ESCI
SJR:
1.031
SNIP:
1.517
CiteScore™:
0.7
ISSN Imprimir: 25724258
Volumes:

Nanoscience and Technology: An International JournalAnteriormente Conhecido Como Nanomechanics Science and Technology: An International Journal
DOI: 10.1615/NanoSciTechnolIntJ.2018024573
pages 97121 GEOMETRIC ASPECTS OF THE THEORY OF INCOMPATIBLE DEFORMATIONS. PART II. STRAIN AND STRESS MEASURES
S. A. Lychev
A. Yu. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 1011 Vernadsky Ave., Moscow, 119526, Russia
K. G. Koifman
A. Yu. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 1011 Vernadsky Ave., Moscow, 119526, Russia RESUMOThe present paper is a continuation of an earlier one (Lychev and Koifman, 2016). It introduces nonEuclidean representations for stress and strain distributions on smooth manifolds endowed
with Riemannian metrics in terms of smooth sections and covectorvalued forms. The application of nonEuclidean geometry makes it possible to formalize incompatible local deformations in the form similar to the conventional deformation gradient. The only difference is that deformation has to be understood in the generalized sense as embedding of a manifold with nonEuclidean (material) connection into Euclidean one.Material connection characterizes the measure of incompatibility of local deformations and plays the role of a material function that characterizes the body as a "construction" assembled from selfstressed elementary parts. Such bodies are the subject of the paper, which will
be referred to as structurally inhomogeneous bodies. The latter are the archetypal objects of study in modeling and optimization for additive manufacturing. Two classes of structurally inhomogeneous bodies are considered. The first class includes bodies with discrete inhomogeneity, and the second class with a continuous one. The first class represents compound bodies whose finite parts are composed with a preliminary deformation. The stress−strain state of such bodies is determined from the equilibrium conditions for the layers and the ideal contact between them. Modeling of the assembly process is reduced to a recurrent sequence of such problems. To find the stress−strain state of bodies
with a continuous inhomogeneity, the stresses and strains in which are represented by sections of bundles, an evolutionary problem is formulated. In a particular case, this problem reduces to nonlinear integral equation. Palavraschave: incompatible deformations, residual stresses, material manifold, nonEuclidean geometry, material connections, Cartan moving frame, contortion, covectorvalued exterior forms of stresses, balance equations
Referências
Articles with similar content:
GEOMETRIC ASPECTS OF THE THEORY OF INCOMPATIBLE DEFORMATIONS. PART I. UNIFORM CONFIGURATIONS
Nanoscience and Technology: An International Journal, Vol.7, 2016, issue 3 S. A. Lychev, K. G. Koifman
OPTIMAL DESIGN OF LAMINATED COMPOSITES
Composites: Mechanics, Computations, Applications: An International Journal, Vol.1, 2010, issue 2 A. R. Khaziev, V. V. Vasiliev
Fast Calculation of Elastic Fields in a Homogeneous Medium with Isolated Heterogeneous Inclusions
International Journal for Multiscale Computational Engineering, Vol.7, 2009, issue 4 Sergey Kanaun
CALCULATION OF THE INTERGRANULAR ENERGY IN TWOLEVEL PHYSICAL MODELS FOR DESCRIBING THERMOMECHANICAL PROCESSING OF POLYCRYSTALS WITH ACCOUNT FOR DISCONTINUOUS DYNAMIC RECRYSTALLIZATION
Nanoscience and Technology: An International Journal, Vol.7, 2016, issue 2 Peter V. Trusov, Nikita S. Kondratev
MODEL OF ANISOTROPIC ELASTOPLASTICITY IN FINITE DEFORMATIONS ALLOWING FOR THE EVOLUTION OF THE SYMMETRY GROUP
Nanoscience and Technology: An International Journal, Vol.6, 2015, issue 2 Mario Fagone, Massimo Cuomo 
Portal Digital Begell  Biblioteca digital da Begell  eBooks  Diários  Referências e Anais  Coleções de pesquisa 