• 폴리머
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• 제25권4호
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• pp.536-544
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• 2001

실험적 사실에 근거하여 고분자 유체의 점탄성 구성방정식에 빈번히 적용되어온 time-strain separability 가설의 타당성을 수학적 안정성 관점에서 분석한다. 안정성 조건으로는 방정식의 빠른 응답과 관련된 Hadamard 안정성과 소산 성질에 의하여 결정되는 소산 안정성이 있으며, asymptotic 분석을 이용한 결과 가설을 따르는 구성방정식은 Hadamard 또는 소산 불안정함이 증명되었다. 응력완화 실험에서 이미 관찰된 짧은 시간영역에서 time-strain separability의 가설이 적용되지 않는다는 사실은 본 결과와 일치한다. 따라서 separability를 구성방정식에 적용하는 것은 수학적 불안정뿐 아니라 열역학적 모순점을 나타내게 되며, 또한 실험에서도 그 타당성의 한계에 주의할 필요가 있다. 더욱이 damping 함수 역시 실제와는 무관한 가상적 값을 제공하므로 damping 함수의 사용은 긴 시간영역에서 응력완화 거동을 기술하기 위한 curve fitting 이상의 의미는 없다 하겠다.

• Korea-Australia Rheology Journal
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• 제14권1호
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• pp.33-45
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• 2002

Recent results obtained for the port-pom model and the constitutive equations with time-strain separability are examined. The time-strain separability in viscoelastic systems Is not a rule derived from fundamental principles but merely a hypothesis based on experimental phenomena, stress relaxation at long times. The violation of separability in the short-time response just after a step strain is also well understood (Archer, 1999). In constitutive modeling, time-strain separability has been extensively employed because of its theoretical simplicity and practical convenience. Here we present a simple analysis that verifies this hypothesis inevitably incurs mathematical inconsistency in the viewpoint of stability. Employing an asymptotic analysis, we show that both differential and integral constitutive equations based on time-strain separability are either Hadamard-type unstable or dissipative unstable. The conclusion drawn in this study is shown to be applicable to the Doi-Edwards model (with independent alignment approximation). Hence, the Hadamardtype instability of the Doi-Edwards model results from the time-strain separability in its formulation, and its remedy may lie in the transition mechanism from Rouse to reptational relaxation supposed by Doi and Edwards. Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the port-pom equations have been derived in the integral/differential form and also in the simplifled differential type by McLeish and carson on the basis of the reptation dynamics with simplifled branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for these constitutive equations. It is proved that the differential model is globally Hadamard stable, and the integral model seems stable, as long as the orientation tensor remains positive definite or the smooth strain history in the flow is previously given. However cautious attention has to be paid when one employs the simplified version of the constitutive equations without arm withdrawal, since neglecting the arm withdrawal immediately yields Hadamard instability. In the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady flow curves, the constitutive equations exhibit severe instability that the solution possesses strong discontinuity at the moment of change of chain dynamics mechanisms.

• 한국유변학회:학술대회논문집
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• 한국유변학회 2000년도 춘계 학술발표회 논문집
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• pp.55-57
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• 2000