聚合物和基底组成的粘接界面广泛地存在于航空航天、汽车工业和电子封装等多个领域。 聚合物和基底之间的界面通常是整个体系中最薄弱的环节， 其在机械载荷作用下的变形与失效行为直接影响服役过程中的可靠性。粘接界面体系的宏观力学行为由其微观结构所决定。 因此， 深入理解粘接界面体系的微观结构与变形机制， 对于粘接界面的力学性能的提高具有重要意义。 本文主要围绕铜-环氧树脂-铜界面体系，研究其在纳米尺度下的拓扑结构特征及其力学性能。 首先，采用分子动力学模拟， 建立了界面体系的纳米尺度模型， 为原子/分子水平的变形失效行为的模拟提供了基础。 然后， 通过图论方法， 将微结构具象化为拓扑结构，量化表征了高交联聚合物界面体系的强度和韧性的主控拓扑特征。 最后， 基于机器学习方法， 分别从拓扑结构和拓扑描述符的角度，建立了粘接界面的微结构与力学性能之间的关联，从而为高性能界面体系设计提供了基础支撑。 主要的研究内容如下：
（1） 采用图论和分子动力学模拟， 研究了拓扑特征对高交联聚合物界面体系的强度和韧性的影响。基于粘接界面的微观结构，提取了主控拓扑特征，包括决定屈服强度的连接度（D）， 以及决定孔洞扩展过程中变形能力的平均节点路径（P） 和承载能力的基础环比例（R）。其中， 平均节点路径及基础环比例共同决定了材料的韧性。 此外，分析了壁面效应对主控拓扑特征的影响。 结果表明，界面屈服强度随着连接度的增加而增加，而韧性则随着平均节点路径和基础环比例的增加而增加。 壁面效应对连接度、 平均节点路径和基础环比例有显著影响。
强的壁面效应导致壁面附近氨基的富集现象以及远离壁面区域交联反应不充分的现象，从而导致较低的连接度和较小的基础环比例，即较低的屈服强度以及孔洞扩展过程中较差的承载能力。随着壁面效应的减弱， 连接度逐渐增加，而平均节点路径和基础环比例呈现出先增加后减小的趋势， 这表明粘接界面韧性存在一个优化的壁面效应。界面强韧主控拓扑特征的量化表征为聚合物-基底粘接界面体系的力学性能调控提供了新的方法。
（2） 采用图卷积网络（GCN） 模型预测了交联聚合物界面体系力学性能，包括屈服强度（σy）、极限强度（σu）、 失效应变（εu） 和韧性（Γ）。 使用表征拓扑结构的图模型作为图卷积网络的输入， 并通过学习图中节点的特征实现图级目标的预测。 结果表明， 所采用的 GCN 模型对力学性能预测的准确率均超过88%。其中， 模型对失效应变和极限强度的预测效果优于韧性和屈服强度。具体而言，图卷积网络模型对失效应变、极限强度、韧性和屈服强度预测的 R2值分别为 0.73、0.64、 0.51 和 0.43。值得注意的是，使用加和聚合器的图卷积网络模型略优于使用均值聚合器的模型。此外， 线性回归算法和全连接神经网络回归算法提供了相似的预测结果。 进一步分析了输入节点特征对预测效果的影响，发现节点的紧密中心性对图卷积网络模型的预测准确性起到关键作用， 对全局力学性能（如失效应变、 极限强度和韧性） 具有更为显著的影响。此外， 模型参数的敏感性分析表明， 适当的超参数可以在不降低预测准确率的前提下， 提高有限数据集的计算效率。 因此， 图卷积网络模型能够有效预测具有复杂拓扑结构的界面体系的力学性能， 为聚合物拓扑结构设计及力学性能提升提供了新的途径。
（3） 提出了度量交联聚合物界面体系拓扑结构的描述符， 并利用机器学习方法探讨了描述符与力学性能之间的关联。描述符包括交联前参数、图论参数、典型拓扑参数和取向序参数。 通过皮尔森相关系数的筛选，排除了高度相关的描述符， 以提高模型的计算效率。 随后， 训练了随机森林回归（RFR）、 梯度增强回归（GBR）、 支持向量机回归（SVR） 和人工神经网络（ANN） 四种机器学习模型， 结果显示人工神经网络模型表现最佳， 其对四个力学性能的预测准确率均超过 89%。 人工神经网络模型对失效应变、 极限强度、 韧性和屈服强度预测的R2 值分别为 0.78， 0.70， 0.55 和 0.53。 与使用拓扑结构作为输入的图卷积网络相比， 采用拓扑描述符作为输入的人工神经网络预测效率更高、 效果更好。 人工神经网络模型对失效应变、 极限强度、 韧性和屈服强度预测的 R2 值分别提高了6.8%、 9.4%、 7.8%和 23.3%。 进一步的研究发现， 人工神经网络模型在预测偏态数据方面具有更好的表现。 此外， Sobol 分析揭示了各描述符对力学性能的影响，并识别出了在不同力学性能预测中的主控描述符，为不同应用场景下界面体系力学性能优化提供了明确了设计对象。

Adhesive interfaces between polymers and substrates widely exist in aerospace structures, automotive industry, and electronic packages. The interface between polymers and substrates is the weakest point in the entire system, and the deformation and failure behavior of the interface under mechanical loadings directly affect the reliability during service. It is known that the macro-behaviors of adhesive interfaces are determined by the microstructures. Thus, understanding the microstructure and deformation mechanisms is important for enhancing the mechanical properties of adhesive interfaces. This dissertation focuses on the microstructural characteristics and mechanical properties of copper-epoxy-copper interfacial systems at the nanoscale. First, A nanoscale model of the interfacial system was established using molecular dynamics (MD) simulation, which provides a basis for the simulation of deformation failure behavior at the atomic/molecular level. Then, the microstructures were visualized as topologies through graph theory methods to quantitatively
characterize the dominant topological features of the strength and toughness of the highly crosslinked polymer interfacial systems. Finally, based on the machine learning approach, the relationship between microstructure and mechanical properties of adhesive interfaces was established from the perspective of topological structures and topological descriptors, respectively, providing a basis for designing high-performance interface systems. The main research content is as follows:
(1) We used graph theory and molecular dynamic simulations to investigate the influence of topological characteristics on the strength and toughness of highly cross-linked polymer interface systems. Based on the microstructure of the adhesive system, we extracted the dominant topological characteristics, including the connectivity degree (D) that determines the yield strength, and the average node-path (P) and the simple cycles proportions (R) that determine the deformability and load-bearing capacity during the void propagation respectively, which co-determine the toughness. The influence of the wall-effect on the dominant topological characteristics was also analyzed. The results showed that the interfacial yield strength increases with the increase of D, while