Atomistic Finite Deformation Simulations: A Discussion on Length Scale Effects in Relation to Mechanical Stresses

1999 ◽  
Vol 121 (2) ◽  
pp. 114-119 ◽  
Author(s):  
Mark F. Horstemeyer ◽  
M. I. Baskes
Keyword(s):  
Continuum Mechanics ◽  
Simple Shear ◽  
Finite Deformation ◽  
Scale Effects ◽  
Embedded Atom Method ◽  
Length Scale ◽  
Size Scale ◽  
Embedded Atom ◽  
Spatial Size ◽  
The Continuum

In this study, atomistic finite deformation calculations employing the Embedded Atom Method show three items of interest related to continuum field theory. First, a spatial size scale effect on the yield stress is found. In these calculations, mechanical yield point occurred from dislocation initiation at the edge of the numerical specimens. The spatial size scale continued to affect the plastic response up to strains of 30 percent in simple shear for nickel oriented at 〈011〉. The second point is related to the continuum mechanics observation about oscillating global shear stress under simple shear conditions is shown to dampen as the spatial size scale increases. As the spatial length scale increases, the continuum rotational effect coupled with the increase in dislocation population reduces the oscillatory behavior. This confirms the notion proposed by Bammann and Aifantis (1987) in that when more dislocations are initiated with different orientations of the Burger’s vectors then the oscillations decrease. Finally, a length scale bridging idea is proposed by relating a continuum single degree of freedom loss coefficient, which relates the plastic energy to the total strain energy, to varying sizes of blocks of atoms. This study illustrates the usefulness of employing the Embedded Atom Method to study mechanisms related to continuum mechanics quantities.

Contact Compression of Self-assembled Nano- and Micro-scale Pyramid Structures on Au (100) Surface

2003 ◽  
Vol 788 ◽  
Author(s):  
J. Wang ◽  
D. Ward ◽  
W. A. Curtin ◽  
K.-S. Kim
Keyword(s):  
Molecular Dynamics ◽  
Plastic Deformation ◽  
Limit Analysis ◽  
Scale Effects ◽  
Dynamics Simulation ◽  
Length Scale ◽  
Slope Change ◽  
Self Similar ◽  
Pyramid Structures ◽  
The Continuum

ABSTRACTA process of self-assembly induced by electro-chemical etching was used to produce nano and micrometer scale pyramid-structures on (100) surfaces of gold. The pyramids grew in a self-similar fashion with the facets aligned in (114) plane. Using the unique characteristics of the self-similar pyramid structure, plastic compression of the pyramids by a flat-surface platen was performed to study length scale effects in the plastic deformation. A continuum limit analysis and a finite element simulation as well as molecular dynamics simulations were carried out to predict the deformation and load-displacement behavior of the pyramid compression. The limit analysis predicts that the load of compression is proportional to the square of the contact-compression displacement. The continuum analysis provides estimation on the asymptotic behavior of the elastic-plastic load-deflection response of the pyramid under compression for a large value of displacement. The three dimensional molecular dynamics simulation was utilized to study the dislocation activities during the early stage of the pyramid compression. Experiments were also carried out by pressing the pyramids with an atomically flat mica surface. The deformation of the compressed pyramid was measured using an Atomic Force Microscope (AFM). The continuum analyses predict size independent values of the slope change of the pyramid facets near the contact edge, caused by plastic deformation. However, atomistic simulation predicts an opposite value of the slope change to the prediction of the continuum analyses. The AFM measurements of the slope change show size dependent transition from the prediction of the continuum analyses to that of the atomistic simulations. The transition data provide an apparent characteristic length of the size dependence of plastic deformation in a small volume. Molecular dynamics show that at very small length scale the size effect is strongly influenced by surface adhesion effects.

Comparison of Various Object Stress Rates under Simple Shear

2013 ◽  
Vol 650 ◽  
pp. 407-413 ◽  
Author(s):  
Dong Keon Kim ◽  
Jong Wan Hu
Keyword(s):  
Continuum Mechanics ◽  
Simple Shear ◽  
Finite Deformation ◽  
Deformation Theory ◽  
Numerical Results ◽  
The Other ◽  
Stress Rate ◽  
Shear Problem ◽  
Finite Deformation Theory ◽  
Objective Stress

Object Stress rates to predict the behavior of material have been researched based on numerically and theoretically for researchers who study continuum mechanics due to its complexity. This study focused on the various objective stress rates which assumed the finite deformation theory. Eight object stress rates (Oldroyd, Truesdell, Cotter–Rivlin, Jaumann, Green–Naghdi, Eulerian, grangian, and logarithmic object stress rates) were introduced using continuum mechanics and analyzed to derive the numerical solution to the simple shear problem. Numerical results from each object stress rate were analyzed and compared with the results of the other stress rates. Finally, the appropriate object stress rate for the simple shear problem was determined based on the numerical results from eight objects stress rates.

