Atomistic Simulation and Elastic Theory of Surface Steps

1995 ◽  
Vol 399 ◽  
Author(s):  
L. E. Shilkrot ◽  
D. J. Srolovitz
Keyword(s):  
Interaction Energy ◽  
Elastic Field ◽  
Elastic Half Space ◽  
Elastic Theory ◽  
Elastic Model ◽  
Displacement Fields ◽  
Surface Steps ◽  
Line Force ◽  
Step Step ◽  
Force Dipole

ABSTRACTAtomistic computer simulations and anisotropic elastic theory are employed to determine the elastic fields of surface steps and vicinal surfaces. The displacement field of and interaction energies between <100> steps on an {001} Ni surface are determined using atomistic simulations and EAM potentials. The step-step interaction energy found from the simulations is consistent with a surface line force dipole elastic model of a step. We derive an anisotropic form for the elastic field associated with a surface line force dipole using a two dimensional surface Green tensor for a cubic elastic half-space. Both the displacement fields and step-step interaction energy predicted by the theory are shown to be in excellent agreement with the simulations.

Elastic Interaction of Defects on Crystal Surfaces

1999 ◽  
Vol 121 (2) ◽  
pp. 129-135 ◽  
Author(s):  
Demitris Kouris ◽  
Alonso Peralta ◽  
Karl Sieradzki
Keyword(s):  
Interaction Energy ◽  
Surface Defects ◽  
Film Growth ◽  
Crystal Surface ◽  
Elastic Field ◽  
Elastic Interaction ◽  
Flow Mode ◽  
Elastic Model ◽  
Far Field ◽  
Embedded Atom

Surface defects corresponding to adatoms, vacancies and steps interact, affecting and often dominating kinetic processes associated with thin-film growth. A discrete harmonic model for the evaluation of the interaction energy between surface defects is presented. It is based on the concept of eigenstrains and allows for the accurate evaluation of the elastic field, both at the immediate vicinity of the defects, as well as in the far field. Results for the interaction energy suggest conditions for which a body-centered-cubic crystal surface will grow in a stable, two-dimensional, step-flow mode. In order to verify the accuracy of the discrete elastic model, we present results of atomic simulations that incorporate Embedded Atom Method (EAM) potentials. The discrete elastic model results compare favorably with results from our atomic EAM simulations and agree with the far-field predictions of continuum elastic theory.

scholarly journals Surface waves in multilayered elastic media I. Rayleigh and Love waves from buried sources in a multilayered elastic half-space

1964 ◽  
Vol 54 (2) ◽  
pp. 627-679
Author(s):  
David G. Harkrider
Keyword(s):  
Surface Waves ◽  
Frequency Domain ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Half Space ◽  
Love Waves ◽  
Displacement Fields ◽  
Matrix Formulation ◽  
Total Displacement ◽  
Rayleigh And Love Waves

ABSTRACT A matrix formulation is used to derive integral expressions for the time transformed displacement fields produced by simple sources at any depth in a multilayered elastic isotropic solid half-space. The integrals are evaluated for their residue contribution to obtain surface wave displacements in the frequency domain. The solutions are then generalized to include the effect of a surface liquid layer. The theory includes the effect of layering and source depth for the following: (1) Rayleigh waves from an explosive source, (2) Rayleigh waves from a vertical point force, (3) Rayleigh and Love waves from a vertical strike slip fault model. The latter source also includes the effect of fault dimensions and rupture velocity. From these results we are able to show certain reciprocity relations for surface waves which had been previously proved for the total displacement field. The theory presented here lays the ground work for later papers in which theoretical seismograms are compared with observations in both the time and frequency domain.

Line Force in a Two-Phase Orthotropic Medium

1982 ◽  
Vol 49 (1) ◽  
pp. 55-61 ◽  
Author(s):  
R. S. Wu ◽  
Y. T. Chou
Keyword(s):  
Free Surface ◽  
Elastic Field ◽  
Space Application ◽  
Orthotropic Medium ◽  
Method Of Images ◽  
Two Phase ◽  
Special Cases ◽  
Line Force ◽  
Technological Interest

Based on the generalized method of images, the elastic field of an in-plane line force acting in a two-phase orthotropic medium is analyzed. Several special cases of technological interest are deduced from the general solution, including the case of a line force applied on the free surface of a half space. Application of the results to the determination of the elastic field of an edge dislocation in a semi-infinite orthotropic medium is illustrated.

