XFEM modeling and homogenization of magnetoactive composites

Spieler, C.; Kästner, Markus; Goldmann, Joseph; Brummund, Jörg; Ulbricht, Volker

doi:10.1007/s00707-013-0948-5

Cited by 47 publications

(31 citation statements)

References 42 publications

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“…XFEM is therefore used to model the heterogeneous material structure of the problem mentioned above. The implemented higher-order XFEM formulation for the solution of stationary magnetic and coupled magneto-mechanical field problems in the context of small deformations is extensively described in [17,31]. In this work, we are using bilinear and biquadratic quadrilateral elements which are labeled Q4 and Q8, respectively.…”

Section: Brief Outline Of the Extended Finite Element Methodsmentioning

confidence: 99%

“…If it is advantageous, cylindrical coordinates are used, e.g., to evaluate jump conditions. Since only small deformations are considered here, it is possible to perform a staggered solution for both linear problems as already published in [31]. A large deformation formulation focusing on the constitutive modeling is described, e.g., in [32].…”

Section: Problem Descriptionmentioning

confidence: 99%

“…To this end, homogenization techniques are applied to coupled magneto-mechanical problems. Beside analytic approaches [27], computational homogenization schemes [16,19,31] allow to model complex material structures and a broad class of constitutive behavior. The numeric solution of the corresponding boundary value problems (BVP) of representative volume elements of the local material structure is typically based on the finite element method (FEM) or related modeling strategies like the extended finite element method (XFEM).…”

Section: Introductionmentioning

confidence: 99%

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Analytic and numeric solution of a magneto-mechanical inclusion problem

2014

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In this paper, exact solutions for the primary field variables and their first derivatives are derived for the coupled magneto-mechanical problem of a circular inclusion embedded in an infinite surrounding. Both material domains possess linear and isotropic material properties. The assumed planarity of all fields enables and recommends the description with analytic functions depending on the complex variable z. The well-known technique of a complex stress potential satisfying the bipotential equation is used and adapted to coupled magneto-mechanical problems. The provided analytic expressions are of special interest for the validation of numeric solutions of coupled magneto-mechanical boundary value problems. In this contribution, they are applied to analyze the convergence behavior of an extended finite element formulation for coupled magneto-mechanical problems. Based on the analytic results, proper boundary conditions are prescribed to the numeric model. The convergence in terms of polynomial degree and mesh refinement of the implemented element formulation is proved by computing the L 2 and the energy norm which requires the knowledge of the exact solution. The generality of the proposed formulas allows for the deduction of some other kind of problems, e.g., the pure mechanical displacement and stress field of a bimaterial setting or the stress concentration around a circular hole.

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Section: Brief Outline Of the Extended Finite Element Methodsmentioning

confidence: 99%

Section: Problem Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analytic and numeric solution of a magneto-mechanical inclusion problem

2014

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“…In general, high-resolution finite-element simulation methods are necessary to capture this effect. 48,71 Strictly speaking, the homogeneity assumption in our analytical treatment is only valid for point-like inclusions. The closest situation to match these homogeneity assumptions may be the bulk behavior in a material consisting of chains that on the one hand span the whole sample 54 and on the other hand are composed of small-sized magnetic particles of sufficiently high magnetic moment.…”

Section: Mesoscopic Modelmentioning

confidence: 99%

Bridging from particle to macroscopic scales in uniaxial magnetic gels

Menzel

2014

The Journal of Chemical Physics

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Connecting the different length scales of characterization is an important, but often very tedious task for soft matter systems. Here, we carry out such a procedure for the theoretical description of anisotropic uniaxial magnetic gels. The so-far undetermined material parameters in a symmetry-based macroscopic hydrodynamic-like description are determined starting from a simplified mesoscopic particle-resolved model. This mesoscopic approach considers chain-like aggregates of magnetic particles embedded in an elastic matrix. Our procedure provides an illustrative background to the formal symmetry-based macroscopic description. There are presently other activities to connect such mesoscopic models as ours with more microscopic polymer-resolved approaches; together with these activities, our study complements a first attempt of scale-bridging from the microscopic to the macroscopic level in the characterization of magnetic gels.

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“…[398][399][400][401][402][403][404][405] for thermomechanical problems, Refs. [406][407][408][409] for magnetomechanical problems, Refs. [410][411][412][413][414][415][416] for electromechanical problems, and Refs.…”

Section: Beyond Purely Elastic Problemsmentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

190

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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XFEM modeling and homogenization of magnetoactive composites

Cited by 47 publications

References 42 publications

Analytic and numeric solution of a magneto-mechanical inclusion problem

Analytic and numeric solution of a magneto-mechanical inclusion problem

Bridging from particle to macroscopic scales in uniaxial magnetic gels

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

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