Machine Learning in the Modeling of Composite Materials and Structures: A Review

Machine learning is increasingly used in many engineering fields thanks to the widespread digital data, growing computing power, and advanced algorithms. Although many machine learning models have been used in the modeling of composite materials and structures, there are still some unsolved issues that hinders the acceptance of machine learning models in the practical design and analysis of composite materials and structures. Moreover, the emerging machine learning techniques are posting new challenges in the data-based design paradigm. This presentation aims to give a state-of-art literature review of the machine learning methods (especially neural networks) in the nonlinear constitutive modeling, multiscale surrogate modeling, and uncertainty quantification and design optimization of composite materials and structures. This review has been designed to focus on the discussion of the benefits of machine learning methods to the above problems. Moreover, challenges and opportunities in each key problem are identified and discussed. This presentation is expected to open the discussion of future research scope and new directions to enable efficient, robust, and accurate data-driven modeling of composite materials and structures.

With the increasing complexity of the microstructures in advanced heterogeneous materials, the nonlinear mechanisms are becoming more and more complex, which cannot be fully captured by the existing physical laws. Machine learning models provide an alternative to discover the unknown physics or mechanisms missing in the physics-based constitutive laws. For the multiscale modeling problems, researchers try to directly link the homogenized behavior at the macroscale to the corresponding microstructure. A sub-scale modeling, either at microscale or mesoscale, is required for each integration point at the macroscale. In general, such expensive computations are not practical for the real engineering design and analysis. Machine learning models can be used to construct surrogate models to replace the expensive simulations. In addition to developing nonlinear constitutive models and performing multiscale modeling, uncertainty quantification and design optimization is another challenging and important topic in modeling composite materials and structures. This challenge is also implicitly connected to the aforementioned two challenges. For the design optimization of composite materials, a key problem is to explore a huge design space in an efficient way as there are often a number of design parameters across different scales. For the uncertainty quantification problems, part of the uncertainties comes from the model form such as the constitutive models.

The machine learning used in the modeling of composites can be categorized by the training data -- whether the data is produced to inform the models or by the physical models. The data in the first scenario often comes from experiments and machine learning models are used to describe phenomena in complex systems where we do not yet have a good physical understanding. Learning unknown constitutive models is a typical application of this kind of machine learning models. The data in the second scenario usually comes from computer simulations where we have established physical models and machine learning is to provide an efficient tool to replace the expensive simulations and to interpret large scale computed data. Constructing surrogate models to accelerate multiscale modeling is a typical application of this kind of machine learning models. Although most recent works are focused on neural networks especially deep learning neural networks, other machine learning methods used in the modeling of composite materials and structures in recent years are also reviewed and discussed.