Constitutive Equations for Engineering Materials: Elasticity and Modeling (Volume 37) (Studies in Applied Mechanics, Volume 37) - Tapa dura

Volume 1 deals with the development of stress-strain models for metals, concrete and soils based on the principles of elasticity. It shows how these models can be applied to engineering practice. The volume is divided into three parts. Part one is concerned with the basic concepts in elasticity. The necessary concepts and notations of vector and tensor analysis are first developed in Chapter 1, since these are not familiar terms for civil engineers. The next two chapters are concerned with the concepts of stress and strain, and develop the basic equations of equilibrium and kinematics which can be discussed without assuming a specific constitutive equation. Basic assumptions of elastic stress-strain relations are plausibly explained in Chapter 4, and mathematical and physical reasonings are used to derive general constitutive equations from them, first in tensor forms, and then in matrix forms that are deemed of interest for engineering applications. Part two is devoted to specific formulations and applications of the elasticity-based models to reinforced concrete materials. The two major sources of nonlinearity in reinforced concrete, cracking of the concrete and plasticity of the reinforcement and of the compression concrete, are discussed in two chapters. Part three is devoted to soil elasticity and failure criteria. Here the specific formulations and applications of the elasticity-based models to soil type of media are developed in detail. Volume 2 extends the elasticity-based stress-strain models to the plastic range and develops plasticity-based models for engineering applications and is divided into four parts. Parts one and two contain a sufficient comprehensive treatment of the classical theory of plasticity and its applications to metal structures. Parts three and four present a state-of-the-art coverage of concrete plasticity and soil plasticity.