Physics-based data-driven modeling of composite materials and structures through machine learning
Composite materials have been successfully applied in various industries, such as aerospace, automobile, and wind turbines, etc. Although the material properties of composites are desirable, the behaviors of composites are complicated. Many efforts have been made to model the constitutive behavior and failure of composites, but a complete and validated methodology has not been completely achieved yet. Recently, machine learning techniques have attracted many researchers from the mechanics field, who are seeking to construct surrogate models with machine learning, such as deep neural networks (DNN), to improve the computational speed or employ machine learning to discover unknown governing laws to improve the accuracy. Currently, the majority of studies mainly focus on improving computational speed. Few works focus on applying machine learning to discover unknown governing laws from experimental data. In this study, we will demonstrate the implementation of machine learning to discover unknown governing laws of composites. Additionally, we will also present an application of machine learning to accelerate the design optimization of a composite rotor blade.
To enable the machine learning model to discover constitutive laws directly from experimental data, we proposed a framework to couple finite element (FE) with DNN to form a fully coupled mechanics system FE-DNN. The proposed framework enables data communication between FE and DNN, which takes advantage of the powerful learning ability of DNN and the versatile problem-solving ability of FE. To implement the framework to composites, we introduced positive definite deep neural network (PDNN) to the framework to form FE-PDNN, which solves the convergence robustness issue of learning the constitutive law of a severely damaged material. In addition, the lamination theory is introduced to the FE-PDNN mechanics system to enable FE-PDNN to discover the lamina constitutive law based on the structural level responses.
We also developed a framework that combines sparse regression with compressed sensing, which leveraging advances in sparsity techniques and machine learning, to discover the failure criterion of composites from experimental data. One advantage of the proposed approach is that this framework does not need Bigdata to train the model. This feature satisfies the current failure data size constraint. Unlike the traditional curve fitting techniques, which results in a solution with nonzero coefficients in all the candidate functions. This framework can identify the most significant features that govern the dataset. Besides, we have conducted a comparison between sparse regression and DNN to show the superiority of sparse regression under limited dataset. Additionally, we used an optimization approach to enforce a constraint to the discovered criterion so that the predicted data to be more conservative than the experimental data. This modification can yield a conservative failure criterion to satisfy the design needs.
Finally, we demonstrated employing machine learning to accelerate the planform design of a composite rotor blade with strength consideration. The composite rotor blade planform design focuses on optimizing planform parameters to achieve higher performance. However, the strength of the material is rarely considered in the planform design, as the physic-based strength analysis is expensive since millions of load cases can be accumulated during the optimization. Ignoring strength analysis may result in the blade working in an unsafe or low safety factor region since composite materials are anisotropic and susceptible to failure. To reduce the computational cost of the blade cross-section strength analysis, we proposed to construct a surrogate model using the artificial neural network (ANN) for beam level failure criterion to replace the physics-based strength analysis. The surrogate model is constructed based on the Timoshenko beam model, where the mapping is between blade loads and the strength ratios of the cross-section. The results showed that the surrogate model constraint using machine learning can achieve the same accuracy as the physics-based simulation while the computing time is significantly reduced.