scholarly journals Differential Geometry Approach to Continuous Model of Micro-Structural Defects in Finite Elasto-Plasticity

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2340
Author(s):  
Sanda Cleja-Ţigoiu
Keyword(s):  
Point Defects ◽  
Torsion Tensor ◽  
Decomposition Theorem ◽  
The Body ◽  
Lattice Defects ◽  
Structural Defects ◽  
Metric Tensor ◽  
Plastic Distortion ◽  
Elasto Plasticity ◽  
Differential Manifold

This paper concerns finite elasto-plasticity of crystalline materials with micro-structural defects. We revisit the basic concepts: plastic distortion and decomposition of the plastic connection. The body is endowed with a structure of differential manifold. The plastic distortion is an incompatible diffeomorphism. The metric induced by the plastic distortion on the intermediate configuration (considered to be a differential manifold) is a key point in the theory, in defining the defects related to point defects, or extra-matter. The so-called plastic connection is metric, with plastic metric tensor expressed in terms of the plastic distortion and its adjoint. We prove an appropriate decomposition of the plastic connection, without any supposition concerning the non-metricity of plastic connection. All types of the lattice defects, dislocations, disclinations, and point defects are described in terms of the densities related to the elements that characterize the decomposition theorem for plastic connection. As a novelty, the measure of the interplay of the possible lattice defects is introduced via the Cartan torsion tensor. To justify the given definitions, the proposed measures of defects are compared to their counterparts corresponding to a classical framework of continuum mechanics. Thus, their physical meanings can be emphasized at once.

scholarly journals Reconfiguration of Point Defects in FCC and HCP Metals at Initial Stage of Recovery Process/ Rekonfiguracja Struktury Defektów Sieciowych W Początkowym Stadium Zdrowienia Metali O Sieci Rsc I Hz

2014 ◽  
Vol 59 (4) ◽  
pp. 1321-1325
Author(s):  
G. Boczkal ◽  
M. Perek-Nowak
Keyword(s):  
Point Defects ◽  
Recovery Time ◽  
Recovery Process ◽  
Lattice Defects ◽  
Initial Stage ◽  
Analysis Of Change

Abstract The conducted studies regarded the analysis of change of structure of point defects occurring during initial stage of recovery of FCC (Al, Cu) and HCP (Ti, Mg and Zn) metals at temperature close to Th =0.5Tm. The changes in resistivity of the deformed and later recovered samples were measured. The recovery time was 1, 2, 3, 4 or 5 min. The observed changes were correlated with reorganization of arrangement of lattice defects during annealing.

Defect-induced vibrational response of multi-walled carbon nanotubes using resonance Raman spectroscopy

2005 ◽  
Vol 20 (12) ◽  
pp. 3368-3373 ◽  
Author(s):  
S.A. Curran ◽  
J.A. Talla ◽  
D. Zhang ◽  
D.L. Carroll
Keyword(s):  
Carbon Nanotubes ◽  
Raman Spectroscopy ◽  
Acid Treatment ◽  
Defect Formation ◽  
Double Resonance ◽  
Resonance Raman ◽  
The Body ◽  
Structural Defects ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

We systematically introduced defects onto the body of multi-walled carbon nanotubes through an acid treatment, and the evolution of these defects was examined by Raman spectroscopy using different excitation wavelengths. The D and D′ modes are most prominent and responsive to defect formation caused by acid treatment and exhibit dispersive behavior upon changing the excitation wavelengths as expected from the double resonance Raman (DRR) mechanism. Several weaker Raman resonances including D″ and L1 (L2) + D′ modes were also observed at the lower excitation wavelengths (633 and 785 nm). In addition, specific structural defects including the typical pentagon-heptagon structure (Stone–Wales defects) were identified by Raman spectroscopy. In a closer analysis we also observed Haeckelite structures, specifically Ag mode response in R5,7 and O5,6,7.

Recent Progress in Understanding of Lattice Defects in Czochralski-Grown Germanium: Catching-up with Silicon

2005 ◽  
Vol 108-109 ◽  
pp. 683-690 ◽  
Author(s):  
Jan Vanhellemont ◽  
Steven Hens ◽  
J. Lauwaert ◽  
Olivier De Gryse ◽  
Piet Vanmeerbeek ◽  
...  
Keyword(s):  
Point Defects ◽  
Recent Progress ◽  
Lattice Defects ◽  
Interstitial Oxygen ◽  
Intrinsic Point Defects ◽  
Catching Up

Recent progress is presented in the understanding of grown-in defects in Czochralskigrown germanium crystals with special emphasis on intrinsic point defects, on vacancy clustering and on interstitial oxygen. Whenever useful the results are compared with those obtained for silicon.

