Atomistic vs. continuum models of nanoporous elastic solid: Stress fields, size-dependent effective stiffness and surface constants

2022 ◽  
pp. 104223
Author(s):  
Volodymyr I. Kushch
Keyword(s):  
Elastic Solid ◽  
Effective Stiffness ◽  
Stress Fields ◽  
Continuum Models ◽  
Size Dependent ◽  
Solid Stress

Mathematical Modeling of a Solid–Liquid Mixture with Mass Exchange Between Constituents

2006 ◽  
Vol 11 (6) ◽  
pp. 575-595 ◽  
Author(s):  
L. Fusi ◽  
A. Farina ◽  
D. Ambrosi
Keyword(s):  
Mathematical Modeling ◽  
Liquid Mixture ◽  
Solid Phase ◽  
Deformation Gradient ◽  
Elastic Solid ◽  
Solid Deformation ◽  
Solid Stress ◽  
Phase Deformation ◽  
Mass Conversion ◽  
Solid Liquid

The mechanical behavior of a mixture composed by an elastic solid and a fluid that exchange mass is investigated. Both the liquid flow and the solid deformation depend on how the solid phase has increased (diminished) its mass, i.e. on the mass conversion between constituents. The model is developed introducing a decomposition of the solid phase deformation gradient. In particular, exploiting the criterion of maximization of the rate of entropy production, we determine an explicit evolution equation for the so-called growth tensor which involves directly the solid stress tensor. An example of a possible choice of the constitutive functions is also presented.

Size-dependent Phase Transformations During Point Loading of Silicon

2000 ◽  
Vol 15 (8) ◽  
pp. 1754-1758 ◽  
Author(s):  
A. B. Mann ◽  
D. van Heerden ◽  
J. B. Pethica ◽  
T. P. Weihs
Keyword(s):  
Phase Transformations ◽  
Strong Dependence ◽  
The Body ◽  
Ex Situ ◽  
Stress Fields ◽  
Rhombohedral Structure ◽  
Size Dependent ◽  
Transmission Electron ◽  
Contact Size

Using a unique combination of in situ electrical and acoustical measurements and ex situ transmission electron microscopy, the phase transformations of silicon during point loading were shown to exhibit a strong dependence on the size of the deformed volume. For nanometer-size volumes of silicon, the final phase was the body centered cubic structure BC8, but for larger volumes it was amorphous. The size dependence was explained by considering how shear stress fields vary with contact size and how interfacial effects between the silicon substrate and the BC8 phase determine its stability. For both small and large contacts the presence of a nonmetallic phase (assumed to be the Rhombohedral structure R8) was observed.

Steady-State Crack Propagation in Stressed Elastic Solid

2011 ◽  
Vol 462-463 ◽  
pp. 495-500
Author(s):  
Nikolay I. Chekunaev
Keyword(s):  
Asymptotic Behavior ◽  
Steady State ◽  
Crack Propagation ◽  
Rayleigh Waves ◽  
Elastic Solid ◽  
The Self ◽  
Stress Fields ◽  
Self Similar ◽  
Loaded Crack ◽  
Similar Growth

A crack, symmetrically propagating in elastic material, was considered as superposition of surface Rayleigh waves. The self-similar growth of face loaded crack was considered in detail. Exact expressions of deformation and stress fields in the crack’s surrounding were found and asymptotic behavior of stress near cracks’ tips was also obtained. A condition that determines the crack’s velocity of self-similar propagation was found.

The Stress Fields Caused by a Circular Cylindrical Inclusion

1992 ◽  
Vol 59 (2S) ◽  
pp. S107-S114 ◽  
Author(s):  
Hisao Hasegawa ◽  
Ven-Gen Lee ◽  
Toshio Mura
Keyword(s):  
Exact Solutions ◽  
Strain Energy ◽  
Elastic Solid ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Axisymmetric Stress ◽  
Displacement Fields ◽  
Elastic Fields ◽  
Stress And Displacement Fields ◽  
Interior Points

Exact solutions are presented in closed forms for the axisymmetric stress and displacement fields caused by a solid or hollow circular cylindrical inclusion (with uniform axial eigenstrain prescribed) in an infinite elastic solid. The same expressions are obtained for the elastic fields for interior and exterior points of the inclusion. Although Eshelby’s solutions for ellipsoidal inclusions are uniform in the interior points, the present solutions do not show the uniformity. When the length of inclusion becomes infinite, the present solutions agree with Eshelby ’s results. The strain energy is also shown. The method of Green’s function is used.

