Work conjugate pair of stress and strain in molecular dynamics

• Main Authors: Leyu Wang, James D. Lee, Cing-Dao Kan
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2016-07-01
• Series: International Journal of Smart and Nano Materials
• Subjects: 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
• Online Access: http://dx.doi.org/10.1080/19475411.2016.1233141

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.