Two-scale computational homogenization of electro-elasticity at finite strains

Keip, Marc‐André; Steinmann, Paul; Schröder, Jörg

doi:10.1016/j.cma.2014.04.020

Cited by 92 publications

(70 citation statements)

References 52 publications

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“…In the last years, multiphysics problems have been addressed using multiscale homogenization methods, such as [96,125,120,8] for thermomechanical problems, [50,11] for magnetomechanical problems, [104,57,79] for electromechanical problems, among others. On the other hand, after the groundbreaking contribution of Bendsoe and Kikuchi [6] in which the homogenization method is used to design optimal topology structures several authors have dabbled into this actual research topic [1,106,128,56,22].…”

Section: Review Of Multiscale Methodsmentioning

confidence: 99%

Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method

Otero

Oller

Martı́nez

2016

Arch Computat Methods Eng

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Aquesta és una còpia de la versió author's final draft d'un article publicat a la revista Archives of computational methods in engineering. Abstract The continuous increase of computational capacity has encouraged the extensive use of multiscale techniques to simulate the material behaviour on several fields of knowledge. In solid mechanics, the multiscale approaches which consider the macro-scale deformation gradient to obtain the homogenized material behaviour from the micro-scale are called first-order computational homogenization. Following this idea, the second-order FE2 methods incorporate high-order gradients to improve the simulation accuracy. However, to capture the full advantages of these high-order framework the classical Boundary Value Problem (BVP) at the macro-scale must be upgraded to high-order level, which complicates their numerical solution. With the purpose of obtaining the best of both methods i.e. firstorder and second-order, in this work an enhanced-firstorder computational homogenization is presented. The proposed approach preserves a classical BVP at the macro-scale level but taking into account the high-order gradient of the macro-scale in the micro-scale solution. The developed numerical examples show how the proposed method obtains the expected stress distribution at the micro-scale for states of structural bending loads. Nevertheless, the macro-scale results achieved are the same than the ones obtained with a first-order framework because both approaches share the same macroscale BVP.

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Section: Review Of Multiscale Methodsmentioning

confidence: 99%

Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method

Otero

Oller

Martı́nez

2016

Arch Computat Methods Eng

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“…See Refs. [363] and [414] for further discussions about computation of macro Piola tangent in the discrete formulation. Once M A is calculated, all the ingredients to perform the full FE 2 simulation are provided.…”

Section: -20 / Vol 68 September 2016mentioning

confidence: 99%

“…[406][407][408][409] for magnetomechanical problems, Refs. [410][411][412][413][414][415][416] for electromechanical problems, and Refs. [417] and [418] for hydromechanical problems, see also 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

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185

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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“…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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Two-scale computational homogenization of electro-elasticity at finite strains

Cited by 92 publications

References 52 publications

Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method

Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method

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

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

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