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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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.
In: Mechanics of Time-Dependent Materials, Vol. 1, No. 3, 1998, p. 269-291.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 -