The thermal conductivity of materials dictates their functionality and reliability, especially for materials with complex microstructural topologies, such as woven composites. In this paper, we develop a physics-informed machine-learning architecture built specifically for solving thermal conductivity problems. Originally developed for mechanical problems, we extend and develop a deep material network (DMN) that incorporates (i) principles from thermal homogenization directly into the network architecture in which nodes propagate heat flux and temperature gradient (as opposed to stress and strain in the original ‘mechanical’ DMN) and (ii) nodal rotations to capture the topological complexity of the materials’ microstructure. The result is a ‘thermal’ DMN better suited for thermal conductivity problems than the ‘mechanical’ deep material network. We demonstrate the ability of this ‘thermal’ DMN to act as an accurate reduced order model with a significantly smaller number of degrees of freedom on two different woven microstructures examples. Our results show that the ‘thermal’ DMN can not only accurately predict the averaged effective thermal conductivity of these complex weaved composite structures but also the distribution of local heat flux and temperature gradients. Based on these performances, we show how this ‘thermal’ DMN can be exercised for rapid uncertainty and sensitivity analyses to assess microstructure effects and variability of the properties of the composite’s constituents, a task that would be otherwise computationally prohibitive with direct numerical simulations. Based on its architecture, the ‘thermal’ DMN opens possibilities for multiscale, multiphysics simulations for a heterogeneous structure, especially when coupled with its mechanical counterpart.

中文翻译：

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解决导热问题的深层材料网络：在编织复合材料中的应用


材料的导热性决定了它们的功能和可靠性，特别是对于具有复杂微观结构拓扑的材料，例如编织复合材料。在本文中，我们开发了一种专门用于解决导热问题的物理信息机器学习架构。最初是为机械问题而开发的，我们扩展和开发了一个深层材料网络 (DMN)，它将 (i) 热均匀化原理直接融入到网络架构中，其中节点传播热通量和温度梯度（与原始材料中的应力和应变相反） “机械”DMN）和（ii）节点旋转以捕获材料微观结构的拓扑复杂性。结果是“热”DMN 比“机械”深层材料网络更适合解决导热问题。我们在两个不同的编织微结构示例中证明了这种“热”DMN 能够充当精确的降阶模型，且自由度数明显较少。我们的结果表明，“热”DMN 不仅可以准确预测这些复杂编织复合结构的平均有效导热系数，还可以准确预测局部热通量和温度梯度的分布。基于这些性能，我们展示了如何运用这种“热”DMN 进行快速不确定性和敏感性分析，以评估复合材料成分的微观结构效应和性能的变异性，否则直接数值模拟的计算量将难以完成这项任务。基于其架构，“热”DMN 为异质结构的多尺度、多物理场模拟提供了可能性，特别是与机械对应物结合时。