1. Introduction to the theory of composites and porous media.
1.1. Mathematical Foundations.
1.2. Introduction to homogenization.
1.3. Asymptotic methods.
2. Computational methods
2.1. Symbolic representations of coefficients of the effective conductivity formula
2.2. Algorithms for computing basic sums.
2.3. Computing all basic sums of a given order. Recurrence algorithm and its effectiveness.
2.4. Basic sums as geometric features of images containing random distributions of objects. Application to classification problem of abstract data and the effectiveness.
3. Hexagonal array of elastic cylinders
3.1. Essentials of the long series derivation.
3.2. Critical point calculation with various methods. Calculation of the critical index and amplitude.
3.3. Discussion of the ansatz for construction of the starting approximation. Unified approach to the square and hexagonal lattices.
3.4. Derivation of the asymptotic formula in various limit cases (rigid and soft inclusions, incompressible media, negative Poisson’s coefficient).
4. Applied Theory of Regular 2D Composites.
4.1. Super-rigid inclusions. Particular cases with varying Poisson coefficient.
4.2. Case study of the composite with rigid inclusions and slightly different Poisson coefficients of matrix and inclusions.
4.3. Elasticity of holes. Expansions for shear and bulk moduli.
4.4. Elastic and viscous behavior of 3D composites.
5. Random 2D Composite
5.1. Two-phase composites with non-overlapping inclusions randomly embedded in matrix.
5.2. Review of the numerical results for percolation problem. 5.3. Method of the corrected threshold. Calculation of the critical Index by different methods.
5.4. Random walks and random shaking algorithms.
5.5. Corrected regular lattice approximation and D-Log Pade.
6. Piezoelectric fibrous composites. Effective anti-plane properties..
7. Macroscopic properties of porous media
7.1. Permeability in heterogeneous porous media.
7.2. Introduction to the permeability in heterogeneous porous media and moment equation expansions.
7.3. Permeability of Spatially Periodic Arrays of Cylinders
7.4. Longitudinal permeability for the square array of cylinders.
7.5. Stokes flow through a channel with three-dimensional wavy walls enclosed by two wavy walls.
7.6. 3D Periodic Arrays of Spherical Obstacles.
7.7. Nonlinear correction to Darcy’s law for channels with wavy walls. Solutions to the Navier-Stokes equations in three-dimensional channels enclosed by two wavy walls.
7.8. Sedimentation. Particle Mobility.
8. Application to biological structures
8.1. Effective Viscosity of active suspensions of microswimmers via renormalization approach.
8.2. Effective viscosity of passive suspensions
8.3 Effective viscosity of 2D passive suspensions.
8.4. Mean-Field theory of bacterial suspensions.
8.5. Collective behavior of bacteria.
Applied Analysis of Composite Media: Analytical and Computational Approaches presents formulas and techniques that can used to study 2D and 3D problems in composites and random porous media. The main strength of this book is its broad range of applications that illustrate how these techniques can be applied to investigate elasticity, viscous flow and bacterial motion in composite materials. In addition to paying attention to constructive computations, the authors have also included information on codes via a designated webpage. This book will be extremely useful for postgraduate students, academic researchers, mathematicians and industry professionals who are working in structured media.
- Provides a uniform, computational methodology that can be applied to the main classes of transport and elastic problems by using a combination of exact formulae, advanced simulations and asymptotic methods
- Includes critical phenomena in transport and elastic problems for composites and porous media
- Applies computational methodology to biological structures
- Presents computer protocols/algorithms that can be used for materials design
Materials scientists and engineers involved in the development of composite materials; applied mathematicians and physicists who develop analytical and numerical methods to model problems of elasticity and fluid mechanics in materials; and researchers working at the interface with biology and materials
- No. of pages:
- © Woodhead Publishing 2020
- 1st November 2019
- Woodhead Publishing
- Paperback ISBN:
Vladimir Mityushev is the head of modeling and simulation laboratory at the department of computer science and computational methods at Pedagogical University of Cracow, Kraków, Poland. He is interested in Mathematical modeling and computer simulations, Industrial mathematics and boundary value problems and their applications.
Head of Modeling and Simulation Laboratory, Department of Computer Science and Computational Methods, Pedagogical University of Cracow, Krakow, Poland
P. Drygas, Associate Professor, Department of Mathematical Analysis, University of Rzeszow, Poland Research interests: mathematical modelling, differential equation and statistics.
Associate Professor, Department of Mathematical Analysis, University of Rzeszow, Poland
Simon Gluzman is currently an Independent Researcher (Toronto, Canada) and was formerly a Research Associate at PSU in Applied Mathematics, and past Professor of Applied Mathematics, at Bogoliubov Laboratory of Theoretical Physics. His research interests focus on resummation methods in the theory of random and regular composites and the method of self-similar and rational approximants.
Independent Researcher, Toronto, Canada
Wojciech Nawalaniec is an Associate Professor in applied mathematics at Pedagogical University of Cracow, Kraków. He is interested in Computational methods, such as symbolic computation, mathematical modeling and algorithms.
Associate Professor, Applied Mathematics, Pedagogical University of Cracow, Krakow, Poland