A peridynamic-based machine learning model for one-dimensional and two-dimensional structures

Abstract

With the rapid growth of available data and computing resources, using data-driven models is a potential approach in many scientific disciplines and engineering. However, for complex physical phenomena that have limited data, the data-driven models are lacking robustness and fail to provide good predictions. Theory-guided data science is the recent technology that can take advantage of both physics-driven and data-driven models. This study presents a novel peridynamics-based machine learning model for one-and twodimensional structures. The linear relationships between the displacement of a material point and displacements of its family members and applied forces are obtained for the machine learning model by using linear regression. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The accuracy of the coupled model is verified by considering various examples of a one-dimensional bar and two-dimensional plate. To further demonstrate the capabilities of the coupled model, damage prediction for a plate with a preexisting crack, a two-dimensional representation of a three-point bending test and a plate subjected to dynamic load are simulated.

A physics-guided machine learning model for two-dimensional structures based on ordinary state-based peridynamics

“…  Moreover, it is observed that the obtained coefficients as given in Eq. (A1-A3) for the bondbased machine learning model in this study agree very well with those obtained in [54].…”

“…As given in Section 4, the PD-based ML model is obtained for material points with their 112 surrounding material points. However, for material points that have less than 112 surrounding material points or some broken interactions such as material points near boundary surfaces or near crack surfaces, the developed ML models can produce significant errors [49]. On the other hand, generating training data for these special cases can be very timeconsuming.…”

“…Therefore, in this study, a hybrid approach to couple ML and ordinary state-based peridynamics (OSBPD) models for fracture prediction of 2D structures is presented. Recently, PD based machine learning model is coupled by using bond based PD [49]. However, bond-based PD has limitations on material constants.…”

“…However, bond-based PD has limitations on material constants. As an extension of the previous study in [49], the ordinary state-based PD model is applied for special regions in structures such as near crack surfaces or near boundary areas. Meanwhile, the ML model is used for the remaining regions to reduce the computational cost.…”

Physics‐constrained hierarchical data‐driven modelling framework for complex path‐dependent behaviour of soils

“…FNN-based simulation has since been extended to capture more complex behaviours such as discrete dislocation 14 and fracture. 15 Recurrent neural networks (RNNs) advance FNNs by incorporating time sequence prediction capability and have shown excellent performance in modelling the behaviour of path-dependent materials. [16][17][18] Recently, more versatile data-driven modelling strategies have been tailored to enhance model interpretability and generalisation, such as data-driven multiscale modelling that considers the evolution of microstructural characteristics, [19][20][21][22][23] Bayesian theory based uncertainty modelling [24][25][26] and physicsinformed neural networks that enforce prior knowledge to the neural network as additional constraints for improving robustness.…”