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

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 m...

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Veröffentlicht in:Archives of computational methods in engineering Jg. 25; H. 2; S. 479 - 505
Hauptverfasser: Otero, Fermin, Oller, Sergio, Martinez, Xavier
Format: Journal Article Verlag
Sprache:Englisch
Veröffentlicht: Dordrecht Springer Netherlands 01.04.2018
Springer Nature B.V
Schlagworte:
Anàlisi numèrica
Boundary value problems
COMP-DES-MAT Project
COMPDESMAT Project
Composite materials
Computation
Computer simulation
Deformation
Engineering
Enginyeria mecànica
Homogenization
Materials compostos
Mathematical analysis
Mathematical and Computational Engineering
Mecànica computacional
Multiscale analysis
Numerical analysis
Original Paper
Solid mechanics
Stress concentration
Stress distribution
Àrees temàtiques de la UPC
ISSN:1134-3060, 1886-1784
Online-Zugang:Volltext
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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. first-order and second-order, in this work an enhanced-first-order 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 macro-scale BVP.
AbstractList 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. first-order and second-order, in this work an enhanced-first-order 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 macro-scale BVP.
This is a copy of the author 's final draft version of an article published in the Archives of computational methods in engineering. The final publication is available at Springer via http://dx.doi.org/10.1007/s11831-016-9205-0 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. first-order and second-order, in this work an enhanced-first-order 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 macro-scale BVP. Peer Reviewed
Author Otero, Fermin
Oller, Sergio
Martinez, Xavier
Author_xml – sequence: 1
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  orcidid: 0000-0002-3776-7550
  surname: Otero
  fullname: Otero, Fermin
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  givenname: Xavier
  surname: Martinez
  fullname: Martinez, Xavier
  organization: Centre Internacional de Metodes Numerics en Enginyeria (CIMNE), Departamento de Ciencia e Ingeniería Náutica, FNB, Technical University of Catalonia
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ContentType Journal Article
Publication
Contributor Universitat Politècnica de Catalunya. Departament de Física
Universitat Politècnica de Catalunya. RMEE - Grup de Resistència de Materials i Estructures en l'Enginyeria
Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
Universitat Politècnica de Catalunya. Departament de Ciència i Enginyeria Nàutiques
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  fullname: Universitat Politècnica de Catalunya. RMEE - Grup de Resistència de Materials i Estructures en l'Enginyeria
Copyright CIMNE, Barcelona, Spain 2016
Archives of Computational Methods in Engineering is a copyright of Springer, (2016). All Rights Reserved.
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Snippet The continuous increase of computational capacity has encouraged the extensive use of multiscale techniques to simulate the material behaviour on several...
This is a copy of the author 's final draft version of an article published in the Archives of computational methods in engineering. The final publication is...
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SubjectTerms Anàlisi numèrica
Boundary value problems
COMP-DES-MAT Project
COMPDESMAT Project
Composite materials
Computation
Computer simulation
Deformation
Engineering
Enginyeria mecànica
Homogenization
Materials compostos
Mathematical analysis
Mathematical and Computational Engineering
Mecànica computacional
Multiscale analysis
Numerical analysis
Original Paper
Solid mechanics
Stress concentration
Stress distribution
Àrees temàtiques de la UPC
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Title Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method
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