Three-dimensional constitutive model for shape memory alloys based on microplane model

M. Brocca, L. C. Brinson*, Z. P. Bažant

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

144 Scopus citations


A new model for the behavior of polycrystalline shape memory alloys (SMA), based on a statically constrained microplane theory, is proposed. The new model can predict three-dimensional response by superposing the effects of inelastic deformations computed on several planes of different orientation, thus reproducing closely the actual physical behavior of the material. Due to the structure of the microplane algorithm, only a one-dimensional constitutive law is necessary on each plane. In this paper, a simple constitutive law and a robust kinetic expression are used as the local constitutive law on the microplane level. The results for SMA response on the macroscale are promising: simple one-dimensional response is easily reproduced, as are more complex features such as stress-strain subloops and tension-compression asymmetry. A key feature of the new model is its ability to accurately represent the deviation from normality exhibited by SMAs under nonproportional loading paths.

Original languageEnglish (US)
Pages (from-to)1051-1077
Number of pages27
JournalJournal of the Mechanics and Physics of Solids
Issue number5
StatePublished - May 2002


  • Constitutive relations
  • Microplane model
  • Plasticity
  • Shape memory alloys

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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