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用基于管子理论发展的XPP(extended Pom-Pom)模型描述支化高分子熔体——低密度聚乙烯(LDPE)的分子流变特性,实现了从分子微观结构到宏观响应的跨尺度模拟.引入有限增量微积分(FIC)过程重构了压力稳定质量守恒方程以克服因流体不可压缩性引发的压力场空间分布虚假振荡现象.采用离散的弹性——黏性应力分裂技术(DEVSS)以在缺失纯黏性项情况下保持动量方程弱形式中的椭圆项贡献.利用迎风流线(SU)方法离散黏弹性XPP本构方程中的对流项,以基于Crank-Nicolson隐式差分格式的迭代稳定分步算法求解质量、动量守恒方程和本构方程.采用等低阶有限元模拟了平面黏弹性收缩流,考察了不同Weissenberg数、支化程度和分子结构参数对Pom-Pom分子在收缩流场中流变行为的影响,数值结果与相关文献和试验结果吻合得较好.
The molecular rheological properties of branched polymer melt-low density polyethylene (LDPE) were described by the XPP (extended Pom-Pom) model developed based on the tube theory and the cross-scale simulation from molecular microstructure to macroscopic response was realized. The finite-integral calculus (FIC) process was introduced to reconstruct the pressure-stable mass conservation equation to overcome the spatiotemporal vibrational distribution of the pressure field caused by the incompressibility of fluid.Discrete elastic-viscous stress-splitting (DEVSS) In the absence of purely viscous term, the contribution of the elliptic term in the weak form of the momentum equation is preserved. The convection term in the viscoelastic XPP constitutive equation is discretized by the upwind streamline (SU) method and the iteration based on the Crank-Nicolson implicit difference scheme Stable step-by-step algorithm is used to solve the mass and momentum conservation equations and the constitutive equations. The viscoelastic shrinkage flow is modeled by the lower-order finite element method. The effects of different Weissenberg number, degree of branching and molecular structure parameters on the contraction flow Field rheological behavior, the numerical results and the relevant literature and test results in good agreement.