the toughness increases with the increase of P and R. The wall-effect has a significant influence on the dominant topological characteristics. The strong wall-effect causes the enrichment of amino groups near the wall and insufficient cross-linking away from the wall, leading to the lower D and R, i.e. the lower yield strength and load-bearing capacity during the void propagation. With the attenuation of the wall-effect, the D increases gradually, while the P and the R first increase and then decrease, showing an optimized wall-effect for the toughness of the adhesive interface. Quantitative characterization of the dominant topological characteristics of adhesive interfacial strength and toughness, providing a new way to modulate the mechanical properties of polymer adhesive interface systems.
(2) We employed a graph convolutional network (GCN) model to predict the mechanical properties of a specific cross-linked polymer interfacial system, including yield strength (σy), ultimate strength (σu), failure strain (εu), and toughness (Γ) utilizing molecular dynamics simulations. The graph model representing the topology was used as input to the GCN model, which achieves graph-level predictions by learning node features. The results showed that the adopted GCN model can predict the mechanical properties with over 88% accuracy. The prediction performances for εu
and σu are better than those for Γ and σy, with R2 ~ 0.73 for εu, R2 ~ 0.64 for σu, R2 ~ 0.51 for Γ, and R2 ~ 0.43 for σy. It is worth noting that the GCN model with the sum aggregator slightly outperforms that with the mean aggregator, and that models with linear regression and fully connected neural network regression provide similar predictions. Furthermore, the influence of input node features on prediction performance was also investigated. It was observed that the node closeness centrality is an important graph parameter in prediction. Specifically, node closeness centrality presents a more significant influence on the global mechanical properties of the adhesive interface, such as εu, σu, and Γ. Additionally, sensitivity analysis demonstrated that appropriate hyperparameters can improve computational efficiency without losing accuracy on a restricted set of data. Therefore, the GCN model can effectively predict the mechanical properties of the adhesive interface with complex topologies, which provides a new way for the design of polymer topologies and the
improvement of mechanical properties.

(3) We proposed some descriptors for measuring the topology of crosslinked polymer interfacial systems and used machine learning methods to investigate the correlation between the descriptors and the mechanical properties. These descriptors included pre-crosslinking parameters, graph theory parameters, typical topology parameters, and orientation order parameters. Highly correlated descriptors were
excluded through Pearson correlation coefficient screening to improve the
computational efficiency of the model. Four machine learning models, namely, random forest regression (RFR), gradient boosting regression (GBR), support vector regression (SVR), and artificial neural network (ANN), were trained. It was observed that the ANN model has the best performance with a prediction accuracy of more than 89% for all four mechanical properties. Specifically, the R2 values for εu, σu, Γ, and σy predicted by the ANN model were 0.78, 0.70, 0.55, and 0.53, respectively. Compared to the GCN that used graph models as inputs, the ANN model with topological descriptors as inputs had better performance in terms of both prediction efficiency and effectiveness. Specifically, the ANN model improved the R2 values for εu, σu, Γ, and σy by 6.8%, 9.4%, 7.8%, and 23.3%, respectively. Further studies showed that the ANN model performs better in predicting data with skewed distributions. In addition，Sobol analysis revealed the influence of different topological descriptors on each
mechanical property and identified the topological descriptors that contribute the most to different mechanical properties, which provides a clear design object for the optimization of the mechanical properties of the interface system in different application scenarios.