Consistent machine learning for topology optimization with microstructure-dependent neural network material models

Harikrishnan Vijayakumaran, Jonathan B. Russ, Glaucio H. Paulino, Miguel A. Bessa*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such structures in the presence of nonlinearities remains a challenge due to the expense of computational homogenization methods and the complexity of differentiably parameterizing the microstructural response. A solution to this challenge lies in machine learning techniques that offer efficient, differentiable mappings between the material response and its microstructural descriptors. This work presents a framework for designing multiscale heterogeneous structures with spatially varying microstructures by merging a homogenization-based topology optimization strategy with a consistent machine learning approach grounded in hyperelasticity theory. We leverage neural architectures that adhere to critical physical principles such as polyconvexity, objectivity, material symmetry, and thermodynamic consistency to supply the framework with a reliable constitutive model that is dependent on material microstructural descriptors. Our findings highlight the potential of integrating consistent machine learning models with density-based topology optimization for enhancing design optimization of heterogeneous hyperelastic structures under finite deformations.

Original languageEnglish
Article number106015
Number of pages32
JournalJournal of the Mechanics and Physics of Solids
Volume196
DOIs
Publication statusPublished - 2025

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

  • Deep learning
  • Functionally-graded materials
  • Material-integrated design
  • Multi-scale structures
  • Neural networks
  • Topology optimization

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