A rate-sensitive constitutive model for anisotropic cellular materials — Application to a transversely isotropic polyurethane foam

Pei Li, Y.B. Guo, V.P.W. Shim

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)


Constitutive models that describe anisotropic mechanical behaviour have generally focused on incompressible materials such as metals. However, many cellular materials such as foams and wood are compressible, and their mechanical response is both direction- and rate-dependent. To describe the anisotropic behaviour of these compressible cellular materials, a rate-sensitive constitutive model is proposed to capture their large deformation, dynamic response to compression, which cellular materials are often subjected to; this is based on a model proposed by the authors (Li et al., 2018). Anisotropy of yielding is captured via a 4th order tensor, whereby appropriate assumptions enable the 21 parameters to be determined from only six fundamental experimental tests, i.e. uniaxial compression along three principal directions and simple shear corresponding to three principal planes. Anisotropy of the post-yield response is characterized by a hardening matrix containing six hardening functions, and these are also determined by the six basic experimental tests. By inverting the hardening function matrix, the Cauchy stresses are scaled back to define a modified stress space, whereby the yield surface remains stationary; this enables anisotropic post-yield behaviour to be expressed in a simplified form. To incorporate rate-sensitivity, the six hardening functions are cast in terms of both effective plastic strain and strain rate. Assuming that rate-sensitivity of the post-yield response follows that of the yield stress, the proposed model is applied to predict the stress-strain and deformation response of a transversely isotropic crushable polyurethane foam reported in (Li et al., 2019). Good correlation between the predicted and experimental results demonstrates that the proposed model using the assumed form of rate-sensitivity, is able to adequately capture the large deformation mechanical behaviour and rate-dependence of anisotropic cellular materials beyond yield.
Original languageEnglish
Pages (from-to)43-58
Number of pages16
JournalInternational journal of solids and structures
Early online date9 Sept 2020
Publication statusPublished - 1 Dec 2020
Externally publishedYes


  • Anisotropic cellular material
  • Rate-sensitive constitutive model
  • Polyurethane foam
  • Large deformation
  • Post-yield response


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