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Virtual Elements for Thermo-mechanical Problems

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Virtual Element Methods in Engineering Sciences

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Abstract

Many engineering problems require an analysis that takes into account more than one field. These are known as coupled problems which can be split in two distinct categories. The first category relates to problems in which the physical domains overlap and coupling occurs via the differential equations of the different physical phenomena. In the second category problems are investigated in which coupling occurs only at the domain interfaces, like in fluid-structure interaction. Here we will concentrate on the first category. Examples are thermo-mechanical, phase field and electro-mechanical problems, among others. The single fields are governed by different physical models. In general, the behaviour of each field is influenced by the other fields that are present in the model. Additional complexity arises for the proper setup of numerical simulation procedures when the partial differential equations, describing the single fields, are of different type. Hence, coupled multi-field and multi-physics problems span on one side a vast area of applications and on the other side they are demanding with respect to discretizations and algorithms.

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Notes

  1. 1.

    The operator \( \mathbb {D}_\nabla ^{(3,1)} \) does not have to be computed explicitly when using automatic software generation as in Sect. 3.1.5.

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Authors and Affiliations

  1. Institute for Continuum Mechanics, Leibniz University Hannover, Garbsen, Germany

    Peter Wriggers

  2. Institute of Mechanics and Computational Mechanics, Leibniz University Hannover, Hannover, Germany

    Fadi Aldakheel

  3. Institute of Continuum Mechanics, Leibniz University Hannover, Garbsen, Germany

    Blaž Hudobivnik

Authors
  1. Peter Wriggers
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  2. Fadi Aldakheel
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  3. Blaž Hudobivnik
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Correspondence to Peter Wriggers .

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Wriggers, P., Aldakheel, F., Hudobivnik, B. (2024). Virtual Elements for Thermo-mechanical Problems. In: Virtual Element Methods in Engineering Sciences. Springer, Cham. https://doi.org/10.1007/978-3-031-39255-9_9

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  • DOI: https://doi.org/10.1007/978-3-031-39255-9_9

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