用记忆学习聚合物流动的本构关系

Naoki Seryo, Takeshi Sato, J. J. Molina, T. Taniguchi
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引用次数: 5

摘要

我们开发了一种学习策略来推断具有记忆的聚合物流应力的本构关系。我们对本构关系的函数形式不作任何假设,除了它们应该以微分形式表示为局部应力和应变率张量的函数。特别是,我们使用高斯过程回归从小规模(固定应变率)微观聚合物模拟产生的应力轨迹推断本构关系。为简单起见,我们使用Hookean哑铃表示作为微观模型,但该方法本身可以推广到更现实的描述。然后使用所学的本构关系进行宏观流动模拟,使我们能够以一种解释微观聚合物动力学的方式更新流体中的应力分布。利用学习到的本构关系得到的结果与微观/宏观自由度直接耦合的全多尺度模拟结果以及麦克斯韦本构关系给出的精确解析解非常吻合。我们能够完全捕捉到流动的历史依赖,以及流体中的弹性效应。我们希望提出的学习/模拟方法不仅可以用于研究纠缠聚合物流动的动力学,还可以用于研究具有类似长度和时间尺度层次结构的其他软物质系统的复杂动力学。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Learning the constitutive relation of polymeric flows with memory
We develop a learning strategy to infer the constitutive relation for the stress of polymeric flows with memory. We make no assumptions regarding the functional form of the constitutive relations, except that they should be expressible in differential form as a function of the local stress- and strain-rate tensors. In particular, we use a Gaussian Process regression to infer the constitutive relations from stress trajectories generated from small-scale (fixed strain-rate) microscopic polymer simulations. For simplicity, a Hookean dumbbell representation is used as a microscopic model, but the method itself can be generalized to incorporate more realistic descriptions. The learned constitutive relation is then used to perform macroscopic flow simulations, allowing us to update the stress distribution in the fluid in a manner that accounts for the microscopic polymer dynamics. The results using the learned constitutive relation are in excellent agreement with full Multi-Scale Simulations, which directly couple micro/macro degrees of freedom, as well as the exact analytical solution given by the Maxwell constitutive relation. We are able to fully capture the history dependence of the flow, as well as the elastic effects in the fluid. We expect the proposed learning/simulation approach to be used not only to study the dynamics of entangled polymer flows, but also for the complex dynamics of other Soft Matter systems, which possess a similar hierarchy of length- and time-scales.
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