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27
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Introduction
My interests are on geometric description of incompatible local deformations, surface growth, theory of defects, oriented media, accretion.
Skills and Expertise
Education
September 2009 - July 2015
Publications
Publications (27)
This book is intended to provide a systematic treatment of those parts of modern differential geometry that are essential for modeling of incompatible finite deformations in solids. Included are discussions of generalized deformation and stress measures on smooth manifolds, geometrical formalization for structurally inhomogeneous bodies, various de...
The subject of the present paper is a material connection that describes the sources of incompatibility in growing solids. There are several possibilities to introduce such a connection on the body manifold, which provides formal description of a body as a continuous collection of material particles. Two of them are discussed in detail. The first s...
The present paper is intended to show the close interrelationship between non-linear models of solids, produced with additive manufacturing, and models of solids with distributed defects. The common feature of these models is the incompatibility of local deformations. Meanwhile, in contrast with the conventional statement of the problems for solids...
The work develops differential-geometric methods for modeling of finite incompatible deformations of hyperelastic solids. Deformation incompatibility can be caused, for example, by inhomogeneous temperature fields and distributed defects. As a result, residual stresses and distortion of geometric shape of the body occur. These factors determine the...
The work develops differential-geometric methods for modeling
incompatible deformations and stresses caused by them in
hyperelastic supermassive bodies within the framework of special and
general relativity. Particular attention is paid to a unified
geometric language used both for modeling distributed defects and
gravitational interaction. It is s...
The Lagrangian approach for modeling of relativistic elastic solid with distributed defects
is developed. The influence of defects on stress-strain state of the solid is taken into account
within differential-geometric framework, which allows to describe the corresponding deformation
incompatibility in terms of material connection curvature. The sp...
The present paper develops a general approach to deriving nonlinear equations of motion for solids whose material points possess additional degrees of freedom. The essential characteristic of this approach is theaccount of incompatible deformations that may occur in the body due to distributed defects or in the result of the some kind of process li...
In present paper the generalized kinematics for oriented media is discussed. The approach suggested is based on the geometrical formalism, developed in the theory of connection on principle bundles. This makes it possible to take into account a range of orientations, associated with an elementary volume of underlying body, while classical Cosserat...
The present paper aims to develop geometrical approach for finite incompatible deformations arising in growing solids. The phenomena of incompatibility is modeled by specific affine connection on material manifold, referred to as material connection. It provides complete description of local incompatible deformations for simple materials. Meanwhile...
In the present paper the model for growing oriented solid is developed. Such solids have no global stress-free shape in Euclidean physical space due to the distributed defects, "recorded" into the solid during growing process. Nonetheless, in the framework of geometric approach in continuum mechanics the desired stress-free reference shape can be f...
In the present paper, the finite deformations of a laminated inhomogeneous spherical shell are studied. A laminated shell can be considered as a limit case for multilayered shells when the thickness of each layer tends to zero while their quantity tends to infinity. Such a limit might be useful in modeling of multilayered structures with large amou...
In the paper the relationship between pure geometrical concepts of the theory of affine connections, physical concepts related with non-linear theory of distributed defects and concepts of non-linear continuum mechanics for bodies with variable material composition is discussed. Distinguishing feature of the bodies with variable material compositio...
Control and optimization of manufacturing processes play essential role in LbL (layer-by-layer) technologies. Optimal control allows one, in particular, to reduce the residual stresses in produced details. The present paper provides an example of such optimization. The LbL-structure under study is represented as a hyperelastic hollow cylinder with...
In the present paper a differential-geometric approach is developed to modeling of residual stresses in layered (LbL) structures obtained as a result of successive curing of thin layers of material. The objects of modeling are the structures obtained by sequential adsorption of a large number of thin layers. During this assembling, the internal (re...
Настоящая статья посвящена формализации мер деформаций в неевклидовых пространствах для простого тела. Привлечение положений неевклидовой геометрии позволяет: i) определить глобальную единообразную отсчетную форму для тел со структурной неоднородностью, вызванной послойным созданием тела в ходе аддитивного процесса; ii) определить глобальную актуал...
Презентация к докладу на 60-й Научной конференции МФТИ. Секция управления динамическими системами.
Geometric methods and their applications in the theory of structurally inhomogeneous bodies are discussed. This methods are based on the representation
of a body and physical space in terms of differentiable manifolds which are endowed with specific Riemannian metrics and affine
connections, non-Euclidian in general. Affine connection on the physic...
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. Incompatibl...
Работа посвящена моделированию напряженно--деформированного состояния системы, возникающей в результате процессов послойного нанесения материала на подложку. Такие процессы используются в аддитивных технологиях (например, в стереолитографии и молекулярной эпитаксии). В качестве модели предложена система криволинейных мембран, попарно механически св...
