Physics-informed Neural Networks (PINN) for computational solid mechanics: Numerical frameworks and applications

For solving the computational solid mechanics problems, despite significant advances have been achieved through the numerical discretization of partial differential equations (PDEs) and data-driven framework, it is still hard to seamlessly integrate imperfect, limited, sparse and noisy data into existing algorithms. Besides the expensive tasks and struggling completion of mesh-based and meshless-based solutions in complex computational domain, the high-dimensional solid mechanics problems governed by parameterized PDEs cannot be tackled. Furthermore, addressing inverse solid mechanics problems, especially with incomplete descriptions of physical laws, are often prohibitively expensive and require obscure formulations and elaborate codes. Since the physics-informed neural networks (PINN) was originally introduced by Raissi et al. in 2019, it has been recognized as effective surrogate solvers for PDEs while respecting any given laws, data, initial and boundary conditions of solid mechanics. PINN has emerged as a promising approach to mitigate the shortage of available training data, enhance model generalizability, and ensure the physical plausibility of results. The prior physics information can act as a regularization agent that constrains the space of admissible solutions to a manageable size, enabling it to quickly steer itself towards the right solution. To catch up with the latest developments of PINN in computational solid mechanics, this work summarizes the recent advances in the field. We first introduce the foundational concepts of PINN, including the framework, architecture, algorithms, code and associated software packages. We then discuss the applications of PINN in constitutive modeling and its inverse problem, identification, evaluation, and prediction of damage in solid materials and structures. Finally, we address the current capabilities and limitations of PINN in computational solid mechanics, and present perspectives on emerging opportunities and open challenges of the prevailing trends.