Hybrid nonlinear surrogate models for fracture behavior of polymeric nanocomposites

Mohammed F. Badawy, Mohammed A. Msekh, Khader M. Hamdia, Maria K. Steiner, Tom Lahmer, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


We present a hybrid nonlinear surrogate model for fracture in polymeric nanocomposites. The phase field method is employed to model fracture in the polymer matrix. Since the stochastic analysis on the output of the mechanical model is prohibitively expensive, surrogate models (SM) are very attractive alternatives. In order to get an optimal and robust solution, we propose a hybrid nonlinear surrogate model (HSM) for the prediction of the fracture toughness of PNC. It is constructed with the use of the polynomial regression and the Kriging interpolation. The support data for such HSM is generated by a phase-field model for brittle fracture with six chosen input parameters. The validation of the surrogate model and by this its qualitative assessment is done based on a scanning test set algorithm. The constructed and assessed HSM is then used to present the behavior of fracture toughness of PNC with respect to various input parameters with very low computational costs and high accuracy. Within the domain of interest, the analysis shows that Young's modulus of the matrix has no optimum value, in which, the higher input value causes higher response. On the other hand the volume fraction of clay platelets at about 5% showed stability of the response, in which, the higher input value leads to no change in the response.

Original languageEnglish
Pages (from-to)64-75
Number of pages12
JournalProbabilistic Engineering Mechanics
Publication statusPublished - 2017 Oct

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Ltd


  • Brittle fracture
  • Cross-validation
  • Phase-field model
  • Polymer nanocomposites
  • Surrogate model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Civil and Structural Engineering
  • Nuclear Energy and Engineering
  • Condensed Matter Physics
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering


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