This paper investigates the optimization of 2D and 3D composite structures
using machine learning (ML) techniques, focusing on fracture toughness and
crack propagation in the Double Cantilever Beam (DCB) test. By exploring the
intricate relationship between microstructural arrangements and macroscopic
properties of composites, the study demonstrates the potential of ML as a
powerful tool to expedite the design optimization process, offering notable
advantages over traditional finite element analysis. The research encompasses
four distinct cases, examining crack propagation and fracture toughness in both
2D and 3D composite models. Through the application of ML algorithms, the study
showcases the capability for rapid and accurate exploration of vast design
spaces in composite materials. The findings highlight the efficiency of ML in
predicting mechanical behaviors with limited training data, paving the way for
broader applications in composite design and optimization. This work
contributes to advancing the understanding of ML's role in enhancing the
efficiency of composite material design processes.

通过机器学习技术优化 2D 和 3D 复合结构，研究断裂韧性和裂纹扩展在双悬臂梁（DCB）试验中的应用，揭示微观结构排列与复合材料宏观性能之间的复杂关系，证明了机器学习作为强大工具在设计优化过程中的潜力，相较于传统有限元分析具有明显优势。研究包含四个不同案例，分别检查 2D 和 3D 复合模型中的裂纹扩展和断裂韧性。通过应用机器学习算法，研究展示了在复合材料设计中对庞大设计空间进行快速准确探索的能力。研究结果强调了机器学习在有限训练数据下预测机械行为的效率，为复合材料设计和优化的广泛应用铺平了道路。该研究对提高复合材料设计过程中机器学习的效率做出了贡献。

基于机器学习进行优化断裂韧性的复合材料设计

Composite Material Design for Optimized Fracture Toughness Using Machine  Learning

In this study, a novel approach that combines the principles of peridynamic
(PD) theory with PINN is presented to predict quasi-static damage and crack
propagation in brittle materials. To achieve high prediction accuracy and
convergence rate, the linearized PD governing equation is enforced in the
PINN's residual-based loss function. The proposed PD-INN is able to learn and
capture intricate displacement patterns associated with different geometrical
parameters, such as pre-crack position and length. Several enhancements like
cyclical annealing schedule and deformation gradient aware optimization
technique are proposed to ensure the model would not get stuck in its trivial
solution. The model's performance assessment is conducted by monitoring the
behavior of loss function throughout the training process. The PD-INN
predictions are also validated through several benchmark cases with the results
obtained from high-fidelity techniques such as PD direct numerical method and
Extended-Finite Element Method. Our results show the ability of the nonlocal
PD-INN to predict damage and crack propagation accurately and efficiently.

本研究提出了一种将弹性力学理论与 PINN 相结合的新方法，用于预测脆性材料中的准静态损伤和裂纹传播。通过将线性化的弹性力学方程强制加到 PINN 的基于残差的损失函数中，实现了高预测准确性和收敛速率。通过监测训练过程中损失函数的行为，对所提出的 PD-INN 模型的性能进行评估，并通过与 PD 直接数值方法和扩展有限元方法获得的结果进行验证。我们的结果表明，这种非局部 PDINN 能够准确高效地预测损伤和裂纹的传播。