在自然界和诸多工程应用领域中存在着多种多样的非均质材料。对其本构关系和强度的研究，是固体力学的核心课题之一，不仅能够对材料在技术和工程领域的应用提供指导，还可以加速新型复合材料的设计与开发。为了应对非均质材料复杂性带来的巨大挑战，本文基于人工智能理论，利用深度学习方法，对非均质材料的弹性本构关系和断裂强度进行了研究，并探究了复合材料性能的组合优化设计问题。首先，研究了表面微结构对固体材料弹性行为的影响。通过特征工程，以图像的形式描述了固体表面微结构的几何与力学属性。基于深度学习方法，提出了能够准确有效地预测材料表面弹性属性的卷积神经网络。其次，研究了具有复杂微观结构的复合材料的宏观弹性性质和其组分弹性性质以及微观结构之间的关系。基于深度学习方法，提出了能够准确有效地预测包含任意数量、大小、形状和性质的夹杂的复合材料的力学性能的卷积神经网络。针对复合材料反问题，提出了能够从复合材料的微观结构和宏观有效弹性性质中反演各组成成分力学性质的双端输入的深度学习模型。研究了深度学习模型的结构对提取性能的影响和模型的泛化能力。然后，研究了含微裂纹脆性材料的临界断裂失效行为。通过Kachanov方法，构建了在不同远场载荷作用下的二维含微裂纹脆性试样以及相应临界载荷因子的数据集。提出了可以基于远场载荷和脆性材料的微裂纹分布来准确有效地预测材料的临界载荷因子的深度神经网络模型。接下来，研究了珍珠母砖泥结构的微观特征和宏观力学性能之间的关系。提出了可以有效地发现珍珠母砖泥结构的尺寸和界面强度与力学性能之间关系的全连接神经网络。借助特征工程，提出了能够充分利用砖泥结构胞元之间空间位置关系的卷积神经网络。基于该卷积神经网络，研究了珍珠母砖泥结构的尺寸效应。最后，研究了二维复合材料多种力学性能的组合优化设计问题。基于裂纹相场法，模拟了复合材料I型断裂过程。基于深度学习方法，提出了能够准确高效地根据复合材料的几何结构预测其强度和韧性的卷积神经网络模型。将遗传算法和卷积神经网络相结合，研究了复合材料的强度和韧性的组合优化设计问题。

There are a wide variety of heterogeneous materials that exist in nature and many engineering application fields. The prediction of constitutive relation and strength of heterogeneous materials is one of the core topics of solid mechanice, which can not only provide guidance for the application of materials in the field of technology and engineering, but also accelerate the design and development of new composite materials. In order to deal with the great challenges brought by the complexity of heterogeneous materials, in this dissertation, we have proposed a series of deep learning methods based on the artificial intelligence theory to study the elastic constitutive relation and fracture strength of heterogeneous materials and explore the combinational optimization design of composite materials.Firstly, the effect of surface microstructures on the elastic properties of solid materials is investigated. The geometric and mechanical properties of surface microstructures are described in the form of images by feature engineering. Based on the deep learning method, a convolutional neural network that can accurately and effectively predict the surface elastic moduli of microstructured solids is proposed.Secondly, the relationship between the macroscopic elastic properties of composites with complex microstructures and the elastic properties and microstructures of their components is studied. Based on the deep learning method, a convolutional neural network that can accurately and efficiently predict the mechanical properties of composites containing inclusions of arbitrary number, size, shape, and properties is proposed. Aiming at the inverse problem of composites, a dual-input deep learning model that can extract the mechanical properties of each component from the microstructures and macroscopic elastic properties of composites is proposed. The influence of the structure of the deep learning model on the extraction performance and the generalization ability of the model are both studied.Then, the critical fracture failure behavior of brittle materials with microcracks is studied. Using the Kachanov method, a dataset of two-dimensional brittle specimens with microcracks and corresponding critical load factors under different far-field loads is constructed. A neural network model that can accurately and efficiently predict the critical load factor of brittle materials based on the far-field load and micro-crack distribution is proposed.Next, the relationship between microstructure characteristics and macroscopic mechanical properties of brick–mortar structure of nacre is studied. A fully connected neural network that can effectively discover the relationship between the structural size and interface strength of brick–mortar structures of the nacre and its mechanical properties is proposed. With the help of feature engineering, a convolutional neural network is proposed that can make full use of the spatial position relations between brick–mortar structures. Based on this convolutional neural network model, the size effect of brick–mortar structure of the nacre is studied.Finally, the combined optimization design problem of multiple mechanical properties of two-dimensional composites is studied. The type I fracture process of composites is simulated by the crack phase-field method. Based on the deep learning method, a convolutional neural network model that can accurately and efficiently predict the strength and toughness of composites from their geometric structures is proposed. Combining genetic algorithm and convolutional neural network model, the combined optimization design problem of strength and toughness of composites is studied.