Derivation of heterogeneous material laws via data-driven principal component expansions

Hang Yang, Xu Guo*, Shan Tang, Wing Kam Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

58 Scopus citations


A new data-driven method that generalizes experimentally measured and/or computational generated data sets under different loading paths to build three dimensional nonlinear elastic material law with objectivity under arbitrary loadings using neural networks is proposed. The proposed approach is first demonstrated by exploiting the concept of representative volume element (RVE) in the principal strain and stress spaces to numerically generate the data. A computational data-training algorithm on the generalization of these principal space data to three dimensional objective isotropic material laws subjected to arbitrary deformation is given. To validate these data-driven derived material laws, large deformation and buckling analysis of nonlinear elastic solids with reference material models and engineering structure with microstructure are performed. Numerical experiments show that only seven sets of data under different stress loading paths on RVEs are required to reach reasonable accuracy. The requirements for constitutive law such as objectivity are preserved approximately. The consistent tangent modulus is also derived. The proposed approach also shows a great potential to obtain the material law between different scales in the multiscale analysis by pure data.

Original languageEnglish (US)
Pages (from-to)365-379
Number of pages15
JournalComputational Mechanics
Issue number2
StatePublished - Aug 15 2019


  • 3D objective material laws
  • Artificial neural network
  • Computational data-driven
  • Engineering structure with microstructure
  • Principal strain and stress space

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'Derivation of heterogeneous material laws via data-driven principal component expansions'. Together they form a unique fingerprint.

Cite this