Work conjugate pair of stress and strain in molecular dynamics

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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.

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Wang, L., Lee, J. D., & Kan, C. D. (2016). Work conjugate pair of stress and strain in molecular dynamics. International Journal of Smart and Nano Materials, 7(3), 144–178. https://doi.org/10.1080/19475411.2016.1233141

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