Numerical implementation of a neural network based material model in finite element analysis

Y. M.A. Hashash, S. Jung, J. Ghaboussi

Research output: Contribution to journalArticlepeer-review


Neural network (NN) based constitutive models can capture non-linear material behaviour. These models are versatile and have the capacity to continuously learn as additional material response data becomes available. NN constitutive models are increasingly used within the finite element (FE) method for the solution of boundary value problems. NN constitutive models, unlike commonly used plasticity models, do not require special integration procedures for implementation in FE analysis. NN constitutive model formulation does not use a material stiffness matrix concept in contrast to the elasto-plastic matrix central to conventional plasticity based models. This paper addresses numerical implementation issues related to the use of NN constitutive models in FE analysis. A consistent material stiffness matrix is derived for the NN constitutive model that leads to efficient convergence of the FE Newton iterations. The proposed stiffness matrix is general and valid regardless of the material behaviour represented by the NN constitutive model. Two examples demonstrate the performance of the proposed NN constitutive model implementation.

Original languageEnglish (US)
Pages (from-to)989-1005
Number of pages17
JournalInternational Journal for Numerical Methods in Engineering
Issue number7
StatePublished - Feb 21 2004


  • Finite elements
  • Material models
  • Neural networks
  • Numerical implementation
  • Stiffness matrix

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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