### Abstract

Original language | English |
---|---|

Pages (from-to) | 269-291 |

Journal | Mechanics of Time-Dependent Materials |

Volume | 1 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1998 |

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*Mechanics of Time-Dependent Materials*,

*1*(3), 269-291. https://doi.org/10.1023/A:1009720708029

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*Mechanics of Time-Dependent Materials*, vol. 1, no. 3, pp. 269-291. https://doi.org/10.1023/A:1009720708029

**A constitutive equation for the elasto-viscoplastic deformation of glassy polymers.** / Tervoort, T.A.; Smit, R.J.M.; Brekelmans, W.A.M.; Govaert, L.E.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - A constitutive equation for the elasto-viscoplastic deformation of glassy polymers

AU - Tervoort, T.A.

AU - Smit, R.J.M.

AU - Brekelmans, W.A.M.

AU - Govaert, L.E.

PY - 1998

Y1 - 1998

N2 - Abstract Constitutive equations for finite elastic-plastic deformation of polymers and metals are usually formulated by assuming an isotropic relation between the Jaumann rate of the Cauchy-stress tensor and the strain-ratetensor. However, the Jaumann-stress rate is known to display spuriousnon-physical behaviour in the elastic region. Replacing the Jaumann-stress rate by a Truesdell-stress rate results in an adequate description in the elastic region, but gives rise to a volume decrease during plastic flow intensile deformation. In this paper a ’’compressible-Leonov model‘‘ is introduced, in which the elastic volume response is rigorously separated from the elasto-viscoplastic isochoric deformation. This has the advantage that the model can be extended in a straightforward way to include aspectrum of relaxation times. It is shown that in the limit of small elastic strains, the compressible Leonov model reduces to the Jaumann-stress rate model, but diverges from the Truesdell-stress rate model. Finally, a comparison is made of the above mentioned models in ahomogeneous uniaxial tensile test and a homogeneous plane-stress sheartest, using polycarbonate (PC) as a model system. All models considered in this paper are ’’single mode‘‘ models (i.e. one relaxation time), and, therefore, cannot describe the full (non)linear viscoelastic region, northe strain-hardening or strain-softening response.

AB - Abstract Constitutive equations for finite elastic-plastic deformation of polymers and metals are usually formulated by assuming an isotropic relation between the Jaumann rate of the Cauchy-stress tensor and the strain-ratetensor. However, the Jaumann-stress rate is known to display spuriousnon-physical behaviour in the elastic region. Replacing the Jaumann-stress rate by a Truesdell-stress rate results in an adequate description in the elastic region, but gives rise to a volume decrease during plastic flow intensile deformation. In this paper a ’’compressible-Leonov model‘‘ is introduced, in which the elastic volume response is rigorously separated from the elasto-viscoplastic isochoric deformation. This has the advantage that the model can be extended in a straightforward way to include aspectrum of relaxation times. It is shown that in the limit of small elastic strains, the compressible Leonov model reduces to the Jaumann-stress rate model, but diverges from the Truesdell-stress rate model. Finally, a comparison is made of the above mentioned models in ahomogeneous uniaxial tensile test and a homogeneous plane-stress sheartest, using polycarbonate (PC) as a model system. All models considered in this paper are ’’single mode‘‘ models (i.e. one relaxation time), and, therefore, cannot describe the full (non)linear viscoelastic region, northe strain-hardening or strain-softening response.

U2 - 10.1023/A:1009720708029

DO - 10.1023/A:1009720708029

M3 - Article

VL - 1

SP - 269

EP - 291

JO - Mechanics of Time-Dependent Materials

JF - Mechanics of Time-Dependent Materials

SN - 1385-2000

IS - 3

ER -