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

Product Description 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. Review Detailed review of the use of advanced analytical and computational techniques to investigate effective constants in composite materials and random porous media From the Back Cover 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. About the Author P. Drygas, Associate Professor, Department of Mathematical Analysis, University of Rzeszow, Poland Research interests: mathematical modelling, differential equation and statistics. Simon Gluzman is currently an Indepe