This article introduces a computational design framework for obtaining three-dimensional (3D) periodic elastoplastic architected materials with enhanced performance, subject to uniaxial or shear strain. A nonlinear finite element model accounting for plastic deformation is developed, where a Lagrange multiplier approach is utilized to impose periodicity constraints. The analysis assumes that the material obeys a von Mises plasticity model with linear isotropic hardening. The finite element model is combined with a corresponding path-dependent adjoint sensitivity formulation, which is derived analytically. The optimization problem is parametrized using the solid isotropic material penalization method. Designs are optimized for either end compliance or toughness for a given prescribed displacement. Such a framework results in producing materials with enhanced performance through much better utilization of an elastoplastic material. Several 3D examples are used to demonstrate the effectiveness of the mathematical framework.

Original languageEnglish (US)
Pages (from-to)1889-1910
Number of pages22
JournalInternational Journal for Numerical Methods in Engineering
Issue number8
StatePublished - Apr 30 2021


  • adjoint sensitivity analysis
  • energy absorption
  • metamaterials
  • periodic boundary conditions
  • von Mises plasticity

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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