Point Defects in Doped and Undoped Hgl−xCdxTe Alloys

1981 ◽  
Vol 9 ◽  
Author(s):  
H. R. Vydyanath
Keyword(s):  
Point Defects ◽  
Chemical Species ◽  
Lattice Defects ◽  
Mass Action ◽  
Electrical Characteristics ◽  
Law Of Mass Action ◽  
Physicochemical Conditions

EXTENDED ABSTRACTUsing a law of mass action approach in which lattice defects are treated as chemical species, the variation of the defect concentrations as a function of .the physicochemical conditions of preparation has been established via measurements of electrical characteristics which are directly related to the defect concentrations.

scholarly journals Derivation of Field Equations in Space with the Geometric Structure Generated by Metric and Torsion

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Nikolay Yaremenko
Keyword(s):  
Curvature Tensor ◽  
Geometric Structure ◽  
Jacobi Identity ◽  
Torsion Tensor ◽  
Variation Principle ◽  
Field Equations ◽  
Metric Tensor ◽  
Fundamental Tensor ◽  
Geodesic Lines ◽  
General Field

This paper is devoted to the derivation of field equations in space with the geometric structure generated by metric and torsion tensors. We also study the geometry of the space generated jointly and agreed on by the metric tensor and the torsion tensor. We showed that in such space the structure of the curvature tensor has special features and for this tensor we obtained analog Ricci-Jacobi identity and evaluated the gap that occurs at the transition from the original to the image and vice versa, in the case of infinitely small contours. We have researched the geodesic lines equation. We introduce the tensor παβ which is similar to the second fundamental tensor of hypersurfaces Yn-1, but the structure of this tensor is substantially different from the case of Riemannian spaces with zero torsion. Then we obtained formulas which characterize the change of vectors in accompanying basis relative to this basis itself. Taking into considerations our results about the structure of such space we derived from the variation principle the general field equations (electromagnetic and gravitational).

Magnetic-Field-Induced Modification of Properties of Silicon Lattice Defects

2005 ◽  
Vol 108-109 ◽  
pp. 339-344 ◽  
Author(s):  
V.A. Makara ◽  
L.P. Steblenko ◽  
Yu.L. Kolchenko ◽  
S.M. Naumenko ◽  
O.A. Patran ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Lattice Defects ◽  
Structural Defects ◽  
Silicon Lattice ◽  
Silicon Crystals ◽  
Field Action

A possibility of magnetic-field-induced modification of structural defects in silicon crystals is studied. It is shown that magnetic field action essentially affects the structuredependent properties of Si (mechanical and electrophysical)

scholarly journals Weyl geometry and the nonlinear mechanics of distributed point defects

2012 ◽  
Vol 468 (2148) ◽  
pp. 3902-3922 ◽  
Author(s):  
Arash Yavari ◽  
Alain Goriely
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Point Defect ◽  
Point Defects ◽  
Spherical Inclusion ◽  
The Body ◽  
Inclusion Problem ◽  
Spherically Symmetric ◽  
Residual Stress Field ◽  
Defect Distribution

The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects—where the body is stress-free—is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but both its torsion and curvature tensors vanish. Given a spherically symmetric point defect distribution, we construct its Weyl material manifold using the method of Cartan's moving frames. Having the material manifold, the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the Euclidean ambient space. In the case of incompressible neo-Hookean solids, we calculate explicitly this residual stress field. We consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere. We show that the residual stress field inside the smaller ball is uniform and hydrostatic. We also prove a nonlinear analogue of Eshelby's celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid.

HAMILTONIANS IN OBLIQUE BODY-FRAME: A GEOMETRIC ALGEBRA APPROACH

2005 ◽  
Vol 04 (04) ◽  
pp. 1057-1074
Author(s):  
JANNE PESONEN
Keyword(s):  
Energy Operator ◽  
The Body ◽  
Body Frame ◽  
Metric Tensor ◽  
Inner Products ◽  
Algebra Approach ◽  
Rotational Part ◽  
Vibration Rotation ◽  
Arbitrary Body ◽  
Derivatives Of

In this work, I present a practical way to obtain the vibration-rotation kinetic energy operator for an N-atomic molecule in an arbitrary body-frame [Formula: see text]. The body-frame need not be orthogonal or rigid. In practice, I derive the explicit form of the measuring vectors associated with the body-frame components of the internal angular momentum. Their inner products with the vector derivatives of the shape coordinates give the "Coriolis" part of the metric tensor appearing in the Hamiltonian, and their inner products among themselves give the "rotational" part. As a simple example, the measuring vectors are explicitly derived in an oblique bond-vector body-frame. The metric tensor elements are also derived for a tetra-atomic pyramidal molecule, whose shape is parametrized in bond-angle coordinates.

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