Approximate Models of Mechanics of Composites

Book excerpt: Approximate Models of Mechanics of Composites: An Asymptotic Approach is an essential guide to constructing asymptotic models and mathematical methods to correctly identify the mechanical behavior of composites. It provides methodology for predicting and evaluating composite behavior in various structures, leading to accurate mathematical and physical assessments. The book estimates the error of approximations through comparing asymptotic solutions with the results of numerical and analytical solutions to gain a holistic view of the data. The authors have developed asymptotic models based on mathematical and physical rigorous approaches, which include three-phase models of fibrous composites, a modernized three-phase composite model with cylindrical inclusions, and models of two-dimensional composites of hexagonal structure. Also covered are two-phase models of composites related to the Maxwell formula and a percolation transition model for elastic problems based on the self-consistency method and Padé approximations. By obtaining analytical expressions to effectively characterize composite materials, their physical and geometric parameters can be accurately assessed. This book suits engineers and students working in material science, mechanical engineering, physics, and mathematics, as well as composite materials in industries such as construction, transport, aerospace, and chemical engineering.