Strain Tensors at the Atomic Scale

1999 ◽  
Vol 578 ◽  
Author(s):  
M.F. Horstemeyer ◽  
M.I. Baskes
Keyword(s):  
Weighting Function ◽  
Scalar Potential ◽  
Deformation Gradient ◽  
Local Strain ◽  
Small Strain ◽  
Lattice Parameter ◽  
Atomic Scale ◽  
Inhomogeneous Deformation ◽  
Green Strain ◽  
Strain Tensors

AbstractAlmansi and Green strain tensors are developed for use in large deformation molecular dynamics/statics simulations that employ Embedded Atom Method (EAM) potentials for metals. The strain tensors are formulated with respect to the deformation gradient. A scalar potential function is used with a weighting function that is dependent upon a cutoff radius for the deformation gradient. For a homogeneous or inhomogeneous deformation, a cutoff distance of one lattice parameter can be used to approximate local strain level. Inhomogeneous deformation reveals different results for Almansi and Green strain tensors indicating that the small strain assumption cannot be used to determine large atomic strains.

scholarly journals The Definition Method and Optimization of Atomic Strain Tensors for Nuclear Power Engineering Materials

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Xiangguo Zeng ◽  
Ying Sheng ◽  
Huayan Chen ◽  
Tixin Han
Keyword(s):  
Weight Function ◽  
Optimization Model ◽  
Nuclear Power ◽  
Weighted Least Squares ◽  
Deformation Gradient ◽  
Local Deformation ◽  
Parameters Identification ◽  
Atomic Scale ◽  
Overall Analysis Method ◽  
Strain Tensors

A common measure of deformation between atomic scale simulations and the continuum framework is provided and the strain tensors for multiscale simulations are defined in this paper. In order to compute the deformation gradient of any atomm, the weight function is proposed to eliminate the different contributions within the neighbor atoms which have different distances to atomm, and the weighted least squares error optimization model is established to seek the optimal coefficients of the weight function and the optimal local deformation gradient of each atom. The optimization model involves more than 9 parameters. To guarantee the reliability of subsequent parameters identification result and lighten the calculation workload of parameters identification, an overall analysis method of parameter sensitivity and an advanced genetic algorithm are also developed.

Quasiperiodic interfaces: HREM observations of grain and phase boundaries

1990 ◽  
Vol 48 (4) ◽  
pp. 332-333
Author(s):  
K. L. Merkle
Keyword(s):  
Atomic Structure ◽  
Direct Determination ◽  
Lattice Parameter ◽  
Atomic Scale ◽  
Misfit Dislocations ◽  
Oxide Systems ◽  
Atomic Structures ◽  
Periodic Arrays ◽  
Parameter Ratio ◽  
Metal Metal

The atomic structures of internal interfaces have recently received considerable attention, not only because of their importance in determining many materials properties, but also because the atomic structure of many interfaces has become accessible to direct atomic-scale observation by modem HREM instruments. In this communication, several interface structures are examined by HREM in terms of their structural periodicities along the interface.It is well known that heterophase boundaries are generally formed by two low-index planes. Often, as is the case in many fcc metal/metal and metal/metal-oxide systems, low energy boundaries form in the cube-on-cube orientation on (111). Since the lattice parameter ratio between the two materials generally is not a rational number, such boundaries are incommensurate. Therefore, even though periodic arrays of misfit dislocations have been observed by TEM techniques for numerous heterophase systems, such interfaces are quasiperiodic on an atomic scale. Interfaces with misfit dislocations are semicoherent, where atomically well-matched regions alternate with regions of misfit. When the misfit is large, misfit localization is often difficult to detect, and direct determination of the atomic structure of the interface from HREM alone, may not be possible.

