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纳米力学科学与技术:国际期刊

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ISSN 打印: 2572-4258

ISSN 在线: 2572-4266

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.3 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.7 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.7 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.00023 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.11 SJR: 0.244 SNIP: 0.521 CiteScore™:: 3.6 H-Index: 14

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GEOMETRIC ASPECTS OF THE THEORY OF INCOMPATIBLE DEFORMATIONS. PART I. UNIFORM CONFIGURATIONS

卷 7, 册 3, 2016, pp. 177-233
DOI: 10.1615/NanomechanicsSciTechnolIntJ.v7.i3.10
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摘要

In the present paper, modern differential-geometrical methods for modeling the incompatible finite deformations in solids are developed. The incompatibility of deformations may be caused by a variety of physical phenomena, e.g., distributed dislocations and disclinations, point defects, nonuniform thermal fields, shrinkage, growth, etc. Incompatible deformations result in residual stresses and distortion of the geometric shape of a body. These factors determine the critical parameters of modern high-precision technologies, particularly, of additive manufacturing, and are considered to be Ipso Facto essential constituents in corresponding mathematical models. In this context, the development of methods for their quantitative description is an urgent problem of modern solid mechanics. The methods in question are based on the representation of a body and physical space in terms of differentiable manifolds, namely, material manifold and physical manifold. These manifolds are equipped with specific metrics and connections, non-Euclidian in general. All the work as a whole gives a systematic presentation for the geometric aspects of the theory of finite incompatible deformations and contains partial survey of related papers. It is divided into three parts. The present paper represents the first part. It focuses on the physical interpretation of the non-Euclidean structure of the material and physical manifolds. Affine connection on the physical manifold is defined a priori by considerations which are independent of the properties of the deformable body. It is shown that a two-dimensional rigid surface, which formalizes curved substrate used in the deposition process, may serve as an example of non-Euclidean physical manifold. Affine connection on the material manifold represents the intrinsic properties (inner geometry) of the body and is determined by the field of local uniform configurations which performing its "assembly" of identical and uniform infinitesimal "bricks". Uniformity means that the response functional gives for them the same response on all admissible smooth deformations. As a result of assembling, one obtains body, which cannot be immersed in undistorted state into physical manifold. It is an essential feature of residual stressed bodies produced by additive processes. For this reason, it is convenient to use the immersion into a non-Euclidean space (material manifold with non-Euclidean material connection). To this end it is convenient to formalize the body and physical space are in terms of the theory of smooth manifolds. The deformation is formalized as embedding (or, in special case, as immersion) former manifold into the latter one.

对本文的引用
  1. Lychev S A, Kostin G V, Koifman K G, Lycheva T N, Modeling and Optimization of Layer-by-Layer Structures, Journal of Physics: Conference Series, 1009, 2018. Crossref

  2. Lychev S., Kostin G., Koifman K., Evolution of Stresses and Deformations in Hollow Cylinder with Variable Material Composition: Mathematical Modeling and Optimization ⁎ ⁎The work was performed with financial support from the RFBR No. 18-08-01346 and RFBR No. 18-01-00812., IFAC-PapersOnLine, 51, 2, 2018. Crossref

  3. Lychev Sergey, Koifman Konstantin, Nonlinear evolutionary problem for a laminated inhomogeneous spherical shell, Acta Mechanica, 230, 11, 2019. Crossref

  4. Lychev S. A., Koifman K. G., Material Affine Connections for Growing Solids, Lobachevskii Journal of Mathematics, 41, 10, 2020. Crossref

  5. Lychev S A, Kostin G V, Lycheva T N, Koifman K G, Non-Euclidean Geometry and Defected Structure for Bodies with Variable Material Composition, Journal of Physics: Conference Series, 1250, 1, 2019. Crossref

  6. Lycheva Tatiana, Lychev Sergey, The Simulation the Contact Interaction of the Needle and Brain Tissue, in Advanced Problem in Mechanics II, 2022. Crossref

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