We extend the laminate based framework of direct Deep Material Networks (DMNs) to treat suspensions of rigid fibers in a non-Newtonian solvent. To do so, we derive two-phase homogenization blocks that are capable of treating incompressible fluid phases and infinite material contrast. In particular, we leverage existing results for linear elastic laminates to identify closed form expressions for the linear homogenization functions of two-phase layered emulsions. To treat infinite material contrast, we rely on the repeated layering of two-phase layered emulsions in the form of coated layered materials. We derive necessary and sufficient conditions which ensure that the effective properties of coated layered materials with incompressible phases are non-singular, even if one of the phases is rigid. With the derived homogenization blocks and non-singularity conditions at hand, we present a novel DMN architecture, which we name the Flexible DMN (FDMN) architecture. We build and train FDMNs to predict the effective stress response of shear-thinning fiber suspensions with a Cross-type matrix material. For 31 fiber orientation states, six load cases, and over a wide range of shear rates relevant to engineering processes, the FDMNs achieve validation errors below 4.31% when compared to direct numerical simulations with Fast-Fourier-Transform based computational techniques. Compared to a conventional machine learning approach introduced previously by the consortium of authors, FDMNs offer better accuracy at an increased computational cost for the considered material and flow scenarios.

翻译：本文将基于层合板的直接深度材料网络（DMN）框架扩展至刚性纤维在非牛顿溶剂中的悬浮体系处理。为此，我们推导了能够处理不可压缩流体相与无限材料对比度的两相均质化单元。特别地，我们利用线弹性层合板的现有结果，推导了两相层状乳剂线性均质化函数的闭合表达式。为处理无限材料对比度问题，我们采用以涂层层状材料形式实现的两相层状乳剂重复叠层策略。我们推导了确保含不可压缩相的涂层层状材料等效性质非奇异的充分必要条件，即使其中一相为刚性材料。基于所推导的均质化单元与非奇异性条件，我们提出了一种新型DMN架构，命名为柔性深度材料网络（FDMN）架构。我们构建并训练了FDMN模型，用于预测具有Cross型基体材料的剪切稀化纤维悬浮液的有效应力响应。针对31种纤维取向状态、六种载荷工况，以及在工程工艺相关的宽剪切速率范围内，与基于快速傅里叶变换计算技术的直接数值模拟结果相比，FDMN模型的验证误差低于4.31%。相较于作者团队先前提出的传统机器学习方法，在当前研究的材料与流动场景下，FDMN以更高的计算成本获得了更优的预测精度。