Thermodynamic properties and constitutive relations of crystals at finite temperature

Abstract

The dynamics equation for each individual atom is established directly around the equilibrium state of the system of N atoms based on the inter-atomic potential energy of EAM model. Using the theory of lattice dynamics and periodical boundary condition, the 3N×3N stiffness matrix in eigen equations of vibration frequencies for a parallelepiped crystal is reduced to a 3n×3n matrix of eigen equations of vibration frequencies for a unit lattice. The constitutive relation of the crystal at finite temperature is extracted based on the quantum-mechanical principle. The thermodynamic properties and the stress-strain relationships of crystal Cu with large plastic deformation at different temperatures are calculated, the calculation results agree well with experimental data.