scholarly journals The Nonlinear evolutionary problem for self-stressed multilayered hyperelastic spherical bodies

2020 ◽  
pp. 43-59
Author(s):  
S A Lychev ◽  
T N Lycheva ◽  
K G Koifman
Keyword(s):  
Continuum Mechanics ◽  
Continuous Functions ◽  
Finite Deformations ◽  
Preliminary Deformation ◽  
Multilayered Structures ◽  
Metric Tensor ◽  
Number Of Layers ◽  
Evolutionary Problem ◽  
Reference Shape ◽  
The Individual

The present paper studies the evolutionary problem for self-stressed multilayered spherical shells. Their stress-strain state is characterized by incompatible local finite deformations that arise due to the geometric incompatibility of the stress-free shapes of the individual layers with each other. In the considered problem, these shapes are thin-walled hollow balls that cannot be assembled into a single solid without gaps or overlaps. Such an assembly is possible only with the preliminary deformations of individual layers, which cause self-balanced stresses in them. For multilayered structures with a large number of layers, a smoothing procedure is proposed, as a result of which the piecewise continuous functions defining the preliminary deformation of the layers are replaced by continuous distributions. The reference stress-free shape of a body constructed in this way is defined within the framework of geometric continuum mechanics as a manifold with a non-Euclidean (material) connection. For the problem in question, this connection is determined by the metric tensor and its deviation from the Euclidean connection is characterized by the scalar curvature. Generalized representations for Cauchy and Piola stresses are also obtained by the methods of geometric continuum mechanics. Computations, provided for the discrete structure and body with a non-Euclidean reference shape defined by the approximation of deformation parameters, numerically illustrate the convergency of the solution for the discrete model to corresponded solution for the continuous problem if the number of layers is increasing while their total thickness is constant. In modelling it is assumed that the material of the layers is compressible, homogeneous, hyperelastic, and determined by the first-order Mooney - Rivlin elastic potential. Individual layerwise finite deformations are supposed to be centrally symmetric.

scholarly journals Material Geometry of Binary Composites

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 892
Author(s):  
Marcelo Epstein
Keyword(s):  
Continuum Mechanics ◽  
Mathematical Framework ◽  
Double Groupoid ◽  
The Individual ◽  
Elastic Composites

The constitutive characterization of the uniformity and homogeneity of binary elastic composites is presented in terms of a combination of the material groupoids of the individual constituents. The incorporation of these two groupoids within a single double groupoid is proposed as a viable mathematical framework for a unified formulation of this and similar kinds of problems in continuum mechanics.

Phase Formation in Cr/Co/Au and Cr/Co/Au/Pb(Sn) Multilayered Structures

1990 ◽  
Vol 203 ◽  
Author(s):  
Michael A. Moske ◽  
Paul S. Ho ◽  
Alexander T. Nering ◽  
Birendra N. Agarwala
Keyword(s):  
Multilayer Structure ◽  
Reaction Scheme ◽  
Intermetallic Phases ◽  
Subsequent Reaction ◽  
Multilayered Structures ◽  
X Ray ◽  
Individual Reaction ◽  
Beam Method ◽  
Rapid Dissolution ◽  
The Individual

ABSTRACTThin-film reaction with solder and its influence on stress have been investigated in Cr/Co/Au and Cr/Co/Au/Pb(Sn) structures. Results from X-ray analysis and RBS measurements reveal that without the Pb(Sn) layer the dominant reaction occurs by interdiffusion of Co and Cr followed by the reaction of Cr and Au. In contrast, the addition of the Pb(Sn) layer leads to a rapid dissolution of Au into Pb, which is followed by subsequent reaction of Co and Sn. In this reaction the intermetallic phases CoSn and CoSn2 are formed. These material reactions are correlated with measurements of the mechanical stresses of the multilayer structure during annealing which were carried out using a bending beam method. The overall reaction scheme of the multilayer structure and the individual reaction kinetics are discussed.

A Tree-Structured Algorithm for Reducing Computation in Networks with Separable Basis Functions

1991 ◽  
Vol 3 (1) ◽  
pp. 67-78 ◽  
Author(s):  
Terence D. Sanger
Keyword(s):  
Input Data ◽  
Continuous Functions ◽  
Basis Functions ◽  
Tree Structure ◽  
High Dimensional ◽  
Efficient Computation ◽  
Variable Size ◽  
Differential Delay Equation ◽  
Differential Delay ◽  
The Individual

I describe a new algorithm for approximating continuous functions in high-dimensional input spaces. The algorithm builds a tree-structured network of variable size, which is determined both by the distribution of the input data and by the function to be approximated. Unlike other tree-structured algorithms, learning occurs through completely local mechanisms and the weights and structure are modified incrementally as data arrives. Efficient computation in the tree structure takes advantage of the potential for low-order dependencies between the output and the individual dimensions of the input. This algorithm is related to the ideas behind k-d trees (Bentley 1975), CART (Breiman et al. 1984), and MARS (Friedman 1988). I present an example that predicts future values of the Mackey-Glass differential delay equation.

