Algorithmic two-scale transition for magneto-electro-mechanically coupled problems

Schröder, Jörg; Labusch, Matthias; Keip, Marc‐André

doi:10.1016/j.cma.2015.10.005

Cited by 67 publications

(48 citation statements)

References 89 publications

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“…as considered in thermal problems [15], electrical, and magnetic problems [25]. In the FE 2 technique, the constitutive relations at the micro-scale are given under the fully-coupled forms…”

Section: General Strong Formmentioning

confidence: 99%

“…Considering an arbitrary field X k m , the generalized Hill-Mandel condition results in the averaging relation of the macroscopic generalized stress and its microscopic counterpart [10,25],…”

Section: Extraction Of the Macroscopic Quantitiesmentioning

confidence: 99%

“…This technique has also received the attention from other applications including purely thermal problems [15,16], thermo-mechanical problems [17][18][19], electro-mechanical problems [20][21][22], magneto-mechanical problems [23], electro-magneto-mechanical problems [24,25]. The FE 2 strategy relies on the principle of the separation of scales [6] which leads to assume that the microscopic BVP can be considered in a steady-state and can be formulated in a conventional form for mechanical, thermal, electrical, and magnetic parts.…”

Section: Introductionmentioning

confidence: 99%

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Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method

Nguyễn

Noels

2016

Comput Mech

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Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method Van-Dung Abstract This work provides a unified treatment of arbitrary kinds of microscopic boundary conditions usually considered in the multi-scale computational homogenization method for nonlinear multi-physics problems. An efficient procedure is developed to enforce the multi-point linear constraints arising from the microscopic boundary condition either by the direct constraint elimination or by the Lagrange multiplier elimination methods. The macroscopic tangent operators are computed in an efficient way from a multiple right hand sides linear system whose left hand side matrix is the stiffness matrix of the microscopic linearized system at the converged solution. The number of vectors at the right hand side is equal to the number of the macroscopic kinematic variables used to formulate the microscopic boundary condition. As the resolution of the microscopic linearized system often follows a direct factorization procedure, the computation of the macroscopic tangent operators is then performed using this factorized matrix at a reduced computational time.

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Section: General Strong Formmentioning

confidence: 99%

Section: Extraction Of the Macroscopic Quantitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method

Nguyễn

Noels

2016

Comput Mech

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“…The major benefit of the FE 2 method is the ability to analyse complex mechanical problems with heterogeneous phases that present a variety of behavior at different scales. This idea was originally introduced by Feyel [24], then this method was used and developed by several authors, for example [25,26,27,28,29,30,31].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional FE2 method for the simulation of non-linear, rate-dependent response of composite structures

Tikarrouchine

Chatzigeorgiou

Praud

et al. 2018

Composite Structures

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractIn this paper, a two scale Finite Element method (FE 2 ), is presented to predict the non-linear macroscopic response of 3D composite structures with periodic microstructure that exhibit a timedependent response. The sensitivity to the strain rate requires an homogenization scheme to bridge the scales between the macroscopic boundary conditions applied and the local evaluation of the strain rate. In the present work, the effective response of composite materials where the matrix has a local elasto-viscoplastic behavior with ductile damage are analyzed using periodic homog- investigates the macroscopic response of a complex viscoplastic composite structure with ductile damage and is compared with the mean field Mori-Tanaka method. Finally, 3D corner structure consisting of periodically aligned short fibres composite is analysed under complex loading path.These numerical simulations illustrate the capabilities of the FE 2 strategy under non-linear regime.when time dependent constitutive models describe the response of the constituents

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“…However, the interaction between the applied field and the material response is highly non-linear concerning their magnetization or electric polarization, respectively, as well as their mechanical deformations. Therefore, a realistic and exact modeling of these ferroic properties, see [10], is important to predict the functionality of such devices. In order to simulate the characteristic polarization and mechanical butterfly hysteresis loops for ferroelectric solids, we employ a three-dimensional Preisach model.…”

Section: Introductionmentioning

confidence: 99%

Computational characterization of ferroelectric solids with a 3D Preisach model based on an orientation distribution function

Labusch

Schröder

2016

Proc Appl Math and Mech

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Ferroelectric or ferromagnetic materials show an interaction between mechanical deformations and polarization or magnetization. A few multiferroic materials possess both ferroic properties and exhibit a magneto-electric (ME) coupling. These ME properties can be achieved in two-phase composites, which combine ferroelectric and ferromagnetic characteristics. To predict a realistic material behavior and a more precise ME coefficient, the application of suitable material models which describe the nonlinear hysteretic behavior is of particular importance. In the present contribution we focus on the characterization of a nonlinear ferroelectric material behavior, in terms of a 3D Preisach model based on an orientation distribution function.

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Algorithmic two-scale transition for magneto-electro-mechanically coupled problems

Cited by 67 publications

References 89 publications

Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method

Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method

Three-dimensional FE2 method for the simulation of non-linear, rate-dependent response of composite structures

Computational characterization of ferroelectric solids with a 3D Preisach model based on an orientation distribution function

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