Finite element simulations of the thermomechanically coupled responses of thermal barrier coating systems using an unconditionally stable staggered approach

Thermal barrier coating (TBC) systems have long been used in many engineering applications, such as jet engines and gas turbines. One pressing task is to evaluate their performance and integrity under long-term thermal cycles. This task requires an accurate and efficient time integration technique that is unconditionally stable, since large time steps are required to simulate TBC systems under long-term thermal effects. In this work, we present in detail several numerical methods to model the thermomechanically coupled responses of TBC systems, including a monolithic approach and two staggered approaches based on the isothermal split and the adiabatic split, respectively. We also demonstrate several finite element simulation techniques, such as the periodic boundary conditions and the adaptive mesh refinement, in the modeling of TBC systems. Through several numerical examples, we show that the staggered approach based on the adiabatic split preserves the unconditional stability of individual time integration techniques used for the mechanical phase and the thermal phase of the coupled problem. Moreover, the computational cost is significantly lower compared to the monolithic approach. This work provides an efficient time integration approach to model more complex behaviors of TBC systems under long-term thermal cycles.