A thermomechanical modeling and simulation of viscoplastic large deformation behavior for polymeric materials (1st report, non-coaxiality of constitutive equation originated in strain rate dependence)

Daisuke Murakami, Seiichi Kobayashi, Toshikazu Torigaki, Kazuyuki Shizawa

Research output: Contribution to journalArticle

6 Citations (Scopus)


Polymeric materials have various characteristics of deformation, e.g., strain rate dependence (viscoplasticity) at room temperature, strain localization just after initial yielding and propagation of a localized region with strain hardening. Viscoplasticity has been usually represented by a constitutive equation of plasticity with a hardening law including a plastic strain rate. However, such a modeling is not thermodynamically consistent with the hardening law dependent on strain rate. In this paper, a strain rate tensor is introduced into free energy and a thermodynamic force conjugate to this rate is newly defined. On the basis of the principle of increase of entropy and one of maximal entropy production rate, a non-coaxial constitutive equation of viscoplasticity is derived as a flow rule in which a dissipation function plays the role of plastic potential. It is shown that a strain rate dependent constitutive equation must be always non-coaxial in a thermodynamically consistent theory.

Original languageEnglish
Pages (from-to)674-681
Number of pages8
JournalNippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A
Issue number4
Publication statusPublished - 2002 Apr



  • Constitutive equation
  • Flow rule
  • High polymer materials
  • Large deformation
  • Non-coaxiality
  • Plasticity
  • Thermomechanics
  • Viscoplasticity

ASJC Scopus subject areas

  • Mechanical Engineering

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