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2018 | Buch

Asymptotical Mechanics of Composites

Modelling Composites without FEM

verfasst von: Prof. Dr. Igor V. Andrianov, Prof. Dr. Jan Awrejcewicz, Prof. Dr. Vladyslav V. Danishevskyy

Verlag: Springer International Publishing

Buchreihe : Advanced Structured Materials

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Über dieses Buch

In this book the authors show that it is possible to construct efficient computationally oriented models of multi-parameter complex systems by using asymptotic methods, which can, owing to their simplicity, be directly used for controlling processes arising in connection with composite material systems.

The book focuses on this asymptotic-modeling-based approach because it allows us to define the most important out of numerous parameters describing the system, or, in other words, the asymptotic methods allow us to estimate the sensitivity of the system parameters.

Further, the book addresses the construction of nonlocal and higher-order homogenized models. Local fields on the micro-level and the influence of so-called non-ideal contact between the matrix and inclusions are modeled and investigated.

The book then studies composites with non-regular structure and cluster type composite conductivity, and analyzes edge effects in fiber composite materials. Transition of load from a fiber to a matrix for elastic and viscoelastic composites, various types of fiber composite fractures, and buckling of fibers in fiber-reinforced composites is also investigated. Last but not least, the book includes studies on perforated membranes, plates, and shells, as well as the asymptotic modeling of imperfect nonlinear interfaces.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
Contemporary composite materials are widely used in modern engineering.
Igor V. Andrianov, Jan Awrejcewicz, Vladyslav V. Danishevskyy
Chapter 2. Models of Composite Materials and Mathematical Methods of Their Investigation
Abstract
The linear theory of elasticity yields the following relations between the displacements \({{u}_{i}}\), deformations \({{\varepsilon }_{ij}}\) and stress \({{\sigma }_{ij}}\) in a continuous matter.
Igor V. Andrianov, Jan Awrejcewicz, Vladyslav V. Danishevskyy
Chapter 3. Conductivity of Fibre Composites: Analytical Homogenization Approach
Abstract
Application of the multi-scale asymptotic homogenization method allowed us to separate global and local components of the solution and to reduce the input boundary value problem in a multi-connected domain to a recurrent sequence of local problems, considered within a representative unit cell of the composite structure.
Igor V. Andrianov, Jan Awrejcewicz, Vladyslav V. Danishevskyy
Chapter 4. Conductivity of Particle-Reinforced Composites: Analytical Homogenization Approach
Abstract
In this chapter, we consider the particle-reinforced composites consisting of infinite matrix \({{\varOmega }^{(1)}}\) and spherical inclusions \({{\varOmega }^{(2)}}\), composed of simple cubic (SC) (Fig. 4.1a) and body-centred cubic (BCC) (Fig. 4.1b) lattices.
Igor V. Andrianov, Jan Awrejcewicz, Vladyslav V. Danishevskyy
Chapter 5. Elastic and Viscoelastic Properties of Fibre- and Particle-Reinforced Composites
Abstract
It is known in industry that in order to increase stiffness and loading ability of materials it is suitable to reinforce the material by fibres.
Igor V. Andrianov, Jan Awrejcewicz, Vladyslav V. Danishevskyy
Chapter 6. Local Stresses in Elastic Fibrous Composites
Abstract
Contemporary composite materials are widely used in modern engineering.
Igor V. Andrianov, Jan Awrejcewicz, Vladyslav V. Danishevskyy
Chapter 7. Asymptotic Analysis of Perforated Membranes, Plates and Shells
Abstract
The perforated membranes, plates and shells are widely used in the numerous technical applications, and some examples are shown in the Fig. 7.1.
Igor V. Andrianov, Jan Awrejcewicz, Vladyslav V. Danishevskyy
Chapter 8. Nonlinear Elastic Problems
Abstract
We begin with a multi-layer composite material, composed of interacting components \({{\varOmega }^{(1)}}\) and \({{\varOmega }^{(2)}}\) (Fig. 8.1).
Igor V. Andrianov, Jan Awrejcewicz, Vladyslav V. Danishevskyy
Chapter 9. Conclusion
Abstract
“Similar ideas could be applied for many different applications” - this ritual phrase appears in majority of conclusions of many papers and monographs, and this is valid also in our case.
Igor V. Andrianov, Jan Awrejcewicz, Vladyslav V. Danishevskyy
Backmatter
Metadaten
Titel
Asymptotical Mechanics of Composites
verfasst von
Prof. Dr. Igor V. Andrianov
Prof. Dr. Jan Awrejcewicz
Prof. Dr. Vladyslav V. Danishevskyy
Copyright-Jahr
2018
Electronic ISBN
978-3-319-65786-8
Print ISBN
978-3-319-65785-1
DOI
https://doi.org/10.1007/978-3-319-65786-8

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