Guangyan Liu

Physics‐informed neural networks (PINNs) have emerged as a promising approach for solving a wide range of numerical problems. Nevertheless, conventional PINNs frequently face challenges in model convergence and stability when optimizing complex loss functions containing complex gradients. In this study, a new mesh‐based PINN method, called M‐PINN, is proposed drawing the ideas of the finite element method (FEM). By partitioning the solution domain into several subdomains and incorporating finite element data distribution constraints to the prior estimates of the predicted data distribution of PINN on the solution domain, the M‐PINN approach effectively reduces the optimization difficulty of conventional PINNs. Moreover, it is sometimes difficult to directly obtain precise boundary conditions in some practical applications. This method can be used to solve PINN problems with unknown boundary conditions, thus having wider applicability. In this study, the efficiency of M‐PINN was demonstrated through a standard 2D linear elastic solid mechanics simulation experiment, and its applicability was investigated in depth. The results indicate that the M‐PINN method outperforms traditional PINN and exhibits superior applicability and convergence, especially in cases involving unknown boundary conditions.

Graphite materials serve critical roles as moderators, reflectors and core structural components in high-temperature gas-cooled nuclear reactors. These materials may experience a variety of loads during the reactor operation, including thermal, radiation, fatigue and dynamic loads, potentially leading to crack initiation and propagation. Consequently, it is imperative to investigate the fracture properties of graphite materials. Currently, there exists a dearth of comprehensive studies on the fracture toughness of graphite materials with varying grain sizes, especially regarding dynamic fracture toughness. This study introduces a novel approach utilizing a digital-image-correlation-based virtual extensometer to analyze crack propagation in graphite materials of varying grain sizes. This methodology allows for precise measurement of crack propagation lengths and accurate determination of fracture toughness. Results indicate that static fracture toughness demonstrates an upward trend with increasing grain size of graphite materials. In contrast, under equivalent impact velocities, larger-grain graphite materials exhibit reduced dynamic fracture toughness. Notably, dynamic fracture toughness of the three graphite material types studied shows an increment as the impact velocity increases. The ex-amination of fractured specimen surfaces through scanning electron microscopy provides in-sights into the mechanisms underlying the substantial difference between dynamic and static fracture toughness. The results suggest that heightened impact velocity triggers a transition in fracture mode from intergranular to transgranular fracture, allowing specimens to absorb more energy. This phenomenon significantly enhances dynamic fracture toughness relative to static fracture toughness.

Digital image correlation (DIC) is a widely used photomechanical method for measuring surface deformation of materials. Practical engineering applications of DIC often encounter challenges such as discontinuous deformation fields, noise interference, and difficulties in measuring boundary deformations. To address these challenges, a new, to the best of our knowledge, DIC method called MCNN-DIC is proposed in this study by incorporating mechanical constraints using neural network technology. The proposed method applied compatibility equation constraints to the measured deformation field through a semi-supervised learning approach, thus making it more physical. The effectiveness of the proposed MCNN-DIC method was demonstrated through simulated experiments and real deformation fields of nuclear graphite material. The results show that the MCNN-DIC method achieves higher accuracy in measuring non-uniform deformation fields than a traditional mechanical constraints-based DIC and can rapidly measure deformation fields without requiring extensive pre-training of the neural network.

As one typical heterogeneous material, the heterogeneity of rock micro parameters has an important effect on its macro mechanical behavior. The study of the heterogeneity of micro parameters is more important to reveal the root cause of deformation and failure. However, as a typical heterogeneous material, the current testing and inversion method is not suitable for micro parameters measurement for the rock. Aiming at obtaining the distribution of micro Young’s modulus and micro Poisson’s ratio of the rock, based on the digital image correlation method (DIC) and finite element method (FEM), this paper proposed a parameter field inversion method, namely the DF-PF inversion method. Its inversion accuracy is verified using numerical simulation and laboratory uniaxial compression test. Considering the influences of heterogeneity, stress state and dimension difference, the average inversion error of Young’s modulus field and Poisson’s ratio field are below 10%, and the proportion of elements with an error of less than 15% accounts for more than 86% in the whole specimen model. Compared with the conventional measuring method, the error of macro Young’s modulus and macro Poisson’s ratio calculated by the DF-PF inversion method is less than 2.8% and 9.07%, respectively. Based on the statistical analysis of Young’s modulus field and Poisson’s ratio field, the parameter homogeneity and quantitative function relation between the micro parameter and the principal strain can also be obtained in laboratory tests. The DF-PF inversion method provides a new effective method of testing Young’s modulus field and Poisson’s ratio field of the rocks under complex stress states.

