Work conjugate pair of stress and strain in molecular dynamics

Abstract

Certain stress and strain form a thermodynamic conjugate pair such that their strain energy equals to a scalar-valued potential energy. Different atomistic stresses and strains are analytically derived based on the work conjugate relation. It is numerically verified with both two-body and three-body potentials that the atomistic Kirchhoff stress, first-order Piola–Kirchhoff stress and second-order Piola–Kirchhoff stress are conjugates to atomistic logarithmic strain, deformation gradient and Lagrangian strain, respectively. Virial stress at 0 K based on original volume is the special form of atomistic Kirchhoff stress for pair potential. It is numerically verified that Hencky strain is not conjugate to any stress.

Keywords

• Thermodynamic conjugacy
• logarithmic strain
• atomistic stress
• deformation gradient
• strain energy
• interatomic potential
• Tersoff potential
• atomistic first-order Piola–Kirchhoff stress
• atomistic second-order Piola–Kirchhoff stress
• atomistic Kirchhoff stress
• virial stress