1985
DOI: 10.1007/bf01333961
|View full text |Cite
|
Sign up to set email alerts
|

Constitutive relationships for polymeric materials with power-law distributions of relaxation times

Abstract: Abstract:The linear relaxation modulus of polydisperse polymer melts and solutions can often be approximated by a power law, ct -m over some range of time, t. If, in addition, the nonlinear rheology is given by a separable integral equation, with a strain-dependent factor typical of those observed experimentally, then some commonly observed empirical rules and equations can be readily derived as approximations, namely the Cox-Merz relationship between complex viscosity and steady-state shear viscosity, Bersted… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
28
0
1

Year Published

1985
1985
2019
2019

Publication Types

Select...
4
3

Relationship

1
6

Authors

Journals

citations
Cited by 66 publications
(29 citation statements)
references
References 15 publications
0
28
0
1
Order By: Relevance
“…We follow the approach of Larson (1985) who argued that the nonlinear rheology of complex multiscale materials such as polydisperse polymer melts can be described by using a separable equation of the integral K-BKZ type (Bird, Armstrong, and Hassager (1987)). While Larson selected a single powerlaw relaxation kernel, we extend the analysis to relaxation kernels of the Mittag-Leffler kind.…”
Section: B Nonlinear Viscoelasticity and The K-bkz Modelmentioning
confidence: 99%
See 1 more Smart Citation
“…We follow the approach of Larson (1985) who argued that the nonlinear rheology of complex multiscale materials such as polydisperse polymer melts can be described by using a separable equation of the integral K-BKZ type (Bird, Armstrong, and Hassager (1987)). While Larson selected a single powerlaw relaxation kernel, we extend the analysis to relaxation kernels of the Mittag-Leffler kind.…”
Section: B Nonlinear Viscoelasticity and The K-bkz Modelmentioning
confidence: 99%
“…Larson (1985) has previously shown that by using the integral form of the K-BKZ type equation with a simple power-law relaxation kernel and a suitable strain dependent damping function, the nonlinear rheology of polydisperse polymer melts can be accurately predicted.…”
Section: Introductionmentioning
confidence: 99%
“…Elsewhere [1], was shown that for shear, planar elongation, and simple elongation, the steady-state stress (if a steady-state exists), for a separable integral equation with power-law relaxation modulus is proportional to the strain rate raised to the power m. The demonstration above, that in any steady-state flow, the stress is proportional to the characteristic velocity to the power m, suffices to prove that in any homogeneous steady-state flow, the stress must be proportional to the strain rate raised to the power m. Since constitutive equations are frame invarant, relationships derived from them, such as the proportionality between stress and a power of the strain rate, are expected to be frame invariant also. The concept of a steady flow, is, however, frame dependent; a flow that is steady in one frame will not be so in another.…”
Section: Flows Of Constant Strain Historymentioning
confidence: 97%
“…F in the above equation is the gamma function. The absence of a longest relaxation time implies that the existence of a steady-state stress depends on the elasticity measure being Sufficiently soft -that is, it must grow sufficiently slowly with increasing strain -to prevent the portion of the stress associated with the long relaxation times from becoming unbounded [1], therefore allowing convergence of eq. (2).…”
Section: V(m)mentioning
confidence: 99%
See 1 more Smart Citation