Physics-informed neural network solution for thermo-elastic cavity expansion problem

Abstract

ABSTRACT This paper proposes a physics-informed neural network (PINN) to solve the thermo-elastic coupled cavity expansion problem under plane strain conditions. The solid is modelled as a linear thermo-elastic material, and cavity expansion is driven by a constant temperature and a radial displacement subjected to the inner cavity wall. Governing partial differential equations (PDEs) for the problem is firstly presented, and an analytical solution is available to help benchmark the PINN approach. Then, the PDEs are normalised into dimensionless forms and neural network details for solving the coupled PDEs are demonstrated. Finally, the performance of the PINN approach is shown by comparison with the analytical benchmark solution and it is found that the PINN can predict thermo-elastic cavity expansion behaviour with high accuracy. The PINN approach and the analytical solution can also serve as a benchmark for solving thermo-elastic coupled problems in geotechnical engineering by more advanced PINN.