Structural Properties of InAs/AlSb Superlattices

1995 ◽  
Vol 379 ◽  
Author(s):  
B. Jenichen ◽  
H. Neuroth ◽  
B. Brar ◽  
H. Kroemer
Keyword(s):  
Buffer Layer ◽  
Peak Shift ◽  
Lattice Parameter ◽  
Structural Quality ◽  
Inhomogeneous Deformation ◽  
X Ray ◽  
Peak Broadening ◽  
Short Period ◽  
Intensity Ratios ◽  
Highly Correlated

ABSTRACTShort-period (InAs)6/(AlSb)6 superlattices (SL) with AlAs-like and InSb-like interfaces (IF) grown on a relaxed AlSb buffer layer are studied by X-ray reflectivity and diffractometry measurements. Reflectivity measurements reveal average IF roughnesses between 0.6 and 1.0 nm. Measurements of the diffuse scattering show that the roughness is highly correlated from layer to layer. Triple crystal area scans illustrate that the inhomogeneous deformation of the buffer layer leads to a certain symmetric peak broadening. In the case of AlAs-like IFs an additional broadening of the SL peaks reveals lattice parameter gradients over the superlattice. This asymmetric peak broadening may be attributed to a further relaxation of the superlattice, which is inhomogeneous with depth. The diffusion of As into the AlSb layers leads to a peak shift and modifies the intensity ratios of the different satellite reflections. The best structural quality is achieved for superlattices with InSb-like IFs.

scholarly journals Effect of Fiber and Cement Additives on the Small-Strain Stiffness Behavior of Toyoura Sand

2020 ◽  
Vol 12 (24) ◽  
pp. 10468
Author(s):  
Muhammad Safdar ◽  
Tim Newson ◽  
Colin Schmidt ◽  
Kenichi Sato ◽  
Takuro Fujikawa ◽  
...  
Keyword(s):  
Model Comparison ◽  
Local Strain ◽  
Small Strain ◽  
Experimental Results ◽  
Compression Tests ◽  
Cemented Sand ◽  
Strain Measurements ◽  
Good Comparison ◽  
Toyoura Sand ◽  
Comparison Of The Results

The disposal of 2011 Japan earthquake waste has become an important issue in Japan and it is not realistic or economical to send all of these wastes to landfill sites, due to limited space, high costs, and related environmental issues. In sustainable geotechnical applications, mixing of the separated soils from disaster wastes with additives (e.g., cement and fiber) is required to improve their strength and stiffness characteristics. In this study, monotonic triaxial drained compression tests are performed on medium dense specimens of Toyoura sand-cement-fiber mixtures with different percentages of fiber and cement (e.g., 0–3%) additives. The experimental results indicate that behavior of the mixtures is significantly affected by the concentration of fiber and cement additives. Based on a comprehensive set of test results, modifications to the series of equations were developed that can be used to evaluate the shear modulus and mobilized stress curves at small-strain levels. The experimental results and model comparison show that the elastic threshold strain (γe), reference strain (γr), increases with fiber and cement additives. In addition, the range of curvature parameter, from 0.88 to 1.0, provides a good comparison with the results of small-strain measurements. Overall, the comparison of the results and model shows that the small-strain measurements obtained using local strain transducers fall within the range of model upper and lower bound curves. The results of the unreinforced, fiber, and cemented sand shows a close agreement with the model mean curve, but fiber-reinforced cemented sand shows a good comparison with model upper bound.

scholarly journals The Measurement of the Silicon Lattice Parameter and the Count of Atoms to Realise the Kilogram

MAPAN ◽  
2020 ◽  
Author(s):  
Enrico Massa ◽  
Carlo Paolo Sasso ◽  
Giovanni Mana
Keyword(s):  
International System ◽  
Lattice Parameter ◽  
Atomic Scale ◽  
X Rays ◽  
Planck Constant ◽  
Contrast Imaging ◽  
Silicon Lattice ◽  
System Of Units ◽  
History Of ◽  
Optical Wavelengths

AbstractX-ray interferometry established a link between atomic and macroscopic realisations of the metre. The possibility of measuring the silicon lattice parameter in terms of optical wavelengths opened the way to count atoms, to determine the Avogadro constant with unprecedented accuracy, and, nowadays, to realise the kilogram from the Planck constant. Also, it is a powerful tool in phase-contrast imaging by X-rays and, combined with optical interferometry, in linear and angular metrology with capabilities at the atomic scale. This review tells the history of the development of this fascinating technology at the Istituto Nazionale di Ricerca Metrologica in the last forty years. Eventually, it highlights its contribution to the redefinition of the International System of Units (SI).

