A thermomechanical modeling and simulation of viscoplastic large deformation behavior for polymeric materials (2nd report, vertex model based on flow rule and its finite element analysis)

Daisuke Murakami, Seiichi Kobayashi, Toshikazu Torigaki, Kazuyuki Shizawa

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In the previous 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 associated with a plastic deformation rate is derived as a flow rule in which a dissipation function plays the role of plastic potential. Material moduli in this equation, however, are still not expressed as functions of hardening law. In this paper, the constitutive equation is newly generalized into corner theory which permits an existence of a vertex on dissipation surface. A non-coaxial angle of a plastic deformation rate is related to the non-coaxial angle of a stress rate by use of strain rate sensitivity. Furthermore, a finite element analysis is carried out for a plane strain tension of homopolymer. Some remarkable numerical results of strain localization for homopolymer are discussed in detail.

Original languageEnglish
Pages (from-to)682-690
Number of pages9
JournalNippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A
Volume68
Issue number4
Publication statusPublished - 2002 Apr

Fingerprint

Homopolymerization
Constitutive equations
Strain rate
Plastic deformation
Entropy
Finite element method
Polymers
Free energy
Tensors
Hardening
Thermodynamics
Plastics

Keywords

  • Constitutive equation
  • Finite element method
  • High polymer materials
  • Large deformation
  • Non-coaxiality
  • Plasticity
  • Shear band
  • Vertex
  • Viscoplasticity

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

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title = "A thermomechanical modeling and simulation of viscoplastic large deformation behavior for polymeric materials (2nd report, vertex model based on flow rule and its finite element analysis)",
abstract = "In the previous 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 associated with a plastic deformation rate is derived as a flow rule in which a dissipation function plays the role of plastic potential. Material moduli in this equation, however, are still not expressed as functions of hardening law. In this paper, the constitutive equation is newly generalized into corner theory which permits an existence of a vertex on dissipation surface. A non-coaxial angle of a plastic deformation rate is related to the non-coaxial angle of a stress rate by use of strain rate sensitivity. Furthermore, a finite element analysis is carried out for a plane strain tension of homopolymer. Some remarkable numerical results of strain localization for homopolymer are discussed in detail.",
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AU - Murakami, Daisuke

AU - Kobayashi, Seiichi

AU - Torigaki, Toshikazu

AU - Shizawa, Kazuyuki

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Y1 - 2002/4

N2 - In the previous 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 associated with a plastic deformation rate is derived as a flow rule in which a dissipation function plays the role of plastic potential. Material moduli in this equation, however, are still not expressed as functions of hardening law. In this paper, the constitutive equation is newly generalized into corner theory which permits an existence of a vertex on dissipation surface. A non-coaxial angle of a plastic deformation rate is related to the non-coaxial angle of a stress rate by use of strain rate sensitivity. Furthermore, a finite element analysis is carried out for a plane strain tension of homopolymer. Some remarkable numerical results of strain localization for homopolymer are discussed in detail.

AB - In the previous 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 associated with a plastic deformation rate is derived as a flow rule in which a dissipation function plays the role of plastic potential. Material moduli in this equation, however, are still not expressed as functions of hardening law. In this paper, the constitutive equation is newly generalized into corner theory which permits an existence of a vertex on dissipation surface. A non-coaxial angle of a plastic deformation rate is related to the non-coaxial angle of a stress rate by use of strain rate sensitivity. Furthermore, a finite element analysis is carried out for a plane strain tension of homopolymer. Some remarkable numerical results of strain localization for homopolymer are discussed in detail.

KW - Constitutive equation

KW - Finite element method

KW - High polymer materials

KW - Large deformation

KW - Non-coaxiality

KW - Plasticity

KW - Shear band

KW - Vertex

KW - Viscoplasticity

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