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Work conjugate strain of virial stress

International Journal of Smart and Nano Materials 2016年第1期7卷 39-51页

作者： Leyu Wang Jiaoyan Li James D.Lee Center for Collision Safety and Analysis College of ScienceGeorge Mason UniversityFairfaxVAUSA School of Engineering Brown UniversityProvidenceRIUSA Department of Mechanical and Aerospace Engineering The George Washington UniversityWashingtonDCUSA

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.

关键词： Thermodynamic pair conjugacy virial stress atomic logarithmic strain molecular dynamics interatomic potential strain energy magnesium oxide

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INVESTIGATION ON APPLICABILITY OF VARIOUS stress DEFINITIONS IN ATOMISTIC SIMULATION

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Acta Mechanica Solida Sinica 2009年第6期22卷 644-649页

作者： Ran Xu Bin Liu AML Department of Engineering Mechanics Tsinghua University Beijing 100084 China

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.

关键词： atomic stress virial stress atomistic simulation

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Work conjugate pair of stress and strain in molecular dynamics

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International Journal of Smart and Nano Materials 2016年第3期7卷 144-178页

作者： Leyu Wang James D.Lee Cing-Dao Kan Center for Collision Safety and Analysis College of ScienceGeorge Mason UniversityFairfaxVAUSA Department of Mechanical and Aerospace Engineering the George Washington UniversityWashingtonDC 20052USA

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.

关键词： 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

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