Geometric Indexes of Atomic Configurations and Microscopic Expressions for Elastic Constants of Solids.

Yasui, Yoshihiro; Hoshino, Yutaka; Shizawa, Kazuyuki; Takahashi, Kazuhiro

doi:10.1299/kikaia.66.7

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“…Asymmetric stress, higher-order stress and heat¯ux are expressed as area averages represented by microscopic quantities such as interatomic potential, body force and inertia force and vectors l H nac . The vectors l H na c and P-tensors (Packing-tensors), [17,18], indicate the atomic con®gurations in the mesodomain.…”

Section: Introductionmentioning

confidence: 99%

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Microscopic discussions of macroscopic balance equations for solids based on atomic configurations

Nakane

Shizawa

Takahashi

2000

Archive of Applied Mechanics

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Macroscopic behavior of solids is widely studied from microscopic viewpoints such as molecular dynamics and lattice dynamics. However, there are some dif®culties with the averaging methods in the microscopic expressions of stress, higher-order stress and heat¯ux. In this study, we discuss the microscopic expressions of macroscopic variables and macroscopic balance equations of a solid that is modeled as an assembly of atoms, on the basis of generalized Cosserat continuum theories. The concept of mesodomain is introduced to relate microscopic quantities of atoms to macroscopic quantities of continua. Microscopic expressions of stresses and heat¯ux are described as area averages of microscopic quantities such as velocities of atoms, interatomic potential forces. Balance equations for stress and higher-order stresses are derived from the equations of atomic motion. The energy equation, represented by the averages for the values in the mesodomain, is obtained by dividing the velocity of atoms into macroscopic motion and thermal motion. Since the generalized polar effects are taken into account in this model, derived macroscopic balance equations have the same form as the equations of generalized Cosserat continua. Moreover, microscopic descriptions obtained here show that the higher-order mechanical power of the generalized Cosserat continua is equivalent to the thermodynamic quantities of simple materials. The values of velocities of atoms calculated by molecular dynamics simulation are substituted into the newly obtained microscopic expressions of stress and higher-order stresses. The obtained values of stresses and the theoretical values derived from Eringen's formula correspond well, which demonstrates the usefulness of the present microscopic expressions for the practical application in computer simulations.

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Section: Introductionmentioning

confidence: 99%

“…We have de®ned the tensor P n H j 1 ÁÁÁj s as P-tensor, [17,18]. The velocity of atoms can be divided into macroscopic and thermal motions.…”

Section: Introductionmentioning

confidence: 99%

Microscopic discussions of macroscopic balance equations for solids based on atomic configurations

Nakane

Shizawa

Takahashi

2000

Archive of Applied Mechanics

View full text Add to dashboard Cite

show abstract

Geometric Indexes of Atomic Configurations and Microscopic Expressions for Elastic Constants of Solids.

Cited by 1 publication

References 0 publications

Microscopic discussions of macroscopic balance equations for solids based on atomic configurations

Microscopic discussions of macroscopic balance equations for solids based on atomic configurations

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