Asymmetry of the atomic-level stress tensor in homogeneous and inhomogeneous materials

Ji, Rigelesaiyin; Díaz, Adrián; Li, Weixuan; Xiong, Liming; Chen, Youping

doi:10.1098/rspa.2018.0155

Cited by 21 publications

(17 citation statements)

References 62 publications

(123 reference statements)

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“…Although it was claimed that this area-averaging formulation can remove "unphysical" stress oscillations near the ends of a free surface, it leads to a loss of symmetry of the stress tensor. Apparently, the stress calculated through the area-averaged formula is identical to the experimental measured stress when thermal stress is negligible 45 . In other words, this formulism is applicable when thermal stress is ignored.…”

Section: Atomistic Stress Definitionsupporting

confidence: 53%

Nanoscale self-healing mechanisms in shape memory ceramics

Zhang

Zaeem

2019

npj Comput Mater

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Shape memory (SM) ceramics, such as yttria-stabilized tetragonal zirconia (YSTZ), are a unique family of SM materials that offer unique properties including ultra-high operating temperature, and high resistance to chemical corrosion and oxidation. However, formation of defects is usually observed in SM ceramics during manufacturing and/or by mechanical deformation. To fully take advantage of the SM properties of these ceramics, it is necessary to fully understand the nanostructural evolution of defects under external stimuli. In this study, defect closure behaviors in YSTZ nanopillars are investigated by atomistic simulations. Two characteristic orientations of 011 and [001] are selected to represent the dominant deformation mechanisms of phase transformation and dislocation migration, respectively. With the presence of crack and void, the strength and yield strain of nanopillars are noted to decrease significantly, especially for 011oriented YSTZ nanopillars. Volume expansion associated with the tetragonal to monoclinic phase transformation is observed to promote healing of crack and void. Atom stress analyses reveal stress concentrations along the newly formed monoclinic phase bands. A critical crack width is identified, less than which the crack can be fully closed in compression. Size effect study reveals that an increase in nanopillar size has a positive effect on crack self-healing behavior. For [001]-oriented YSTZ nanopillars, dislocation migration leads to formations of an amorphous phase, which also assist the crack and void closure process. The revealed crack/void healing mechanisms may provide a path for mitigating internal defects that influences the mechanical properties and deformation mechanisms of SM ceramics.

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Section: Atomistic Stress Definitionsupporting

confidence: 53%

Nanoscale self-healing mechanisms in shape memory ceramics

Zhang

Zaeem

2019

npj Comput Mater

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“…Comparisons of MOP and VA using MD simulations show a good agreement for local pressure, after sufficient time averaging, in a spatially homogeneous Lennard-Jones fluid 34,38 . By contrast, significant differences in the calculated results of local stress and heat flux between popular VA formulas and surface formulas are demonstrated for solids with defects or interfaces 36,37,39 .…”

Section: Introductionmentioning

confidence: 88%

“…In addition, the calculation results using the physical definition of mechanical stress show that the two shear stress components are not equal. This means the atomic-level stress tensor near dislocation core is not symmetric 39 .…”

Section: Stresses Near Dislocation Coresmentioning

confidence: 99%

“…The elements are the rectangular primitive unit cells of crystal copper with dimensions 2.556Å by 2.087Å by 2.213Å. This is the smallest element that has one atom at its center and yet is space filling to meet the continuum requirement for the stress field 39 . A detailed study of the effects of mesh and mesh size can be found in [ 39 ].…”

Section: Stresses Near Dislocation Coresmentioning

confidence: 99%

“…This is the smallest element that has one atom at its center and yet is space filling to meet the continuum requirement for the stress field 39 . A detailed study of the effects of mesh and mesh size can be found in [ 39 ]. The mechanical stresses are then measured as the resultant forces per unit area transmitted across the faces of the rectangular elements.…”

Section: Stresses Near Dislocation Coresmentioning

confidence: 99%

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Physical foundation and consistent formulation of atomic-level fluxes in transport processes

Chen

Díaz

2018

Phys. Rev. E

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Irving and Kirkwood derived the transport equations from the principles of classical statistical mechanics using the Dirac delta to define local densities. Thereby, formulas for fluxes were obtained in terms of molecular variables. The Irving and Kirkwood formalism has inspired numerous formulations. Many of the later developments, however, considered it more rigorous to replace the Dirac delta with a continuous volume-weighted averaging function and subsequently defined fluxes as a volume density. Although these volume-averaged flux formulas have dominated the literature for decades and are widely implemented in popular molecular dynamics (MD) software, they are a departure from the well-established physical concept of fluxes. In this work, we review the historical developments that led to the unified physical concept of fluxes for transport phenomena. We then use MD simulations to show that these popular flux formulas conserve neither momentum nor energy; nor do they produce fluxes that are consistent with their physical definitions. We also use two different approaches to derive fluxes for general many-body potentials. The results of the formulation show that atomistic formulas for fluxes can be fully consistent with the physical definitions of fluxes and conservation laws.

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Atomistic Computational Analysis of the Loading Orientation-Dependent Phase Transformation in Graphite under Compression

Peng

Xiong

2019

JOM

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Asymmetry of the atomic-level stress tensor in homogeneous and inhomogeneous materials

Cited by 21 publications

References 62 publications

Nanoscale self-healing mechanisms in shape memory ceramics

Nanoscale self-healing mechanisms in shape memory ceramics

Physical foundation and consistent formulation of atomic-level fluxes in transport processes

Atomistic Computational Analysis of the Loading Orientation-Dependent Phase Transformation in Graphite under Compression

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