Nonlinear finite element modelling of thermo-visco-plastic styrene and polyurethane shape memory polymer foams

Hamid Reza Jarrah, Ali Zolfagharian, Reza Hedayati, Ahmad Serjouei, Mahdi Bodaghi*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
40 Downloads (Pure)


This paper presents nonlinear finite element (FE) models to predict time-and tempera-ture-dependent responses of shape memory polymer (SMP) foams in the large deformation regime. For the first time, an A SMP foam constitutive model is implemented in the ABAQUS FE package with the aid of a VUMAT subroutine to predict thermo-visco-plastic behaviors. A phenomenological constitutive model is reformulated adopting a multiplicative decomposition of the deformation gradient into thermal and mechanical parts considering visco-plastic SMP matrix and glass micro-sphere inclusions. The stress split scheme is considered by a Maxwell element in parallel with a hyper-elastic rubbery spring. The Eyring dashpot is used for modelling the isotropic resistance to the local molecular rearrangement such as chain rotation. A viscous flow rule is adopted to prescribe shear viscosity and stress. An evolution rule is also considered for the athermal shear strengths to simulate macroscopic post-yield strain-softening behavior. In order to validate the accuracy of the model as well as the solution procedure, the numerical results are compared to experimental responses of Styrene and Polyurethane SMP foams at different temperatures and under different strain rates. The results show that the introduced FE modelling procedure is capable of capturing the major phenomena observed in experiments such as elastic and elastic-plastic behaviors, softening plateau regime, and densification.

Original languageEnglish
Article number46
Pages (from-to)1-20
Number of pages20
Issue number3
Publication statusPublished - 2021


  • Finite element model-ling
  • Foams
  • Large deformation
  • Shape memory polymers
  • Thermo-visco-plastic behavior


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