A large deformation framework for shape memory polymers: Constitutive modeling and finite element implementation

2012 ◽  
Vol 24 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Mostafa Baghani ◽  
Reza Naghdabadi ◽  
Jamal Arghavani
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Shape Memory ◽  
Finite Deformation ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Shape Memory Polymers ◽  
Small Strain ◽  
Internal Variables

Shape memory polymers commonly experience both finite deformations and arbitrary thermomechanical loading conditions in engineering applications. This motivates the development of three-dimensional constitutive models within the finite deformation regime. In the present study, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite deformation phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Baghani et al. (2012). In the constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic stored parts (in each phase) is adopted. Moreover, employing the mixture rule, the Green–Lagrange strain tensor is related to the rubbery and glassy parts. In the constitutive model, the evolution laws for internal variables are derived during both cooling and heating thermomechanical loadings. Furthermore, we present the time-discrete form of the proposed constitutive model in the implicit form. Using the finite element method, we solve several boundary value problems, that is, tension and compression of bars and a three-dimensional beam made of shape memory polymers, and investigate the model capabilities as well as its numerical counterpart. The model is validated by comparing the predicted results with experimental data reported in the literature that shows a good agreement.

scholarly journals 2-D finite displacements and strain from particle imaging velocimetry (PIV) analysis of tectonic analogue models with TecPIV

Solid Earth ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1123-1139 ◽  
Author(s):  
David Boutelier ◽  
Christoph Schrank ◽  
Klaus Regenauer-Lieb
Keyword(s):  
Software Package ◽  
Finite Strain ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Small Strain ◽  
Time Lapse ◽  
Image Correlation ◽  
Strain Rate Tensor ◽  
Analogue Models ◽  
Finite Displacements

Abstract. Image correlation techniques have provided new ways to analyse the distribution of deformation in analogue models of tectonics in space and time. Here, we demonstrate, using a new version of our software package (TecPIV), how the correlation of successive time-lapse images of a deforming model allows not only to evaluate the components of the strain-rate tensor at any time in the model but also to calculate the finite displacements and finite strain tensor. We illustrate with synthetic images how the algorithm produces maps of the velocity gradients, small-strain tensor components, incremental or instantaneous principal strains and maximum shear. The incremental displacements can then be summed up with Eulerian or Lagrangian summation, and the components of the 2-D finite strain tensor can be calculated together with the finite principal strain and maximum finite shear. We benchmark the measures of finite displacements using specific synthetic tests for each summation mode. The deformation gradient tensor is calculated from the deformed state and decomposed into the finite rigid-body rotation and left or right finite-stretch tensors, allowing the deformation ellipsoids to be drawn. The finite strain has long been the only quantified measure of strain in analogue models. The presented software package allows producing these finite strain measures while also accessing incremental measures of strain. The more complete characterisation of the deformation of tectonic analogue models will facilitate the comparison with numerical simulations and geological data and help produce conceptual mechanical models.

On the Determination of Entropy From a Scalar Potential for Special Inelastic Materials

1999 ◽  
Author(s):  
George C. Johnson ◽  
Ali Imam
Keyword(s):  
Energy Function ◽  
Helmholtz Free Energy ◽  
Scalar Potential ◽  
Deformation Gradient ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Free Energy Function ◽  
Response Functions ◽  
Constitutive Response

Abstract A known version of the second law of thermodynamics embodying the notion of dissipation is employed to obtain restrictions among constitutive response functions for two classes of inelastic bodies. It is shown that for such bodies the entropy function can be determined once the constitutive relation for the Helmholtz free energy function is specified. In addition the internal energy function is shown to depend exclusively on the temperature and the deformation gradient.

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