Size Dependent Stiffness of Composite Ceramic with Partial Debonding Interphase

2010 ◽  
Vol 105-106 ◽  
pp. 55-58 ◽  
Author(s):  
Xie Quan Liu ◽  
Bao Feng Li ◽  
Lei Zhao ◽  
Guo Hui Zhong
Keyword(s):  
Composite Ceramic ◽  
Effective Stiffness ◽  
Phase Model ◽  
Volume Fractions ◽  
Size Dependent ◽  
Model Method ◽  
Large Influence ◽  
The Matrix

The partial debonding interphase has large influence on the behaviors of composite ceramic. The emerging cause of partial debonding interphase is interpreted and the interaction between particles and partial debonding interphase is accounted for determining the equivalent eigen strains by using the four phase model method. Then the effective stiffness of composite ceramic is estimated. The results show the effective stiffness is associated with the stiffness of the matrix and particles, the volume fractions of particles and partial debonding interphase, the subtending angle and thickness of partial debonding interphase.

Production and STEM examination of controlled-size silver clusters

1983 ◽  
Vol 41 ◽  
pp. 338-339
Author(s):  
M. A. Listvan ◽  
R. P. Andres
Keyword(s):  
Cluster Size ◽  
Metal Clusters ◽  
Experimental Parameter ◽  
Carbon Films ◽  
Metal Species ◽  
Silver Clusters ◽  
Free Jet ◽  
Size Dependent ◽  
Cluster Properties ◽  
Controllable Size

Knowledge of the function and structure of small metal clusters is one goal of research in catalysis. One important experimental parameter is cluster size. Ideally, one would like to produce metal clusters of regulated size in order to characterize size-dependent cluster properties.A source has been developed which is capable of producing microscopic metal clusters of controllable size (in the range 5-500 atoms) This source, the Multiple Expansion Cluster Source, with a Free Jet Deceleration Filter (MECS/FJDF) operates as follows. The bulk metal is heated in an oven to give controlled concentrations of monomer and dimer which were expanded sonically. These metal species were quenched and condensed in He and filtered to produce areosol particles of a controlled size as verified by mass spectrometer measurements. The clusters were caught on pre-mounted, clean carbon films. The grids were then transferred in air for microscopic examination. MECS/FJDF was used to produce two different sizes of silver clusters for this study: nominally Ag6 and Ag50.

Transfer Technique for Electron Microscopy of Membrance Filter Samples

1974 ◽  
Vol 32 ◽  
pp. 554-555
Author(s):  
Lawrence W. Ortiz ◽  
Bonnie L. Isom
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Pore Size ◽  
Membrane Filters ◽  
Size Dependent

A procedure is described for the quantitative transfer of fibers and particulates collected on membrane filters to electron microscope (EM) grids. Various Millipore MF filters (Millipore AA, HA, GS, and VM; 0.8, 0.45, 0.22 and 0.05 μm mean pore size) have been used with success. Observed particle losses have not been size dependent and have not exceeded 10%. With fibers (glass or asbestos) as the collected media this observed loss is approximately 3%.

Simulation of three Dimensional Defect Images in Transmission Electron Microscopy

1976 ◽  
Vol 34 ◽  
pp. 470-471
Author(s):  
W. D. Cooper ◽  
C. S. Hartley ◽  
J. J. Hren
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Three Dimensional ◽  
Crystalline Lattice ◽  
Continuum Models ◽  
Thin Foils ◽  
Transmission Electron ◽  
Microscope Images ◽  
General Computer Program ◽  
General Computer

Interpretation of electron microscope images of crystalline lattice defects can be greatly aided by computer simulation of theoretical contrast from continuum models of such defects in thin foils. Several computer programs exist at the present time, but none are sufficiently general to permit their use as an aid in the identification of the range of defect types encountered in electron microscopy. This paper presents progress in the development of a more general computer program for this purpose which eliminates a number of restrictions contained in other programs. In particular, the program permits a variety of foil geometries and defect types to be simulated.The conventional approximation of non-interacting columns is employed for evaluation of the two-beam dynamical scattering equations by a piecewise solution of the Howie-Whelan equations.

Spindle scaling mechanisms

2020 ◽  
Vol 64 (2) ◽  
pp. 383-396
Author(s):  
Lara K. Krüger ◽  
Phong T. Tran
Keyword(s):  
Cell Size ◽  
Spindle Assembly ◽  
Dependent Manner ◽  
Post Translational Modification ◽  
Size Dependent ◽  
A Cell ◽  
Chromosome Separation ◽  
Spindle Elongation ◽  
Protein Gradients ◽  
Spindle Structure

Abstract The mitotic spindle robustly scales with cell size in a plethora of different organisms. During development and throughout evolution, the spindle adjusts to cell size in metazoans and yeast in order to ensure faithful chromosome separation. Spindle adjustment to cell size occurs by the scaling of spindle length, spindle shape and the velocity of spindle assembly and elongation. Different mechanisms, depending on spindle structure and organism, account for these scaling relationships. The limited availability of critical spindle components, protein gradients, sequestration of spindle components, or post-translational modification and differential expression levels have been implicated in the regulation of spindle length and the spindle assembly/elongation velocity in a cell size-dependent manner. In this review, we will discuss the phenomenon and mechanisms of spindle length, spindle shape and spindle elongation velocity scaling with cell size.

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