Vol. 8, No. 1, 2020

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IBVP for electromagneto-elastic materials: variational approach

Amirhossein Amiri-Hezaveh, Pouyan Karimi and Martin Ostoja-Starzewski

Vol. 8 (2020), No. 1, 47–67
Abstract

This paper aims to establish a variational framework for materials having coupling interactions between electromagnetic and mechanical fields. Based on coupled constitutive equations and the alternative field equations, a general variational form, imposing no restriction on the fields involved, is given. Subsequently, the result is derived for the case when satisfaction of the strain-displacement equation is presumed as a restriction. Next, the variational forms for kinematically admissible processes and, in turn, for kinematically admissible displacement-potential processes are found. Finally, the principles characterizing the stress field instead of the displacement field are formulated. The results of the present work provide a framework in which the satisfaction of initial boundary conditions is inherently considered. The proposed framework furnishes an alternative path for the implementation of numerical approaches for PDEs governing the motion of electromagneto-elastic materials.

Keywords
variational principles, elastodynamics, electromagneto-elastic materials
Physics and Astronomy Classification Scheme 2010
Primary: 46.15.Cc, 75.80.+q, 77.65.-j, 83.10.Ff
Mathematical Subject Classification 2010
Primary: 35A15, 74BXX, 74FXX
Milestones
Received: 21 August 2019
Revised: 17 December 2019
Accepted: 21 January 2020
Published: 11 May 2020

Communicated by David J. Steigmann
Authors
Amirhossein Amiri-Hezaveh
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
Urbana, IL
United States
Pouyan Karimi
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
Urbana, IL
United States
Martin Ostoja-Starzewski
Department of Mechanical Science and Engineering
Institute for Condensed Matter Theory
Beckman Institute for Advanced Science and Technology
University of Illinois at Urbana-Champaign
Urbana, IL
United States