Thermal–mechanical metamaterial analysis and optimization using an Abaqus plugin

Ewan Fong, Kimmo Koponen, Sadik Omairey, Peter Dunning* (Corresponding Author)

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This paper demonstrates how commercial finite element software and
optimization algorithms can be combined to fully explore the design
space of thermal-mechanical metamaterials to reveal trends and new
insight. This is achieved by developing an Abaqus plugin (EasyPBC)
that automates the application of periodic boundary conditions and
computes effective elastic and thermal expansion properties for 2D
and 3D problems. Abaqus is then linked to an optimizer to fully
explore the design space and optimal trade-off between thermal and
mechanical properties for two example metamaterials. The first example is a auxetic 2D star shaped metamaterial, where the proposed
approach is used to create a design envelope for Poisson’s ratio and
thermal expansion coefficient by solving a series of constrained optimization problems. The second example is a 3D metamaterial based on
an octet truss, with additional members to expand the design space.
A multi-objective optimization problem is solved to find the optimal
trade-off between Young’s modulus and thermal expansion coefficient
in a prescribed direction. The results of both examples expand our
knowledge about the range of properties for these metamaterials, and
designs for optimal trade-off between thermal and mechanical properties.
Original languageEnglish
JournalEngineering with Computers
Early online date17 Jun 2023
Publication statusE-pub ahead of print - 17 Jun 2023

Bibliographical note

Open Access via the Springer Agreement


  • metamaterial
  • auxetic
  • non-positive thermal expansion coefficient
  • optimization
  • periodic homogenization


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