Mechanics-related tasks often present unique challenges in achieving accurate geometric and physical representations, particularly for non-uniform structures. Graph neural networks (GNNs) have emerged as a promising tool to tackle these challenges by adeptly learning from graph data with irregular underlying structures. Consequently, recent years have witnessed a surge in complex mechanics-related applications inspired by the advancements of GNNs. Despite this process, there is a notable absence of a systematic review addressing the recent advancement of GNNs in solving mechanics-related tasks. To bridge this gap, this review article aims to provide an in-depth overview of the GNN applications in mechanics-related domains while identifying key challenges and outlining potential future research directions. In this review article, we begin by introducing the fundamental algorithms of GNNs that are widely employed in mechanics-related applications. We provide a concise explanation of their underlying principles to establish a solid understanding that will serve as a basis for exploring the applications of GNNs in mechanics-related domains. The scope of this paper is intended to cover the categorisation of literature into solid mechanics, fluid mechanics, and interdisciplinary mechanics-related domains, providing a comprehensive summary of graph representation methodologies, GNN architectures, and further discussions in their respective subdomains. Additionally, open data and source codes relevant to these applications are summarised for the convenience of future researchers. This article promotes an interdisciplinary integration of GNNs and mechanics and provides a guide for researchers interested in applying GNNs to solve complex mechanics-related tasks.

Conventional experimental approaches used to generate forming limit diagrams (FLDs) for sheet metals at different linear strain paths are not applicable to hot stamping and cold die quenching processes because cooling occurs prior to deformation and consistent values of heating rate, cooling rate, deformation temperature and strain rate are not easy to obtain. A novel biaxial testing system for use in a Gleeble testing machine has been adopted to generate forming limits of sheet metals, including aluminium alloys, magnesium alloys and boron steel, under practical hot stamping conditions in which heating and cooling occur. For example, the soaking temperature is about 900 °C and the deformation temperature range is 550–850 °C for boron steel [1] and the soaking temperature is about 535 °C and the deformation temperature range is 370–510 °C for AA6082 [2]. Resistance heating and air cooling were introduced in this pioneering system and the thermal analysis of different heating and cooling strategies was investigated based on a type of cruciform specimen. FE models with a UAMP subroutine were used to predict temperature fields on a specimen in ABAQUS 6.12. Digital image correlation (DIC) system was used to record strain fields of a specimen by capturing images throughout the deformation history and its post-processing software ARAMIS was used to determine forming limits according to ISO standards embedded in the software. Heating and cooling strategies were determined after the analysis. Preliminary results of forming limit curves at the designated temperatures are presented in order to verify the feasibility of this new method.

In design for forming, it is becoming increasingly significant to develop surrogate models of high-fidelity finite element analysis (FEA) simulations of forming processes to achieve effective component feasibility assessment as well as process and component optimizations. However, surrogate models using traditional scalar-based machine learning methods (SBMLMs) fall short on accuracy and generalizability. This is because SBMLMs fail to harness the location information available from the simulations. To overcome this shortcoming, the theoretical feasibility and practical advantages of innovatively applying image-based machine learning methods (IBMLMs) in developing surrogate models of sheet stamp forming simulations are explored in this study. To demonstrate the advantages of IBMLMs, the effect of the location information on both design variables and simulated physical fields is first proposed and analyzed. Based on a sheet steel stamping case study, a Res-SE-U-Net IBMLM surrogate model of stamping simulations is then developed and compared with a baseline multilayer perceptron (MLP) SBMLM surrogate model. The results show that the IBMLM model is advantageous over the MLP SBMLM model in accuracy, generalizability, robustness, and informativeness. This article presents a promising methodology in leveraging IBMLMs as surrogate models to make maximum use of information from stamp forming FEA results. Future prospective studies that are inspired by this article are also discussed.