•The mechanical properties like shear modulus and Young’s modulus of Al–Cu intermetallic compounds are calculated.•The Poisson’s ratio and B/G ratio of Al–Cu intermetallic compounds are calculated.•The shear anisotropy and elastic anisotropy of Al–Cu intermetallic compounds are obtained.•The Vicker hardness of Al–Cu intermetallic compounds is obtained.•Debye temperature, melting point and thermal conductivity of Al–Cu intermetallic compounds are obtained.The elastic and thermodynamic properties of Al–Cu intermetallic compounds have been investigated by using the first-principles density functional theory (DFT) within the generalized gradient approximation (GGA). The computed lattice constants of Al–Cu are in good agreements with the experimental data. The calculated elastic constants reveal that all of Al–Cu intermetallic compounds are mechanically stable. The shear modulus, Young’s modulus, Poisson’s ratio σ, the ratio B/G, shear anisotropy and elastic anisotropy are also calculated. Finally, the Vicker hardness, Debye temperature, melting point and thermal conductivity have been predicted.

The crystal structural, elastic and thermodynamic properties of antiperovskite-type superconductor CuNNi3 under pressure are investigated by using the density functional theory within the generalized gradient approximation (GGA). The ground-state properties are found to agree with the available experimental data and others theoretical results. The elastic constants, shear modulus and Young׳s modulus, Debye temperature, melting point and minimum thermal conductivity under pressure are calculated, the results show those properties increase monotonically with increasing pressure. Finally, the ductility of CuNNi3 was analyzed using the B/GB/G ratio, Cauchy pressure and Poisson׳s ratio σσ.