Constitutive modeling of two phase materials using the Mean Field method for homogenization

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A Mean-Field homogenization framework for constitutive modeling of materials involving two distinct elastic-plastic phases is presented. With this approach it is possible to compute the macroscopic mechanical behavior of this type of materials based on the constitutive models of the constituent phases. Different homogenization schemes that exist in the literature are implemented in efficient algorithms to be used in full-scale FE simulations. These schemes are compared with each other in terms of efficiency. Additionally two new schemes are proposed which are both computationally efficient and compare in accuracy with the more physically based approaches. Finally the algorithms are demonstrated on FE simulations of sheet metal forming operations and compared with experimental results.
Original languageEnglish
Pages (from-to)93–102
Number of pages10
JournalInternational journal of material forming
Issue number2
Publication statusPublished - 2010


  • Mean field
  • Homogenization
  • Mori–Tanaka
  • Self consistent
  • Dual-phase steels
  • Metal-matrix composites (MMCs)


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