Mechanical Properties of Single and Double-Layered PVA Nanofibers

2013 ◽  
Vol 586 ◽  
pp. 261-264 ◽  
Author(s):  
Pavel Tesárek ◽  
Pavla Ryparová ◽  
Zuzana Rácová ◽  
Vlastimil Králík ◽  
Jiří Němeček ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Tensile Strength ◽  
Unit Area ◽  
Number Of Layers ◽  
Average Tensile Strength ◽  
The Individual

Multi-layered nanofiber textiles can be utilized in many applications. In such case the individual layers are laid in more stages and the question arises whether the connection is perfect. Two kinds of samples of PVA nanotextiles having the weight of 1.3 g/m2 (single-layered, AI) and 2.8 g/m2 (double-layered, AII), respectively. It was shown that mechanical properties, in particular the average tensile strength (24 N/mm for AI and 51 N/mm for AII) and stiffness (950 N/mm for AI and 1600 N/mm for AII), are independent of the number of layers, only their weight per unit area matters. This indicates that the bond between the individual layers is perfect.

Surrogate-Based Modeling and Dimension-Reduction Techniques for Thermo-Fluid and Energy Systems

2011 ◽  
Author(s):  
Young-Chang Cho ◽  
Wenbo Du ◽  
Amit Gupta ◽  
Chien-Chou Tseng ◽  
Ann Marie Sastry ◽  
...  
Keyword(s):  
Active Flow Control ◽  
Energy Systems ◽  
Continuous Functions ◽  
Reduction Techniques ◽  
Design Variables ◽  
Important Input ◽  
Comprehensive Evaluations ◽  
Input Variables ◽  
The Individual ◽  
The Impact

Successful modeling and/or design of thermo-fluid and energy systems often requires one to address the impact of multiple “design variables” on the prescribed outcome. There are often multiple, competing objectives based on which we assess the outcome of optimization. Since accurate, high fidelity models are typically time consuming and computationally expensive, comprehensive evaluations can be conducted only if an efficient framework is available. Furthermore, informed decisions of model/hardware’s overall performance rely on an adequate understanding of the global, not local, sensitivity of the individual design variables on the objectives. The surrogate-based approach, which involves approximating the objectives as continuous functions of design variables from limited data, offers a rational framework to reduce the number of important input variables, i.e., the dimension of a design or modeling space. In this paper, we discuss the fundamental issues that arise in surrogate-based analysis and optimization, highlighting concepts, methods, techniques, as well as practical implications. To aid the discussions of the issues involved, we will summarize recent efforts in investigating cryogenic cavitating flows, active flow control based on dielectric barrier discharge concepts, and Li-ion batteries.

Electromagnetic soundings in the sedimentary basin of southern Ontario—A case history

Geophysics ◽  
1983 ◽  
Vol 48 (3) ◽  
pp. 311-330 ◽  
Author(s):  
E. Gómez‐Trevino ◽  
R. N. Edwards
Keyword(s):  
Apparent Resistivity ◽  
Sedimentary Basin ◽  
Joint Inversion ◽  
Earth Model ◽  
Electrical Model ◽  
Southern Ontario ◽  
Number Of Layers ◽  
Electromagnetic Soundings ◽  
Minimum Number ◽  
The Individual

The results of electrical and electromagnetic (EM) soundings conducted in the sedimentary basin of southern Ontario are presented. The sounding sites are located strategically to take advantage of the dipping nature of the sediments, a progressive study being undertaken from shallow to deep sections. The vertical magnetic field transfer function, estimated with a pseudonoise source EM system, and conventional Schlumberger apparent resistivity are jointly inverted. For each site, the layered earth model containing the minimum number of layers is fitted to the data. The joint inversion enables up to eight distinct layers to be identified at some sites. The nonuniquenesses or ambiguities in each model, for example S (conductivity‐thickness product) equivalence of a deep thin conductive layer, are revealed through an eigensolution analysis. The intrinsic ambiguities of the models of the deeper sections are resolved by a systematic, progressive site‐to‐site correlation of electrical units across the basin. For example, the conductivity of a conductive unit is measurable when it is at a shallow depth. In a deeper section, if the unit appears as a thin layer, it is assigned this value of conductivity removing the S‐equivalence ambiguity. The individual inversions combined with the site‐to‐site correlation produce an overall electrical model of the basin consistent with the known geologic section.

