Machine learning-based constitutive modelling for material non-linearity: A review

Machine learning (ML) models are widely used across numerous scientific and engineering disciplines due to their exceptional performance, flexibility, prediction quality, and ability to handle highly complex problems if appropriate data are available. One example of such areas which has attracted a lot of attentions in the last couple of years is the integration of data-driven approaches in material modeling. There has been several successful researches in implementing ML-based constitutive models instead of classical phenomenological models for various materials, particularly those with non-linear mechanical behaviors. This review paper aims to systematically investigate the literature on ML-based constitutive models for materials and classify these models based on their suitability for material non-linearity including Non-linear elasticity (hyperelasticity), plasticity, visco-elasticity, and visco-plasticity. Furthermore, we also reviewed and compared the ML-based approaches that have been applied for architectured materials as these groups of materials are designed to represent specific material behaviors that might not exist in classical and conventional material categories. The other goal of this review paper is to provide initial steps in understanding of various ML-based approaches for material modeling, including artificial neural networks (ANN), Gaussian processes, random forests (RF), generated adversarial networks (GANs), support vector machines (SVM), different regression models and physics-informed neural networks (PINN). This paper also outlines different data collection methods, types of data, data processing approaches, the theoretical background of the ML models, advantage and limitations of various models, and potential future research directions. This comprehensive review will provide researchers with the knowledge necessary to develop high-fidelity, robust, adaptable, flexible, and accurate data-driven constitutive models for advanced materials.