Equivalent thermo-mechanical parameters for perfect crystals

TL;DR

This paper develops a method to derive equivalent thermo-mechanical parameters for perfect crystals by linking microscopic atomic interactions to macroscopic continuum descriptions, including stress tensors and heat flux.

Contribution

It introduces a novel averaging and long wave approximation approach to connect discrete atomic models with continuum thermo-mechanical parameters for perfect crystals.

Findings

Derived continuum balance equations from microscopic atomic equations.

Expressed macroscopic stress and heat flux in terms of microscopic parameters.

Established a Mie-Gruneisen form equation of state for perfect crystals.

Abstract

Thermo-elastic behavior of perfect single crystal is considered. The crystal is represented as a set of interacting particles (atoms). The approach for determination of equivalent continuum values for the discrete system is proposed. Averaging of equations of particles' motion and long wave approximation are used in order to make link between the discrete system and equivalent continuum. Basic balance equations for equivalent continuum are derived from microscopic equations. Macroscopic values such as Piola and Cauchy stress tensors and heat flux are represented via microscopic parameters. Connection between the heat flux and temperature is discussed. Equation of state in Mie-Gruneisen form connecting Cauchy stress tensor with deformation gradient and thermal energy is obtained from microscopic considerations.