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Topology optimization for three‐dimensional elastoplastic architected materials using a path‐dependent adjoint method
Author(s) -
Abueidda Diab W.,
Kang Ziliang,
Koric Seid,
James Kai A.,
Jasiuk Iwona M.
Publication year - 2021
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6604
Subject(s) - lagrange multiplier , finite element method , isotropy , von mises yield criterion , nonlinear system , plasticity , mathematics , path (computing) , topology optimization , topology (electrical circuits) , structural engineering , mathematical optimization , mathematical analysis , computer science , materials science , engineering , physics , composite material , quantum mechanics , combinatorics , programming language
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.