Hydrodynamic reinforcement in filled polymer systems: numerical simulations and non-linear modeling

本项目的目的是开发一种分析应力和应变放大方法(SSAA)来描述聚合物熔体和网络中的非线性力学响应，这些网络中含有球形和非等距刚性夹杂物，直到中等填充量。当(最小)颗粒尺寸超过聚合物链或链的平均端到端距离时，SSAA在连续体极限内有效。SSAA的一个重要特征是，它通过不聚集的填料颗粒实现纯流体增强，这些颗粒不会与周围的聚合物链和彼此相互吸引或排斥地相互作用。因此，SSAA未来应该能够使流体动力增强效果与其他增强效果明确分开，例如由于存在填料团聚/网络或由于填充聚合物熔体表面的链条局部化而产生的其他增强效果。在填充聚合物熔体的情况下，已经应用于Bird-Carreau模型的稀释极限的SSAA将进一步发展，以适应更高的颗粒体积分数和不同的颗粒长宽比。计划考虑定常剪切流和拉伸流。在填充弹性体的情况下，SSAA将被开发为一些复杂的非线性本构模型，例如用于橡胶弹性的Neo-Hooke模型、Mooney-Rivlin模型和扩展管模型。将流体动力放大系数分离为应力和应变放大系数将通过将解析修正的本构方程的预测与数值均匀化的结果进行直接比较来完成。

The aim of the present project is to develop an analytical stress and strain amplification approach (SSAA) for the description of the non-linear mechanical response in polymer melts and networks containing spherical and anisometric rigid inclusions up to moderate filler loadings. The SSAA is valid in a continuum limit, when the (smallest) size of particles exceeds the average end-to-end distance of polymer chains or strands. An important feature of the SSAA is that it accounts for pure hydrodynamic reinforcement by non-aggregating filler particles which do not interact attractively or repulsively with surrounding polymer chains and each other. Hence, the SSAA should enable in future a clear separation between the effect of hydrodynamic reinforcement and other reinforcement effects arising for example due to the presence of filler agglomerates / network or due to the chain localization on the filler surface.In the case of filled polymer melts, the SSAA which has already been applied to the Bird-Carreau model in the dilute limit, will be further developed for higher volume fractions of particles and different particle aspect ratios. It is planned to consider stationary shear and elongational flows. In the case of filled elastomers, the SSAA will be developed for a number of non-linear constitutive models with increasing complexity such as the Neo-Hooke model, the Mooney-Rivlin model and the extended tube-model for rubber elasticity. The separation of the hydrodynamic amplification factor into the stress and strain amplification factors will be done by direct comparison between predictions of an analytically modified constitutive equation with results from numerical homogenisation.