2 Mechanics of fiber composites Levent Aydin*, Hatice Sec ¸il Artem † , Erkan Oterkus { , Omer Gundogdu § , Hamit Akbulut § *Izmir Katip C ¸ elebi University, Izmir, Turkey, † Izmir Institute of Technology, Izmir, Turkey, { University of Strathclyde, Glasgow, United Kingdom, § Ataturk University, Erzurum, Turkey 2.1 Introduction The objective of this chapter is to emphasize the context in which the mechanics of fiber composites is examined. Constitutive equations describing the stress-strain rela- tions, micromechanics and macromechanics approaches for mechanical analysis are reviewed. Since interfacial mechanics of composites is of primary importance in discussing the material behavior, this concept is also presented with its constitutive and governing equations. Finally, at the end of the chapter, strength failure theories for orthotropic materials and dynamic behavior of composites are discussed. The mechanics of materials contended with stresses, strains, and deformations in engineering structures subjected to mechanical, thermal, and hygral loadings. A common assumption in the mechanics of conventional materials, such as steel and aluminum, is that they are homogeneous and isotropic [1]. However, fiber-reinforced composites are inhomogeneous and nonisotropic. As a result, the analysis of the mechan- ics of fiber-reinforced composites is much more complex than that of conventional mate- rials. The mechanics of fiber-reinforced composite materials is mainly studied at two levels: (1) micromechanics level, in which the interaction of the constituent materials is examined on a microscopic scale. In micromechanical analysis, stiffness, strength, thermal, and moisture expansion coefficients of a lamina are found using the individual properties of constituents (fiber and matrix), (2) macromechanics level, in which the response of a fiber-reinforced composite material to mechanical and thermal loads is studied on a macroscopic scale. The material is assumed to be homogeneous. Stresses, strains, and deflections are determined using the equations of orthotropic elasticity. 2.2 Mechanics of continuous fiber-reinforced composites Composites are materials in which a homogeneous matrix component is reinforced by a stronger and stiffer constituent that is usually continuous or short fibers. Contin- uous fiber-matrix composite materials include unidirectional or woven fiber laminae; laminae are stacked on top of each other at various angles to form a multidirectional laminate. The mechanical analysis of fiber-reinforced composites is performed in two levels: micromechanical and macromechanical analyzes. In the following parts, micromechanical and macromechanical analyzes of continuous-fiber-reinforced composites have been introduced based on classical lamination theory. Fiber Technology for Fiber-Reinforced Composites. http://dx.doi.org/10.1016/B978-0-08-101871-2.00002-3 © 2017 Elsevier Ltd. All rights reserved.