Structural Energetics of Thin Coherently Strained Metallic Overlayers

1986 ◽  
Vol 83 ◽  
Author(s):  
Brian W. Dodson ◽  
Paul A. Taylor
Keyword(s):  
Optimization Procedure ◽  
Embedded Atom Method ◽  
Embedded Atom ◽  
Growth Stability ◽  
Atomistic Calculations ◽  
Bimetallic System ◽  
The Stability ◽  
Bimetallic Structures ◽  
Metal Overlayers ◽  
The Continuum

ABSTRACTUnderstanding of the growth, stability, and structural properties of coherently strained metal overlayers has achieved considerable importance because of the recent discovery of unique interfacial electronic states and catalytic properties of such systems. The structural stability of coherently strained metal films grown on a substrate composed of a different and lattice-mismatched metal is determined via atomistic calculations. An equilibrium energy balance criterion is used, which is evaluated with a Monte Carlo annealing optimization procedure in which the structural energy of the bimetallic system is obtained using the embedded atom method. The stability of coherently strained (100) bimetallic structures chosen from combinations of the fcc metals Ag, Au, Cu, Ni, Pd, and Pt has been studied. The predicted critical thicknesses agree remarkably well with experimental results, but disagree quantitatively with the continuum models.

Thermoelastic damping in nonlocal nanobeams considering dual-phase-lagging effect

2020 ◽  
Vol 26 (11-12) ◽  
pp. 1042-1053 ◽  
Author(s):  
Vahid Borjalilou ◽  
Mohsen Asghari ◽  
Ehsan Taati
Keyword(s):  
Heat Conduction ◽  
Continuum Mechanics ◽  
Scale Effects ◽  
Small Scale ◽  
Phase Lag ◽  
Dual Phase ◽  
Complex Frequency ◽  
Thermoelastic Damping ◽  
Coupled Equations ◽  
The Continuum

This paper aims to present an explicit relation for thermoelastic damping in nanobeams capturing the small-scale effects on both the continuum mechanics and heat conduction domains. To incorporate small-scale effects, the coupled equations of motion and heat conduction are obtained by employing the nonlocal elasticity theory and the dual-phase-lag heat conduction model. Adopting simple harmonic forms for transverse deflection and temperature increment and solving the governing equations, real and imaginary parts of the frequency are extracted. According to the complex frequency approach, a closed-form size-dependent expression for evaluating thermoelastic damping in nanobeams is derived. To clarify the influence of nonlocality and dual-phase-lagging on the amount of thermoelastic damping, numerical results are compared with the ones predicted in the framework of classical continuum and heat conduction theories. Findings reveal that the size effect on both the continuum mechanics and heat conduction modeling of nanobeams is not negligible. A number of parametric studies are also conducted to indicate the effect of beam dimensions, boundary conditions and type of material on the value of thermoelastic damping.

Application of Finite Deformation Theory to the Development of an Orthogonal Cutting Model—Part II: Experimental Investigation and Model Validation

2005 ◽  
Vol 128 (3) ◽  
pp. 767-774 ◽  
Author(s):  
Yuliu Zheng ◽  
Xuefei Hu ◽  
John W. Sutherland
Keyword(s):  
Continuum Mechanics ◽  
Finite Deformation ◽  
Deformation Theory ◽  
Split Hopkinson Pressure Bar ◽  
Orthogonal Cutting ◽  
Hopkinson Pressure Bar ◽  
Mechanics Model ◽  
Finite Deformation Theory ◽  
Cutting Model ◽  
The Continuum

In Part 1 of this paper, a continuum mechanics model of the orthogonal cutting process was developed based on finite deformation theory. In this part of the paper, constitutive equations for O1 and L6 tool steels are developed using the results from split Hopkinson pressure bar tests. Statistically designed orthogonal cutting experiments are conducted to secure process results across a range of cutting conditions. The continuum mechanics model established in Part 1 of this paper is used to simulate all the cutting tests. All the model outputs are calculated and compared with the corresponding cutting experiment results. Good agreement is observed between the model predictions and the experimental results. The continuum mechanics model is successfully used to predict the cutting force, shear angle, and temperature.

Atomistic Simulation Study of Controlled Nanostructure Patterning

2003 ◽  
Vol 775 ◽  
Author(s):  
Byeongchan Lee ◽  
Kyeongjae Cho
Keyword(s):  
Diffusion Barrier ◽  
Atomistic Simulation ◽  
Degrees Of Freedom ◽  
Embedded Atom Method ◽  
Surface Kinetics ◽  
Bulk Properties ◽  
Embedded Atom ◽  
Kinetics Of ◽  
Dissociation Barrier ◽  
Strain Dependent

AbstractWe investigate the surface kinetics of Pt using the extended embedded-atom method, an extension of the embedded-atom method with additional degrees of freedom to include the nonbulk data from lower-coordinated systems as well as the bulk properties. The surface energies of the clean Pt (111) and Pt (100) surfaces are found to be 0.13 eV and 0.147 eV respectively, in excellent agreement with experiment. The Pt on Pt (111) adatom diffusion barrier is found to be 0.38 eV and predicted to be strongly strain-dependent, indicating that, in the compressive domain, adatoms are unstable and the diffusion barrier is lower; the nucleation occurs in the tensile domain. In addition, the dissociation barrier from the dimer configuration is found to be 0.82 eV. Therefore, we expect that atoms, once coalesced, are unlikely to dissociate into single adatoms. This essentially tells that by changing the applied strain, we can control the patterning of nanostructures on the metal surface.

Modified embedded-atom method potentials for the plasticity and fracture behaviors of unary fcc metals

2021 ◽  
Vol 103 (9) ◽  
Author(s):  
Zachary H. Aitken ◽  
Viacheslav Sorkin ◽  
Zhi Gen Yu ◽  
Shuai Chen ◽  
Zhaoxuan Wu ◽  
...  
Keyword(s):  
Embedded Atom Method ◽  
Fcc Metals ◽  
Embedded Atom ◽  
Fracture Behaviors ◽  
Modified Embedded Atom Method
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