Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions

Khader M. Hamdia, Mohammad Silani, Xiaoying Zhuang, Pengfei He, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

347 Citations (Scopus)


The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers by nanosize fillers improves significantly their toughness. The fracture mechanism of the produced polymeric nanocomposites is influenced by different parameters. This paper presents a methodology for stochastic modelling of the fracture in polymer/particle nanocomposites. For this purpose, we generated a 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone. The crack propagation was modelled by the phantom node method. The stochastic model is based on six uncertain parameters: the volume fraction and the diameter of the nanoparticles, Young’s modulus and the maximum allowable principal stress of the epoxy matrix, the interphase zone thickness and its Young’s modulus. Considering the uncertainties in input parameters, a polynomial chaos expansion surrogate model is constructed followed by a sensitivity analysis. The variance in the fracture energy was mostly influenced by the maximum allowable principal stress and Young’s modulus of the epoxy matrix.

Original languageEnglish
Pages (from-to)215-227
Number of pages13
JournalInternational Journal of Fracture
Issue number2
Publication statusPublished - 2017 Aug 1
Externally publishedYes

Bibliographical note

Funding Information:
The authors gratefully acknowledge the support for this research provided by the Deutsche Forschungsgemeinschaft (DFG).


  • Computational mechanics
  • Fracture toughness
  • Interphase
  • Polymeric nanoparticle composites
  • Sensitivity analysis
  • Uncertainty quantification

ASJC Scopus subject areas

  • Computational Mechanics
  • Modelling and Simulation
  • Mechanics of Materials


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