Mechanics of curved composites
This book focuses on mechanical aspects of fiber-reinforced and layered composite materials with a curved structure. The term ``curved structure'' means that the reinforcing layers or fibers are not straight but have some initial curvature. The considered aspects comprise statics, vibration, stability loss, elastic and fracture problems; as a prerequisite, it is assumed that the reader is familiar with the theory of elasticity for anisotropic bodies, with partial differential equations and integral transformations, and also with the finite element method. On this background use is made of the exact equations of elasticity and viscoelasticity for anisotropic bodies, and linear and nonlinear problems are considered in the framework of continuum theory. The book consists of an introduction, ten chapters and two supplements. In the introduction, some necessary information is given on the classification of composite materials and on the classification of curving in their structure. Chapter 1 presents a simple new version of continuum theory for composite materials with periodic plane-curved structure. In doing so, the authors suppose that the curves are small-scale, which means that the period of curvature of reinforcing elements is significantly less than the size of elements of objects fabricated from these composite materials. In chapter 2, a continuum theory for composite materials with general periodic or locally curved structures is discussed, generalizing the analysis of chapter 1. In chapter 3 the theory is combined with finite element method to solve some two- and three-dimensional static and dynamic problems for strips and rectangular plates. In chapters 4-10 the authors study problems of curved composites in the framework of a piecewise-homogeneous body model. First, in chapter 4 plane strain problems of periodically plane-curved composites are considered. Then in chapter 5 the corresponding formulations and solution method are given for three-dimensional problems. In chapter 6, the stress state is investigated in composite materials with locally plane-curved layers. Chapter 7 extends the problem formulations and solution methods to fibrous composites with curved structures. Next, in chapter 8 geometric nonlinearities are taken into account and the influence of nonlinearities on the mechanical behaviour is determined. Chapter 9 deals with the derivation of normalized mechanical properties of composites with periodically curved layers. Finally, in chapter 10 the authors investigate fracture problems for curved composites. In supplement 1, an approach is proposed for the investigation of fracture of viscoelastic unidirectional composites in compression, whereas in supplement 2 the continuum theory of chapter 2 is used to investigate some two-dimensional geometrically nonlinear problems and stability problems for strips. In all, the book is on a high scientific level and it is written not only for graduate researchers but also for mechanical engineers designing composite materials for automobiles, aerospace structures, biomedical structures and civil engineering.
scientific article; zbMATH DE number 1520357