A temperature-based thermodynamically consistent integration scheme for discrete thermo-elastodynamics

• New structure-preserving method based on the temperature as thermodynamical variable.
• It was so far reported the unsuitability to use the temperature.
• We overcame the main drawback derived from using other variables: Dirichlet’s b.c.
• Numerical examples show accuracy, robustness and stability for large time steps.
• Proposed method is starting point for the infinite dimensional case under development.

The formulation of thermodynamically consistent (TC) time integration methods was introduced by a general procedure based on the GENERIC form of the evolution equations for thermo-mechanical problems. The use of the entropy was reported to be the best choice for the thermodynamical variable to easily provide TC integrators. Also the employment of the internal energy was proved to not involve excessive complications. However, attempts towards the use of the temperature in the design of GENERIC-based TC schemes have so far been unfruitful. This paper complements the said procedure to attain TC integrators by presenting a TC scheme based on the temperature as thermodynamical state variable. As a result, the problems which arise due to the use of the entropy are overcome, mainly the definition of boundary conditions. What is more, the newly proposed method exhibits the general enhanced numerical stability and robustness properties of the entropy formulation.