Residual stress within a structural component can significantly affect the mechanical performance and stability of a structure. Therefore, it is crucial to find a way to determine the residual stress distribution to maintain the normal working of structures. Conventional methods for residual stress determination primarily include experimental testing, finite element simulations and inverse identification. However, these methods suffer from disadvantages of high testing costs, long calculation time and low inverse efficiency. To avoid these shortcomings, this study developed a high-performance method based on a deep learning technique. In this method, an artificial neural network was used to replace the finite element calculation in the finite element model updating (FEMU) technique and the residual stress distribution of structural components was inversely obtained based on the measured residual stresses of a finite number of measuring points. Compared with the conventional FEMU technique, the calculation efficiency of the proposed method was considerably improved. Furthermore, the accuracy and efficiency of the method were verified by simulated four-point bending experiments considering an elastic-plastic material.

Digital image correlation (DIC) is a popular photomechanics method for deformation measurement. The conventional subset-based DIC method obtains the displacement vectors at the subset centers, but cannot calculate the deformation on the specimen edges, which may contain very useful information because specimens usually have greater deformation on edges, especially on curved edges due to stress concentration. In this study, the capability of a mesh-based DIC method using 8-node quadrilateral elements (Q8-mesh-DIC) in boundary deformation measurement was investigated and highlighted for specimens with non-uniform deformation. The results were compared with those obtained by some conventional subset-based DIC methods, and the accuracy of the boundary deformation measurement was verified through simulated and real experiments. The Q8-mesh-DIC appears to be more suitable for the boundary deformation measurement of non-uniform deformation fields.

As a natural graded material, bamboo has gradually increasing elastic modulus along the radial direction from the inner to the outer skin. Accurate measurement of the modulus distribution plays an important role in bamboo-based structural design. However, it is difficult to characterise this modulus distribution by using conventional testing approaches on bamboo slices. A more effective method was developed in this study for the inverse identification of gradually varying material properties. The method is based on the digital image correlation and finite element model updating techniques. The radial distribution of the elastic modulus of bamboo was obtained through only one four-point bending test. The inversely identified modulus distribution was verified through uniaxial tensile tests on sliced bamboo strips and microscopic observation of the volume fraction distribution of its vascular bundle. The results showed that the elastic modulus of the bamboo material decreased from the outer skin (20 GPa) to the inner skin (2 GPa), which is in good consistence with the tensile test results on sliced specimens.

Characterizing global mechanical behavior accurately is important for a detailed understanding of the deformation mechanism of rock material. In this paper, a new characterization model of the global mechanical behavior of rock is proposed, based on the structural characteristics of rock deformation. Uniaxial compression tests were carried out using the digital image correlation method and acoustic emission to obtain the interrelationship between mechanical behavior and deformation evolution. The test results show that the appearance of deformation localization leads to non-linear evolution of global mechanical behavior in a rock specimen. Further, due to the gradual evolution of deformation localization bands, the rock specimen evolves from a complete whole to a rock structure with a “weak interlayer”. Thus, the global mechanical behavior of the rock specimen depends heavily on the structural evolution process, especially when close to failure. A simplified characterization model was established according to the deformation process. The finite element method was used to verify the rationality of the proposed structural model. The verification result showed that under uniaxial compression, the structural model can reproduce the global mechanical behavior evolution process of the rock specimen.