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 wor...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.展开更多
Certain stress tensor and strain tensor form a conjugate pair if there exists a scalar valued strain energy function such that the stress tensor is equal to the derivative of strain energy function with respect to the...Certain stress tensor and strain tensor form a conjugate pair if there exists a scalar valued strain energy function such that the stress tensor is equal to the derivative of strain energy function with respect to the strain tensor.Virial stress is widely accepted as the stress measurement in molecular dynamics(MD).However,its conjugate strain is not yet identified.An atomic logarithmic strain is proposed and numerically verified as the conjugate strain of virial stress at 0 K temperature.The strain energy is calculated by virial stress and the proposed atomic logarithmic strain equals to the interatomic potential energy density.This conclusion is numerically verified with(1)Coulomb-Buckingham potential,Lenard-Jones potential,or arbitrary nonlinear pair potential and(2)randomly generated atomic configurations and deformation gradients.Examples are given in determining the stress–strain relation for magnesium oxide with MD simulation.The result shows that the atomic logarithmic strain is identical to engineer-ing strain when deformation is small.展开更多
文摘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.
文摘Certain stress tensor and strain tensor form a conjugate pair if there exists a scalar valued strain energy function such that the stress tensor is equal to the derivative of strain energy function with respect to the strain tensor.Virial stress is widely accepted as the stress measurement in molecular dynamics(MD).However,its conjugate strain is not yet identified.An atomic logarithmic strain is proposed and numerically verified as the conjugate strain of virial stress at 0 K temperature.The strain energy is calculated by virial stress and the proposed atomic logarithmic strain equals to the interatomic potential energy density.This conclusion is numerically verified with(1)Coulomb-Buckingham potential,Lenard-Jones potential,or arbitrary nonlinear pair potential and(2)randomly generated atomic configurations and deformation gradients.Examples are given in determining the stress–strain relation for magnesium oxide with MD simulation.The result shows that the atomic logarithmic strain is identical to engineer-ing strain when deformation is small.
