Nonlinear homogenization for topology optimization

Research output: Contribution to journalArticle


Non-linear homogenization of hyperelastic materials is reviewed and adapted to topology optimization. The homogenization is based on the method of multiscale virtual power in which the unit cell is subjected to either macroscopic deformation gradients or equivalently to Bloch type displacement boundary conditions. A detailed discussion regarding domain symmetry of the unit cell and its effect on uniaxial loading conditions is provided. The density approach is used to formulate the topology optimization problem which is solved via the method of moving asymptotes. The adjoint sensitivity analysis considers response functions that quantify both the displacement and incremental displacement. Notably, the transfer of the sensitivities from the microscale to the macroscale is presented in detail. A periodic filter and thresholding are used to regularize the topology optimization problem and to generate crisp boundaries. The proposed methodology is used to design hyperelastic microstructures comprised of Neo-Hookean constituents for maximum load carrying capacity subject to negative Poisson's ratio constraints.


External organisations
  • Lawrence Livermore National Laboratory
  • University of Illinois at Urbana-Champaign
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computational Mathematics
  • Applied Mechanics
Original languageEnglish
Article number103324
JournalMechanics of Materials
Publication statusPublished - 2020 Jun
Publication categoryResearch