## 1 Introduction  
The non-uniform deformation of solid materials, and in particular the strong non-uniform deformation caused by the concentration of stress at the boundary, is an extremely important issue in stress analysis, material processing, mechanical manufacturing, etc. Modeling the non-uniform deformation of solid materials is important for understanding the behavior of materials for given boundary conditions. By modeling and simulating various levels of stress and strain, researchers can gain insight into the material's mechanical properties and how they affect the material's response to loading. This understanding can then be used to create better materials and designs for specific applications. In previous studies, the finite difference method (FDM) [1,2] and the finite element method (FEM) [3,4] have commonly been used to simulate deformation, which transforms the analytical problem of continuous variables into the numerical problem of discrete variables. These numerical methods have high requirements as regards the spatial discretization of computational domains and the treatment of boundary conditions, the computational performance of which depends heavily on the generation rule of the mesh. Therefore, in order to describe the non-uniform deformation and stress concentration phenomenon as accurately as possible, finer meshes are needed [5], but this may lead to huge computing costs and storage resource requirements. Furthermore, capturing real-time data to construct physical models during physical industrial processes plays an important role in operating digital twin technology. The computational efficiency of a digital twin derived from traditional physical models calculated by conventional numerical methods is quite low and is unable to satisfy the requirements involved in the construction of complex physical models involving complex solid deformation, chemistry, and fluid dynamics [6]. Recently, data-driven deep learning technology has not only revolutionized the fields of image and natural language processing but has also extended its impact to traditional scientific computing domains [7; 8; 9]. Data-driven deep learning techniques offer several advantages over traditional FEMs to overcome its drawbacks [8]. They do not require a pre-defined mathematical model, learn directly from data and can account for complex physical phenomena. They can be trained on large datasets, approximate complex numerical simulations and reduce computational costs. Overall, data-driven deep learning techniques provide a flexible approach to modeling complex physical systems and can overcome the limitations of traditional FEMs. However, as they suffer from serious data dependence issues and a lack of physical interpretability, these data-driven methods easily fall into overfitting, thus limiting their application in many fields, such as physics and solid mechanics, which are not sufficiently rich in data. In recent years, the use of \"AI for science\" has developed rapidly. [PERSON] et al. [10] presented a general physics-informed neural network (PINN) framework to deal with the forward and inverse problems that arise in non-linear PDE systems using small datasets and even potentially without any labeled data. Within a very short time, the PINN framework, as a typical representative of AI used for science, has been vastly applied in many fields, such as fluid dynamics [11; 12], heat conduction [13; 14], geophysics [15; 16; 17], solid mechanics [18; 19; 20; 21], and biomedicine [22]. [PERSON] et al. [11] proposed a physics-constrained DL approach for the surrogate modeling of fluid flows without depending on any labelled data, and the calculated results exhibited excellent agreement in the flow field and forward-propagated uncertainties between the DL surrogate approximations and the first principles numerical simulations. In the heat conduction field, [PERSON] et al. [13] employed a PINN framework in solving both forward and inverse problems related to heat conduction.