Mechanistically informed data-driven modeling of cyclic plasticity via artificial neural networks

Abstract

A mechanistically informed data-driven approach is proposed to simulate the complex plastic behavior of microstructured/homogenized solids subjected to cyclic loading, especially to simulate the Masing effect. Our proposed approach avoids the complicated mathematical construction of an appropriate yield surface, and does not require a large amount of data for training, by virtue of its mechanistic character, which couples the methods and tools of data science to the principles of mechanics. Specifically, a data-processing method is herein advanced to extract specific internal variables that characterize cyclic plastic behavior, which cannot be measured directly via physical experiments. A yield surface, represented by an artificial neural network (ANN), is then trained by stress–strain data and the extracted internal variables. Finally, the ANN is integrated into a finite element computational framework to solve different boundary value problems (BVPs). Results for demonstrative examples are presented, which illustrate the effectiveness and the reliability of the proposed approach for solids containing voids and particles in their microstructure. Compared with direct numerical simulation (DNS), our approach seems to predict the average levels of stress and plastic strain under cyclic loading more efficiently, as well as the regions of strain localization. In addition, results for a homogenized three-dimensional truss structure demonstrate that our approach can accurately describe the evolution of key internal variables. Our mechanistic approach requires much less data than the general pure data-driven methods, which shows a possible computational efficiency compared with the pure data-driven approach. Limitations of our proposed approach are also discussed.