Penetration of a Half Space by a Rectangular Cylinder

1979 ◽  
Vol 46 (3) ◽  
pp. 587-591 ◽  
Author(s):  
A. Cemal Eringen ◽  
F. Balta
Keyword(s):  
Half Space ◽  
Stress Singularity ◽  
Elastic Solid ◽  
Interatomic Interaction ◽  
Elastic Half Space ◽  
Rigid Block ◽  
Field Equations ◽  
Displacement Fields ◽  
Rectangular Cylinder ◽  
Stress And Displacement Fields

The stress and displacement fields are determined in an elastic half space loaded by a rectangular frictionless, rigid block normally at its surface. The semi-infinite solid is considered to be an elastic solid with nonlocal interatomic interaction. The field equations of the nonlocal elasticity and boundary conditions are employed to treat this contact problem. Interestingly the classical stress singularity at the edges of the block are not present in the nonlocal solutions. Consequently the critical applied load for the initiation of penetration of the rigid cylinder into the semi-infinite solid can be determined without recourse to any criterion foreign to the theory. The stress field obtained is valid even for penetrators of submicroscopic width.

scholarly journals Surface Displacements due to a Steadily Moving Point Force

1996 ◽  
Vol 63 (2) ◽  
pp. 245-251 ◽  
Author(s):  
J. R. Barber
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Elastic Half Space ◽  
Point Force ◽  
Two Dimensional ◽  
Normal Surface ◽  
Displacement Fields ◽  
Linear Superposition ◽  
Surface Displacements ◽  
Stress And Displacement Fields

Closed-form expressions are obtained for the normal surface displacements due to a normal point force moving at constant speed over the surface of an elastic half-space. The Smirnov-Sobolev technique is used to reduce the problem to a linear superposition of two-dimensional stress and displacement fields.

Concentration-Dependent Chemical Expansion in Lithium-Ion Battery Cathode Particles

2014 ◽  
Vol 81 (9) ◽  
Author(s):  
Veruska Malavé ◽  
J. R. Berger ◽  
P. A. Martin
Keyword(s):  
Cathode Material ◽  
Hydrostatic Stress ◽  
Lithium Ion ◽  
Elastic Field ◽  
Phase Region ◽  
Electrochemical Process ◽  
Elastic Model ◽  
Chemical Expansion ◽  
Linear Elastic ◽  
Key Parameter

In this work, the effect of the concentration-dependent chemical-expansion coefficient, β, on the chemo-elastic field in lithium-ion cathode particles is examined. To accomplish this, an isotropic linear-elastic model is developed for a single idealistic particle subjected to potentiostatic-discharge and charge conditions. It is shown that β can be a key parameter in demarcating the chemo-stress–strain state of the cathode material undergoing nonlinear volumetric strains. As an example, such strains develop in the hexagonal-to-monoclinic-phase region of LixCoO2 (0.37 ≤ x ≤ 0.55) and, subsequently, the corresponding β is a linear function of concentration. Previous studies have assumed a constant value for β. Findings suggest that the composition-generated chemo-elastic field that is based on a linear-β dramatically affects both the interdiffusion and the mechanical behavior of the LixCoO2 cathode particle. Because the chemo-elastic phenomena emanate in a reciprocal fashion, the resulting linear β-based hydrostatic-stress gradients significantly aid the diffusion of lithium. Thus, diffusion is accelerated in either electrochemical process that the cathode material undergoes.

scholarly journals MODERN MOVEMENTS OF THE CRUST SURFACE IN GORNY ALTAI FROM GPS DATA

2019 ◽  
Vol 10 (1) ◽  
pp. 123-146
Author(s):  
V. Yu. Timofeev ◽  
D. G. Ardyukov ◽  
A. V. Timofeev ◽  
E. V. Boiko
Keyword(s):  
Anomalous Behavior ◽  
Strike Slip ◽  
Elastic Model ◽  
Displacement Fields ◽  
Epicentral Zone ◽  
Lateral Strike Slip ◽  
Altai Region ◽  
Gorny Altai ◽  
Vertical Fault ◽  
The Right

