A novel boundary-based machine learning approach for 2D crack analysis in elastic and piezoelectric materials
Peijun Zhang, Yan Gu, Longtao Xie, Okyay Altay, Chuanzeng Zhang, В. А. Бабешко
Abstract
In this study, we propose a novel boundary-based machine learning (BBML) approach for analyzing two-dimensional (2D) in-plane crack problems in linear elastic and piezoelectric materials. The proposed approach integrates a machine learning (ML) method based on artificial neural networks (NNs) with the boundary integral equations (BIEs), enabling an efficient and accurate evaluation of the characteristic fracture mechanics parameters. To capture the local asymptotic behavior of the crack-tip field, novel special crack-tip elements based on NNs (CTNNs) are developed to improve the modeling accuracy of the electromechanical fields in close neighboring regions near the crack-tips. These special CTNNs integrate the local asymptotic characteristics of the crack-tip fields into the neural network framework, ensuring an enhanced accuracy in capturing the intricate stress singularities and high deformation gradients near the crack-tips. Compared to the conventional simulation tools in fracture mechanics, the present BBML approach offers several distinct advantages. Firstly, by embedding higher-order terms of the asymptotic crack-tip field into the neural networks, the method achieves a more accurate and reliable representation of the near-tip fields, even by using relatively large crack-tip elements. Secondly, the CTNNs incorporate important information about the varying near-tip singularity orders, and thus improve the versatility and robustness of the method for solving crack problems involving complex and diverse crack-tip geometries. Moreover, compared to the domain-based ML (DBML) approach, the proposed novel BBML method demonstrates an excellent computational efficiency due to the dimensionality reduction achieved by utilizing the analytical BIEs. Numerical examples confirm that the proposed novel BBML approach can serve as a reliable, robust and accurate numerical simulation tool for addressing 2D linear elastic and piezoelectric fracture mechanics problems, offering several substantial advantages over diverse conventional numerical approaches.