ABSTRACT
This chapter presents a brief treatment of the theory of elasticity. It examines the concepts of stress, strain, constitutive relations, and various forms of energy. The chapter presents the equations of linear elasticity and considers the question of uniqueness of solutions to these equations. It also considers the plane stress simplification. The rigorous solutions of three-dimensional problems of elasticity are few. The body force distribution is an intensity function and is generally evaluated per unit mass or per unit volume of the material acted on. A normal stress directed outward from the interface is termed a tensile stress and is taken by definition as positive. A mixture of signs for coordinate directions corresponding to shear stress and the unit normal indicates a negative value for the shear stress. The chapter describes the stress tensor arising from equilibrium considerations and the strain tensor arising from kinematic considerations.