In 2000–2017, the GPS technology was first applied to study inter-seismic, co-seismic and post-seismic processes in the crust of the Altai Mountains (Gorny Altai). Our study aims at investigating the fields of displacement and deformation in the Gorny Altai region as a part of Asia.The 3D displacement fields are reconstructed for the period before the M 7.3 Chuya earthquake that occurred in the southern sector of the Altai GPS network (49° to 55°N, and 81° to 89°E)on 27 September 2003.Anomalous behavior features are discovered in the displacement orientations, as well as in the distribution of velocities and deformation in the zone of the future earthquake.The spatial displacement pattern defined for the period of co-seismic displacements corresponds to the right-lateral strike-slip along the vertical fault. The fault depth is estimated using the elastic model and the experimental data (change in displacement from 0.30 m to 0.02 m at the distances of 14 km and 84 km from the fault, respectively); it amounts to 8–10 km.The co-seismic deformation field is investigated.In the post-seismic stage (2004–2017), displacements revealedin the epicentral zone show the right-lateral strike-slip along the fault at the rate of 2 mm/yr. Therefore, two-layer viscoelastic models can be considered. The estimated viscosity of the lower crust ranges from 6×1019to 3×1020Pa×s, and the elastic upper crust thickness is 25 km. Analyzed are modern movements in the Gorny Altai region outside the Chuya earthquake area.The results of our study show that modern horizontal displacements occur in the NNW direction at the rate of 1.1 mm/yr, which is twice lower than the displacement rate before the earthquake.

Elastic Half Space under Axisymmetric Surface Loading and Influence of Couple Stresses

2020 ◽  
Vol 897 ◽  
pp. 129-133
Author(s):  
Jintara Lawongkerd ◽  
Toan Minh Le ◽  
Suraparb Keawsawasvong ◽  
Suchart Limkatanyu ◽  
Jaroon Rungamornrat
Keyword(s):  
Half Space ◽  
Integral Transform ◽  
Couple Stress Theory ◽  
Elastic Field ◽  
Elastic Half Space ◽  
Small Scale ◽  
Internal Length ◽  
Stress Theory ◽  
Axisymmetric Surface ◽  
Small Scale Effect

This paper presents the complete elastic field of a half space under axisymmetric surface loads by taking the influence of material microstructures into account. A well-known couple stress theory is adopted to handle such small scale effect and the resulting governing equations are solved by the method of Hankel integral transform. A selected numerical quadrature is then applied to efficiently evaluate all involved integrals. A set of results is also reported to not only confirm the validity of established solutions but also demonstrate the capability of the selected mathematical model to simulate the size-dependent characteristic of the predicted response when the external and internal length scales are comparable.

The Elastic Field of an Elliptic Cylindrical Inclusion in a Laminate With Multiple Isotropic Layers

1999 ◽  
Vol 66 (1) ◽  
pp. 165-171 ◽  
Author(s):  
H. G. Beom ◽  
Y. Y. Earmme
Keyword(s):  
Plate Theory ◽  
Elastic Field ◽  
Cylindrical Inclusion ◽  
Transverse Displacement ◽  
Laminated Plate ◽  
Displacement Fields ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Main Plane ◽  
Interior Points

An elliptic cylindrical inclusion with an eigenstrain in an infinite laminate composed of multiple isotropic layers is analyzed. The problem is formulated by using the classical laminated plate theory in which displacement fields in the laminated plate are expressed in terms of in-plane displacements on the main plane and transverse displacement. Employing a method based on influence functions, an integral type solution to the equilibrium equation is expressed in terms of the eigenstrain. Closed-Form solutions for the elastic fields are obtained by evaluating the integrals explicitly for interior points and exterior points of the ellipse. The elastic fields caused by an elliptic cylindrical inhomogeneity with an eigenstrain in the infinite laminate are determined by the equivalent eigenstrain method. Solutions for a finite laminate with an eigenstrain in a circular cylindrical inhomogeneity are also obtained in terms of material and geometric parameters for each layer composing the laminate.

Sign in / Sign up

Export Citation Format

Share Document