Structural and Electronic Properties of Pb/Cu Multilayers

1989 ◽  
Vol 160 ◽  
Author(s):  
D. Neerinck ◽  
K. Temst ◽  
H. Vanderstraeten ◽  
C. Van Haesendonck ◽  
Y. Bruynseraede ◽  
...  
Keyword(s):  
Electronic Properties ◽  
Mean Free Path ◽  
Diffraction Spectrum ◽  
Superconducting Transition ◽  
X Ray Diffraction ◽  
Multilayered Structures ◽  
X Ray ◽  
Structural And Electronic Properties ◽  
The Individual ◽  
Interfacial Scattering

AbstractWe have performed extensive structural and electronic transport measurements of Pb/Cu multilayered structures. The high-angle x-ray diffraction spectrum indicates the presence of continuous interfacial disorder. In the low-angle x-ray spectrum, pronounced minima occur at positions given by q = 2π/Λ, where Λ is the bilayer thickness. This is in sharp contrast to the results for Pb/Ge (crystalline/amorphous) multilayers, where minima are observed at positions q = 2π / tPb with tPb the Pb thickness. These low-angle x-ray spectra can be explained by taking into account lateral coherence and continuously distributed thickness fluctuations. The effect of this interfacial disorder on the electronic properties is investigated by measuring the low-temperature resistivity and the superconducting transition temperature of the multilayers. The calculated values for the elastic mean free path in the individual layers confirm the presence of strong interfacial scattering. The thickness dependence of the critical temperature is explained by taking into account an interfacial barrier with penetration probability σ ≃ 0.5.

The Ultrastructure of Monkey Gingival Epithelium

1967 ◽  
Vol 25 ◽  
pp. 16-17
Author(s):  
C.N. Sun
Keyword(s):  
Epithelial Cells ◽  
Macaca Nemestrina ◽  
Stratum Granulosum ◽  
Solution Ph ◽  
Gingival Epithelial Cells ◽  
Stratum Spinosum ◽  
Cell Layers ◽  
Gingival Epithelium ◽  
The Individual ◽  
Different Thickness

The present study demonstrates the ultrastructure of the gingival epithelium of the pig tail monkey (Macaca nemestrina). Specimens were taken from lingual and facial gingival surfaces and fixed in Dalton's chrome osmium solution (pH 7.6) for 1 hr, dehydrated, and then embedded in Epon 812.Tonofibrils are variable in number and structure according to the different region or location of the gingival epithelial cells, the main orientation of which is parallel to the long axis of the cells. The cytoplasm of the basal epithelial cells contains a great number of tonofilaments and numerous mitochondria. The basement membrane is 300 to 400 A thick. In the cells of stratum spinosum, the tonofibrils are densely packed and increased in number (fig. 1 and 3). They seem to take on a somewhat concentric arrangement around the nucleus. The filaments may occur scattered as thin fibrils in the cytoplasm or they may be arranged in bundles of different thickness. The filaments have a diameter about 50 A. In the stratum granulosum, the cells gradually become flatted, the tonofibrils are usually thin, and the individual tonofilaments are clearly distinguishable (fig. 2). The mitochondria and endoplasmic reticulum are seldom seen in these superficial cell layers.

A Study of the Ultrastructure of Visual Cell Outer Segment Membranes, Using a Water-Miscible Embedding Medium and Differential Staining

1972 ◽  
Vol 30 ◽  
pp. 50-51
Author(s):  
Anthony J. Godfrey
Keyword(s):  
Outer Segment ◽  
Protein Denaturation ◽  
Uranyl Acetate ◽  
Differential Staining ◽  
Visual Cell ◽  
Lead Citrate ◽  
Chick Retina ◽  
Dark Staining ◽  
Embedding Medium ◽  
The Individual

Aldehyde-fixed chick retina was embedded in a water-containing resin of glutaraldehyde and urea, without dehydration. The loss of lipids and other soluble tissue components, which is severe in routine methods involving dehydration, was thereby minimized. Osmium tetroxide post-fixation was not used, lessening the amount of protein denaturation which occurred. Ultrathin sections were stained with 1, uranyl acetate and lead citrate, 2, silicotungstic acid, or 3, osmium vapor, prior to electron microscope examination of visual cell outer segment ultrastructure, at magnifications up to 800,000.Sections stained with uranyl acetate and lead citrate (Fig. 1) showed that the individual disc membranes consisted of a central lipid core about 78Å thick in which dark-staining 40Å masses appeared to be embedded from either side.

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