Inverse metamaterial design combining genetic algorithms with asymptotic homogenization schemes

Francisco Dos Reis, Nikolaos Karathanasopoulos

Research output: Contribution to journalArticlepeer-review


In the current work, a numerical method for the inverse engineering of metamaterials is elaborated. The method is based on the combination of asymptotic homogenization schemes with genetic algorithms and it makes use of the complete set of parameters contained in the target compliance tensor. As such, it can be used to compute lattice unit-cell patterns that meet target macroscale elastic, shear, Poisson's ratio and normal to shear strain coupling performances for the first time. The elaborated formulation applies to both constant and variable target relative density metamaterial designs, identifying metamaterial architectures within and beyond orthotropy. Different relevant case-study examples are provided, highlighting the potential of the formulation to capture a wide range of effective metamaterial behaviors. The accuracy of the results is additionally verified through commercial code, dedicated Abaqus finite element models, as well as through experimental testing of 3D-printed, periodic metamaterial samples. The scheme has a substantially low computational cost, so that a wide range of inverse engineering tasks can be performed within a computing time of a few minutes, using regular power, personal computing machines.

Original languageEnglish (US)
Article number111702
JournalInternational Journal of Solids and Structures
StatePublished - Aug 15 2022


  • Auxetic
  • Genetic algorithm
  • Homogenization
  • Inverse design
  • Lattice
  • Metamaterial
  • Optimization
  • Stiffness

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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