An electro-mechanically coupled computational multiscale formulation for electrical conductors

Kaiser, Tobias; Menzel, Andreas

doi:10.1007/s00419-020-01837-6

Cited by 11 publications

(10 citation statements)

References 29 publications

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“…[35]. Focusing on electrical conductors, a multiscale method was recently proposed in [19] subject to the assumption of infinitesimal deformations.…”

Section: Multiscale Modellingmentioning

confidence: 99%

“…In accordance with the restrictions on the electric current density vector posed by (19), a linear relation between the (spatial) electric current density vector and the (spatial) electric field vector is adopted at the microscale, namely…”

Section: Microscale Materials Modelsmentioning

confidence: 99%

“…From a materials science point of view, piezo-and dielectric moduli are in the focus of the latter works, whereas the electrical conductivity tensor is the primary material parameter that characterises the process studied in the present contribution. More specifically speaking, the present contribution is a direct extension of the fundamental developments on multiscale formulations for electrical conductors discussed in [19], subject to the assumption of linearised kinematics, to a finite deformation setting. This extension is essential to capture the effect of (inhomogeneous) geometry changes at the microscale on the effective macroscale conductivity tensor.…”

Section: Introductionmentioning

confidence: 99%

“…For the convenience of the reader, the article is organised similar to its small strain analogue [19]: Based on Maxwell's equations of electromagnetism, the governing set of partial differential equations of the electromechanically coupled continuum under consideration is briefly summarised in Sect. 2.…”

Section: Introductionmentioning

confidence: 99%

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A finite deformation electro-mechanically coupled computational multiscale formulation for electrical conductors

Kaiser

Menzel

2021

Acta Mech

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Motivated by the influence of deformation-induced microcracks on the effective electrical properties at the macroscale, an electro-mechanically coupled computational multiscale formulation for electrical conductors is proposed. The formulation accounts for finite deformation processes and is a direct extension of the fundamental theoretical developments presented by Kaiser and Menzel (Arch Appl Mech 91:1509–1526, 2021) who assume a geometrically linearised setting. More specifically speaking, averaging theorems for the electric field quantities are proposed and boundary conditions that a priori fulfil the extended Hill–Mandel condition of the electro-mechanically coupled problem are discussed. A study of representative boundary value problems in two- and three-dimensional settings eventually shows the applicability of the proposed formulation and reveals the severe influence of microscale deformation processes on the effective electrical properties at the macroscale.

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“…[35]. Focusing on electrical conductors, a multiscale method was recently proposed in [19] subject to the assumption of infinitesimal deformations.…”

Section: Multiscale Modellingmentioning

confidence: 99%

Section: Microscale Materials Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A finite deformation electro-mechanically coupled computational multiscale formulation for electrical conductors

Kaiser

Menzel

2021

Acta Mech

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“…with e denoting the electric field vector, see e.g. [14,17] for a derivation based on Maxwell's equations of electromagnetism.…”

Section: Electrical Sub-problemmentioning

confidence: 99%

Fundamentals of electro-mechanically coupled cohesive zone formulations for electrical conductors

Kaiser

Menzel

2021

Comput Mech

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Motivated by the influence of (micro-)cracks on the effective electrical properties of material systems and components, this contribution deals with fundamental developments on electro-mechanically coupled cohesive zone formulations for electrical conductors. For the quasi-stationary problems considered, Maxwell’s equations of electromagnetism reduce to the continuity equation for the electric current and to Faraday’s law of induction, for which non-standard jump conditions at the interface are derived. In addition, electrical interface contributions to the balance equation of energy are discussed and the restrictions posed by the dissipation inequality are studied. Together with well-established cohesive zone formulations for purely mechanical problems, the present developments provide the basis to study the influence of mechanically-induced interface damage processes on effective electrical properties of conductors. This is further illustrated by a study of representative boundary value problems based on a multi-field finite element implementation.

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An adaptive wavelet-based collocation method for solving multiscale problems in continuum mechanics

2022

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Computational multiscale methods are highly sophisticated numerical approaches to predict the constitutive response of heterogeneous materials from their underlying microstructures. However, the quality of the prediction intrinsically relies on an accurate representation of the microscale morphology and its individual constituents, which makes these formulations computationally demanding. Against this background, the applicability of an adaptive wavelet-based collocation approach is studied in this contribution. It is shown that the Hill–Mandel energy equivalence condition can naturally be accounted for in the wavelet basis, (discrete) wavelet-based scale-bridging relations are derived, and a wavelet-based mapping algorithm for internal variables is proposed. The characteristic properties of the formulation are then discussed by an in-depth analysis of elementary one-dimensional problems in multiscale mechanics. In particular, the microscale fields and their macroscopic analogues are studied for microstructures that feature material interfaces and material interphases. Analytical solutions are provided to assess the accuracy of the simulation results.

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An electro-mechanically coupled computational multiscale formulation for electrical conductors

Cited by 11 publications

References 29 publications

A finite deformation electro-mechanically coupled computational multiscale formulation for electrical conductors

A finite deformation electro-mechanically coupled computational multiscale formulation for electrical conductors

Fundamentals of electro-mechanically coupled cohesive zone formulations for electrical conductors

An adaptive wavelet-based collocation method for solving multiscale problems in continuum mechanics

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