Local stress and heat flux in atomistic systems involving three-body forces

Chen, Youping

doi:10.1063/1.2166387

Cited by 121 publications

(123 citation statements)

References 25 publications

Supporting

Mentioning

122

Contrasting

Order By: Relevance

“…For many-body potentials, the calculation of the microscopic heat current is a highly nontrivial task [36][37][38][39]. Recently, a well-defined expression valid for a general classical many-body potential has been derived as [40] …”

Section: A Green-kubo Methodsmentioning

confidence: 99%

Thermal conductivity decomposition in two-dimensional materials: Application to graphene

et al. 2017

View full text Add to dashboard Cite

Two-dimensional materials have unusual phonon spectra due to the presence of flexural (out-of-plane) modes. Although molecular dynamics simulations have been extensively used to study heat transport in such materials, conventional formalisms treat the phonon dynamics isotropically. Here, we decompose the microscopic heat current in atomistic simulations into in-plane and out-of-plane components, corresponding to in-plane and outof-plane phonon dynamics, respectively. This decomposition allows for direct computation of the corresponding thermal conductivity components in two-dimensional materials. We apply this decomposition to study heat transport in suspended graphene, using both equilibrium and nonequilibrium molecular dynamics simulations. We show that the flexural component is responsible for about two-thirds of the total thermal conductivity in unstrained graphene, and the acoustic flexural component is responsible for the logarithmic divergence of the conductivity when a sufficiently large tensile strain is applied.

show abstract

Section: A Green-kubo Methodsmentioning

confidence: 99%

Thermal conductivity decomposition in two-dimensional materials: Application to graphene

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Equation (2) is the stress -force relationship that has been proven to be valid at the microscopic quantum mechanics level 3,[31][32][33] , the classical mechanics level 34 , and the macroscopic continuum mechanics level 35 . Interpretation of Eq.…”

Section: Existing Microscopic Stress Formulas and Their Inconsistmentioning

confidence: 99%

The origin of the distinction between microscopic formulas for stress and Cauchy stress

Chen¹

2016

EPL

Self Cite

View full text Add to dashboard Cite

-Stress is calculated routinely in atomistic simulations. The widely used microscopic stress formulas derived from classical or quantum mechanics, however, are distinct from the concept of Cauchy stress, i.e., the true mechanical tress. This work examines various atomistic stress formulations and their inconsistencies. Using standard mathematic theorems and the law of mechanics, we show that Cauchy stress results unambiguously from the definition of internal force density, thereby removing the long-standing confusion about the atomistic basis of the fundamental property of Cauchy stress, and leading to a new atomistic formula for stress that has clear physical meaning and well-defined values, satisfies conservation law, and is fully consistent with the concept of Cauchy stress. I. INTRDUCTIONEnergy, force, stress are basic concepts in the characterization of the state of condensed matter. Stress, in particular, is a key concept that links theory, simulation, and experiment. It has also been a subject of theoretical interest, as it can be used to establish correspondence between classical and quantum mechanics and between particle and continuum mechanics. Both the classical and quantum mechanical virial theorems show that the systemwide average stress in many-body systems is determined by the kinetic energy and the virial of the potential, [1][2][3][4][5][6][7][8] generally referred to as the kinetic and potential part of stress, respectively. In contrast, the atomistic formula for local stress remains a subject of debate. The critical issue is that no correspondence has been established between atomistic formulas for local stress and the fundamental concept of Cauchy stress. [8][9][10][11] Cauchy stress, also known as the true mechanical stress, is defined as the force that the material on one side of a surface element exerts on the material on the other side, divided by the area of the surface.12 It is a measure of the intensity of internal forces, has a clear physical origin, is the actual physical quantity measured in experiments, and is applicable on all scales. Atomistic stress formulas, on the other hand, were derived from classical or quantum mechanics as a function of the forces and positions of atoms, and is what have been used in ab initio calculations 13 as an intrinsic property of the quantummechanical ground state of matter, or in classical molecular dynamics or coarse-grained atomistic simulations to predict strength 14 , fracture toughness 15, 16 , hardness 17 , or to quantify the effect of local stress on ferroelectricity 18 , thermal conductivity 19,20 , phase transition 21, 22 , etc. There are numerous computational efforts that have attempted to understand the difference between various atomistic formulas for local stress and that between atomistic stress and Cauchy stress 8-11, 19, 23-25 . For example, FIG. 1 compares the stress at a dislocation core predicted by atomistic simulations using two most popular atomistic formulas with that by classical elasticity. While both atomistic s...

show abstract

“…Substituting equations (3.10-12) and (3.14) into the relations of mass, momentum and energy conservation where is the heat flux, the Hardy stress at a material point is expressed as (3.18) Equation (3.18) has been shown to be valid for the multi-body potentials [73]. The relative velocity between the atomistic velocity and material velocity is considered in the kinetic term and represents the weight of the bond length between atom and atom as Step Function 3 rd order Function…”

Section: Hardy Stressmentioning

confidence: 99%

Applicability of Continuum Fracture Mechanics in Atomistic Systems

Cheng

Sun

2011

Volume 8: Mechanics of Solids, Structures and Fluids; Vibration, Acoustics and Wave Propagation

View full text Add to dashboard Cite

Stress intensity factor is one of the most significant fracture parameters in linear elastic fracture mechanics (LEFM). Due to its simplicity, many researchers directly employed this concept to explain their results from molecular simulation. However, stress intensity factor defines the amplitude of the singular stress, which is the product of continuum elasticity. Under atomistic systems without the stress singularity, the concept of stress intensity factor must be examined. In addition, the difficulty of studying the stress intensity factor in atomistic systems may be traced back to the ambiguous definition of the local atomistic stress. In this study, the definition of the local virial stress is adopted. Subsequently, through the consideration of K-dominance, the approximated stress intensity factor based on the atomistic stress can be projected within a reasonable region. Moreover, the influence of cutting interatomic bonds to create traction free crack surfaces and the critical stress intensity factor is also discussed.

show abstract

Local stress and heat flux in atomistic systems involving three-body forces

Cited by 121 publications

References 25 publications

Thermal conductivity decomposition in two-dimensional materials: Application to graphene

Thermal conductivity decomposition in two-dimensional materials: Application to graphene

The origin of the distinction between microscopic formulas for stress and Cauchy stress

Applicability of Continuum Fracture Mechanics in Atomistic Systems

Contact Info

Product

Resources

About