Book excerpt: The application of composite materials to engineering components has spurred a ma jor effort to analyze such materials and the structures made from them. Most researchers workin~ in mechanics of composite structures understand that composite materials pro vide umque advantages but also present complex and challenging problems to researchers. The complex inelastic behavior and variety of failure modes of composite structures are a result of the strength and stiffness properties of constituents and their complex interac tions. Macromechanical constitutive models based on gross composite properties cannot realistically represent local interactions, and thus have serious limitations. The composite materials that are of most interest to engineering applications are often "brittle" in their behavior, in the sense that the strength and life of the material systems is controlled or greatly influenced by events or processes which involve volumes of material whose dimen sions are small compared to the global dimensions of the element. This is also true in ductile systems where local nonlinearity may contribute to local behavior which controls global response.