### 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 language | English |
---|---|

Pages (from-to) | 682-690 |

Number of pages | 9 |

Journal | Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A |

Volume | 68 |

Issue number | 4 |

Publication status | Published - 2002 Apr |

### Fingerprint

### 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

*Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*,

*68*(4), 682-690.

**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).** / Murakami, Daisuke; Kobayashi, Seiichi; Torigaki, Toshikazu; Shizawa, Kazuyuki.

Research output: Contribution to journal › Article

*Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*, vol. 68, no. 4, pp. 682-690.

}

TY - JOUR

T1 - 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)

AU - Murakami, Daisuke

AU - Kobayashi, Seiichi

AU - Torigaki, Toshikazu

AU - Shizawa, Kazuyuki

PY - 2002/4

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

UR - http://www.scopus.com/inward/record.url?scp=2242424511&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2242424511&partnerID=8YFLogxK

M3 - Article

VL - 68

SP - 682

EP - 690

JO - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

JF - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

SN - 0387-5008

IS - 4

ER -