Structural and Multidisciplinary Optimization

, Volume 59, Issue 2, pp 461–483 | Cite as

Design of periodic elastoplastic energy dissipating microstructures

  • Ryan Alberdi
  • Kapil KhandelwalEmail author
Research Paper


The design of periodic elastoplastic microstructures for maximum energy dissipation is carried out using topology optimization. While the topology optimization of elastic microstructures has been performed in numerous studies, microstructural design considering inelastic behavior is relatively untouched due to a number of reasons which are addressed in this study. An RVE-based multiscale model is employed for computational homogenization with periodic boundary constraints, satisfying the Hill-Mandel principle. The plastic anisotropy which may be prevalent in materials fabricated through additive manufacturing processes is considered by modeling the constitutive behavior at the microscale with Hoffman plasticity. Discretization is done using enhanced assumed strain elements to avoid locking from incompressible plastic flow under plane strain conditions and a Lagrange multiplier approach is used to enforce periodic boundary constraints in the discrete system. The design problem is formulated using a density-based parameterization in conjunction with a SIMP-like material interpolation scheme. Attention is devoted to issues such as dependence on initial design and enforcement of microstructural connectivity, and a number of optimized microstructural designs are obtained under different prescribed deformation modes.


Architectured microstructures Nonlinear topology optimization RVE-based multiscale models Computational homogenization Anisotropic plasticity 


Funding information

The presented work is supported in part by the US National Science Foundation through Grant CMMI-1762277. Any opinions, findings, conclusions, and recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil, Environmental EngineeringEarth Sciences University of Notre DameNotre DameUSA

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