Thermodynamics of elastocaloric cooling and heat pump cycles

•Systematic thermodynamic description of elastocaloric cooling cycles.•Stirling eC cycle can be used to describe the temperature-dependent material COP.•An incomplete Brayton eC cycle does not always benefit cycle COP.•Work recovery is necessary for high-efficient eC materials.•The relation between numerical models and thermodynamic descriptions is revealed. Elastocaloric cooling is an emerging solid-state cooling technology and has experienced fast development over the last decade. This study aims to systematically introduce the thermodynamic description of elastocaloric cooling and heat pump cycles by derivation from the classical first law and the second law of thermodynamics. The thermodynamic cycle description is then used to discuss the temperature and path-dependent material COP. The impact of incomplete phase transition is analyzed and compared to previous results in the literature. The importance of work recovery and heat recovery is also revisited. Finally, the relationship between the thermodynamic cycle description and the simulation models is discussed.