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
How to correctly extract Cauchy stress from the atomistic simulations is a crucial issue in studying the mechanical behaviours of atomic systems, but is still in controversy. In this paper, three typical atomistic sim...How to correctly extract Cauchy stress from the atomistic simulations is a crucial issue in studying the mechanical behaviours of atomic systems, but is still in controversy. In this paper, three typical atomistic simulation examples are used to validate various existing stress definitions. It is found that the classical virial stress fails in predicting the stresses in these examples, because the velocity depends on the choice of the local average volume or the reference frame velocity and other factors. In contrast, the Lagrangian cross-section stress and Lagrangian virial stress are validated by these examples, and the instantaneous Lagrangian atomic stress definition is also proposed for dynamical problems.展开更多
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
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.
基金supported by the National Natural Science Foundation of China (Grant Nos10702034,10732050 and 90816006)the National Basic Research Program of China (973 Program 2007CB936803,2010CB832701)
文摘How to correctly extract Cauchy stress from the atomistic simulations is a crucial issue in studying the mechanical behaviours of atomic systems, but is still in controversy. In this paper, three typical atomistic simulation examples are used to validate various existing stress definitions. It is found that the classical virial stress fails in predicting the stresses in these examples, because the velocity depends on the choice of the local average volume or the reference frame velocity and other factors. In contrast, the Lagrangian cross-section stress and Lagrangian virial stress are validated by these examples, and the instantaneous Lagrangian atomic stress definition is also proposed for dynamical problems.
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.
