FE/MCT: Macroscopic CFD Simulations of Glass-Forming Fluids using Material Laws from Microscopic Theory

我们发展了玻璃形成流体流动的多尺度描述。为此，我们将计算流体力学（CFD）模拟与微观理论相结合，给出了强粘弹性流体非线性响应的物质规律（本构方程）。利用瞬态积分（ITT）形式导出了广义Green-Kubo关系，该关系将微观相关函数与远离平衡态的粗粒流体应力张量联系起来。将玻璃化转变（MCT）的模式耦合理论与ITT结合使用，提供了一个微观上合理的封闭材料模型。所得的本构方程具有明显的时程积分特征。为了在Navier-Stokes方程的水平上处理这类积分本构方程，实现了先进的有限元方法（FEM）格式，从而能够解决玻璃成型流体流动中明显的瞬态效应和记忆效应。使用这些工具，我们解决了玻璃在施加载荷下的缓慢变形，以及在不同加工条件下制备材料时产生的非晶软物质材料的历史依赖材料特性的出现。

We develop a multi-scale description of the flow of glass-forming fluids. To this end we combine computational fluid dynamics (CFD) simulations with microscopic theory to provide material laws (constitutive equations) of the nonlinear response of the strongly viscoelastic fluid. The integration-through transients (ITT) formalism is used to derive generalized Green-Kubo relations that link microscopic correlation functions to the coarse-grained fluid stress tensor far from equilibrium. The mode-coupling theory of the glass transition (MCT) is used together with ITT to provide a microscopically justified closed material model. The resulting constitutive equations are characterized by pronounced time-history integrals. Advanced Finite Element method (FEM) schemes are realized in order to deal with such integral constitutive equations on the level of the Navier-Stokes equations, to be able to address the pronounced transients and memory effects in the flow of glass-forming fluids. Using these tools, we address the slow deformation of glasses under applied load and the emergence of history-dependent material properties of amorphous soft-matter materials that arise when the material is prepared under different processing conditions.