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Multiscale Modeling of Heterogeneous Structures pp 113–127Cite as

Unified Approach to Sensitivity Analysis Based Automation of Multi-scale Modelling

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Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 86))

Abstract

Use of different kinds of multi-scale methods is limited with specifications of the problem to be solved. Standard two-level finite element homogenization approach \(\text {FE}^2\) is appropriate for problems with weakly coupled scales. If the difference between two scales is finite, or in the region of high gradients the \(\text {FE}^2\) multi-scale approach fails, then some sort of domain decomposition method can be applied. Our motivation was to create computational environment, where the multi-scale code is automatically derived and various types of multi-scale approaches can be freely mixed. The described approach uses an advanced feature of software tools AceGen and AceFEM, that is automatic generation of the finite element codes for analytical first and second order sensitivity analysis with respect to prescribed essential boundary conditions as a unifying factor. The automatic-differentiation-based formulation (ADB) enables unification and automation of various multi-scale approaches for an arbitrary nonlinear, time dependent, coupled problem (e.g. general finite strain plasticity).

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Acknowledgements

The financial support for this work was obtained from the Slovenian Research Agency within the PhD Grant Agreement (annex No: 630-34/2015-7).

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Authors and Affiliations

  1. Faculty of Civil and Geodetic Engineering, Jamova cesta 2, 1000, Ljubljana, Slovenia

    N. Zupan & J. Korelc

Authors
  1. N. Zupan
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  2. J. Korelc
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Correspondence to N. Zupan .

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Editors and Affiliations

  1. University of Zagreb, Zagreb, Croatia

    Jurica Sorić

  2. Institute of Continuum Mechanics, Leibniz Universität Hannover, Hannover, Germany

    Peter Wriggers

  3. LMT Cachan, Cachan, France

    Olivier Allix

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Zupan, N., Korelc, J. (2018). Unified Approach to Sensitivity Analysis Based Automation of Multi-scale Modelling. In: Sorić, J., Wriggers, P., Allix, O. (eds) Multiscale Modeling of Heterogeneous Structures. Lecture Notes in Applied and Computational Mechanics, vol 86. Springer, Cham. https://doi.org/10.1007/978-3-319-65463-8_6

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  • DOI: https://doi.org/10.1007/978-3-319-65463-8_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-65462-1

  • Online ISBN: 978-3-319-65463-8

  • eBook Packages: EngineeringEngineering (R0)

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