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Relaxation of an Energy Model for the Triangle-to-Centred Rectangle Transformation

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The Role and Importance of Mathematics in Innovation

Part of the book series: Mathematics for Industry ((MFI,volume 25))

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Abstract

We model and analyze the two-dimensional triangle-to-centred rectangle transformation of elastic crystals. By considering a Ginzburg–Landau type model, we compute the relaxation of the total energy both in the case of compressible and incompressible materials and construct some possible explicit microstructures as the approximate solutions of a non-convex minimization problem.

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Acknowledgments

The research of PC was partially supported by the ERC under the EU’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement no. 291053.

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Authors and Affiliations

  1. Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan

    Pierluigi Cesana

  2. Australia Branch, Department of Mathematics and Statistics, La Trobe University, Bundoora, VIC, 3086, Australia

    Pierluigi Cesana

Authors
  1. Pierluigi Cesana
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Corresponding author

Correspondence to Pierluigi Cesana .

Editor information

Editors and Affiliations

  1. Informatics and Statistics, CSIRO Mathematics Informatics and Statistics, Canberra, Aust Capital Terr, Australia

    Bob Anderssen

  2. Mathematics & Statistics Dept, La Trobe Univ Mathematics & Statistics Dept, Bundoora, Victoria, Australia

    Philip Broadbridge

  3. Inst of Math for Industry, Kyushu University Inst of Math for Industry, Fukuoka, Fukuoka, Japan

    Yasuhide Fukumoto

  4. Inst of Math for Industry, Kyushu University, Fukuoka, Japan

    Naoyuki Kamiyama

  5. Inst of Math for Industry, Kyushu University Inst of Math for Industry, Fukuoka, Japan

    Yoshihiro Mizoguchi

  6. AG Mathematical Geometry Processing, Freie Univ Berlin AG Mathematical Geometry Processing, Berlin, Germany

    Konrad Polthier

  7. Inst of Math for Industry, Kyushu University Inst of Math for Industry, Fukuoka, Japan

    Osamu Saeki

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Cesana, P. (2017). Relaxation of an Energy Model for the Triangle-to-Centred Rectangle Transformation. In: Anderssen, B., et al. The Role and Importance of Mathematics in Innovation. Mathematics for Industry, vol 25. Springer, Singapore. https://doi.org/10.1007/978-981-10-0962-4_11

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  • DOI: https://doi.org/10.1007/978-981-10-0962-4_11

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-0961-7

  • Online ISBN: 978-981-10-0962-4

  • eBook Packages: EngineeringEngineering (R0)

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