TY - JOUR

T1 - Stress field formulation of linear electro-magneto-elastic materials

AU - Amiri-Hezaveh, A.

AU - Karimi, P.

AU - Ostoja-Starzewski, M.

N1 - Funding Information:
The comments of an anonymous reviewer helped improve this paper. This work was partially supported by the NSF (grant CMMI-1462749).
Publisher Copyright:
© The Author(s) 2019.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - A stress-based approach to the analysis of linear electro-magneto-elastic materials is proposed. Firstly, field equations for linear electro-magneto-elastic solids are given in detail. Next, as a counterpart of coupled governing equations in terms of the displacement field, generalized stress equations of motion for the analysis of three-dimensional (3D) problems Are obtained – they supply a more convenient basis when mechanical boundary conditions are entirely tractions. Then, a sufficient set of conditions for the corresponding solution of generalized stress equations of motion to be unique are detailed in a uniqueness theorem. A numerical passage to obtain the solution of such equations is then given by generalizing a reciprocity theorem in terms of stress for such materials. Finally, as particular cases of the general 3D form, the stress equations of motion for planar problems (plane strain and Generalized plane stress) for transversely isotropic media are formulated.

AB - A stress-based approach to the analysis of linear electro-magneto-elastic materials is proposed. Firstly, field equations for linear electro-magneto-elastic solids are given in detail. Next, as a counterpart of coupled governing equations in terms of the displacement field, generalized stress equations of motion for the analysis of three-dimensional (3D) problems Are obtained – they supply a more convenient basis when mechanical boundary conditions are entirely tractions. Then, a sufficient set of conditions for the corresponding solution of generalized stress equations of motion to be unique are detailed in a uniqueness theorem. A numerical passage to obtain the solution of such equations is then given by generalizing a reciprocity theorem in terms of stress for such materials. Finally, as particular cases of the general 3D form, the stress equations of motion for planar problems (plane strain and Generalized plane stress) for transversely isotropic media are formulated.

KW - Stress formulation

KW - alternative equations of motion

KW - elastodynamics

KW - electro-magneto-elastic materials

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U2 - 10.1177/1081286519857127

DO - 10.1177/1081286519857127

M3 - Article

AN - SCOPUS:85068319230

SN - 1081-2865

VL - 24

SP - 3806

EP - 3822

JO - Mathematics and Mechanics of Solids

JF - Mathematics and Mechanics of Solids

IS - 12

ER -