Applied Analysis of Composite Media: Analytical and Computational Results for Materials Scientists and Engineers (Woodhead Publishing Series in Composites Science and Engineering) - Softcover

Über die Autorinnen und Autoren

P. Drygas, Associate Professor, Department of Mathematical Analysis, University of Rzeszow, Poland
Research interests: mathematical modelling, differential equation and statistics.

Simon Gluzman is presently an Independent Researcher (Toronto, Canada) and formerly a Research Associate at PSU in Applied Mathematics. He is interested in Re-summation methods in theory of random and regular composites and the method of self-similar and rational approximants.

Vladimir Mityushev is the Professor of Cracow University of Technology, a leader of the research group www.materialica.plus. He is interested in mathematical modeling and computer simulations, Industrial mathematics and boundary value problems and their applications.
.

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.

Von der hinteren Coverseite

Symbolic-numerical computations are widely used to deduce new formulae, which is important for researchers and engineers studying effective constants in composite materials. In this new book, the authors discuss how to apply advanced computational techniques to investigate and model problems in composite materials, such as elasticity and fluid mechanics in porous media. The focus is on derivation of accurate working formulae in the form useful to material scientists and engineers. Accurate solutions for the realistic problems of conductivity, elasticity, flow in porous media, and rheology are obtained and presented in the form of explicit analytical expressions.

Composites with non-overlapping inclusions that are randomly embedded in the matrix are investigated in detail. Special attention is given to critical regimes related to the optimal packing of inclusions and to the extremal physical constants of rigid and soft inclusions. Concrete material cases are studied and working formulae are suggested.

Investigation of the effective constants for regular and random structures is based on the general approach of the RVE (representative volume element) and the corresponding e-sums. The techniques were systematically presented in the authors previous volume- Computational Analysis of Structured Media by S. Gluzman, V. Mityushev, W. Nawalaniec (GMN), (published in October 2017, Elsevier). The proposed method yields effective algorithm in symbolic-numeric form to compute e-sums as discrete multiple convolutions. In this book, the authors systematically describe the algorithms, to give codes or pseudo-codes, to investigate the complexity of computations. They proceed then to application of the methods developed in GMN to various composite materials constructed from various physical materials.

The proposed book always presents constructive solutions to boundary value problems from the field of material science. The results are applied to derivation of working formulae for basic macroscopic properties of composites and porous media that are useful for engineers. New, significantly more accurate formulae for the effective properties are deduced for engineering applications. Algorithms and symbolic-numerical computations are widely used and systematically described.

The book contains pseudocodes of developed algorithms as well as their implementations in Mathematica. In particular, presented computational methods refer to calculations of e-sums, the principal features which represent random media. The symbolic derivation of their graphs is based on the infinite series for effective conductivity. The accompanying webpage www.materialica.plus will contain extended information and numerical data. Animations and interactive panels will also be installed on the webpage for users.