamic equations, incorporating all couplings within a framework of small deformations, is found in [31], where gauge transformations are furthermore introduced, in order to decouple the differential equations of electrodynamics.…”

Section: Coupling Phenomena and Strong Formulation Of The Boundary Value Problemmentioning

confidence: 99%

A monolithic approach toward coupled electrodynamic–thermomechanical problems with regard to weak formulations

Ricoeur

Wingen

2021

Acta Mech

View full text Add to dashboard Cite

Weak formulations of boundary value problems are the basis of various numerical discretization schemes. They are classically derived applying the method of weighted residuals or a variational principle. For electrodynamical and caloric problems, variational approaches are not straightforwardly obtained from physical principles like in mechanics. Weak formulations of Maxwell’s equations and of energy or charge balances thus are frequently derived from the method of weighted residuals or tailored variational approaches. Related formulations of multiphysical problems, combining mechanical balance equations and the axioms of electrodynamics with those of heat conduction, however, raise the additional issue of lacking consistency of physical units, since fluxes of charge and heat intrinsically involve time rates and temperature is only included in the heat balance. In this paper, an energy-based approach toward combined electrodynamic–thermomechanical problems is presented within a classical framework, merging Hamilton’s and Jourdain’s variational principles, originally established in analytical mechanics, to obtain an appropriate basis for a multiphysical formulation. Complementing the Lagrange function by additional potentials of heat flux and electric current and appropriately defining generalized virtual powers of external fields including dissipative processes, a consistent formulation is obtained for the four-field problem and compared to a weighted residuals approach.

show abstract

Section: Coupling Phenomena and Strong Formulation Of The Boundary Value Problemmentioning

confidence: 99%

A monolithic approach toward coupled electrodynamic–thermomechanical problems with regard to weak formulations

Ricoeur

Wingen

2021

Acta Mech

View full text Add to dashboard Cite

show abstract

New forms of the fundamental solutions for 3D magnetoelectroelasticity equations

Dziatkiewicz

2021

Applied Mathematical Modelling

View full text Add to dashboard Cite

Modeling the dynamic magneto-mechanical response of magnetic shape memory alloys based on Hamilton’s principle: The numerical algorithm

Fan,

Steinmann,

Wang

2023

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

Electrodynamic-mechanical boundary value problems and gauge transformations in rigid dielectrics with constitutive magnetoelectric coupling

Cited by 3 publications

References 10 publications

A monolithic approach toward coupled electrodynamic–thermomechanical problems with regard to weak formulations

A monolithic approach toward coupled electrodynamic–thermomechanical problems with regard to weak formulations

New forms of the fundamental solutions for 3D magnetoelectroelasticity equations

Modeling the dynamic magneto-mechanical response of magnetic shape memory alloys based on Hamilton’s principle: The numerical algorithm

Contact Info

Product

Resources

About