Two-scale homogenization of electromechanically coupled boundary value problems

Schröder, Jörg; Keip, Marc‐André

doi:10.1007/s00466-012-0715-9

Cited by 81 publications

(49 citation statements)

References 28 publications

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“…We employ the so-called FE 2 methodology [3,[8][9][10], implemented for the coupled magneto-elasto-static system of equations [11]. In the following, we denote a macroscopic quantity with an overline {•}.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

A multiscale view on shape effects in the computational characterization of magnetorheological elastomers

Rambausek

Keip

Miehé

2016

Proc Appl Math and Mech

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Section: Theoretical Frameworkmentioning

confidence: 99%

A multiscale view on shape effects in the computational characterization of magnetorheological elastomers

Rambausek

Keip

Miehé

2016

Proc Appl Math and Mech

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“…in this context see the fundamental work [47] and, in the framework of electro-mechanics, [44]. This condition is fulfilled under the assumption of periodic boundary conditions (c.f.…”

Section: Micro-macro Transitionmentioning

confidence: 99%

“…This condition is fulfilled under the assumption of periodic boundary conditions (c.f. [44]) which can be given in terms of the fluctuations of the displacements as well as the electric and magnetic potentials { w, φ, ϕ} and the corresponding fluxes as…”

Section: Micro-macro Transitionmentioning

confidence: 99%

“…Without derivation we write down the final result of the algorithmic tangent moduli, c.f. [44] (in matrix notation):…”

Section: Algorithmically Consistent Linearization On the Macroscalementioning

confidence: 99%

“…[27][28][29][30][31][32][33][34][35][36][37][38]. Recently, the method has been extended to the homogenization of coupled phenomena as for instance in the framework of thermo-and electro-mechanics [39][40][41][42][43][44][45][46]. The outline of the paper is as follows.…”

Section: Introductionmentioning

confidence: 99%

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Two‐scale computational homogenization of magneto‐electric composites

Keip

Labusch

Schröder

2013

Proc Appl Math and Mech

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This contribution presents a two-scale computational homogenization framework for the micro-macro simulation of magnetoelectro-mechanically coupled materials. Energetically consistent micro-macro transition conditions will be derived from a generalized form of the classical Hill-Mandel condition. A focus of the work is on the computation of effective magnetoelectric moduli which are derived on the basis of an algorithmically consistent linearization of the macroscopic field equations. The method will be applied to the homogenization of magneto-electric composites which are composed of piezomagnetic and piezoelectric phases. The effective magneto-electric moduli of two-phase composites will be computed.

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