Chapter 2 - Fundamentals of Mechanics of Solids

Abstract

The purpose of this chapter is to discuss the fundamentals of mechanics of solids. The behavior of composite materials whose micro- and macrostructures are much more complicated than those of traditional structural materials such as metals, concrete, and plastics is governed by general laws and principles of mechanics. This chapter elucidates these principles. This chapter demonstrates stress transformations under rotation of a coordinate frame. It also demonstrates stress formation under a special position in which the shear stresses acting on the coordinate planes vanish. Such coordinate axes are called the principal axes, and the normal stresses that act on the corresponding coordinate planes are referred to as the principal stresses. The equations of Solid Mechanics can be also derived from variational principles that establish the energy criteria according to which the actual state of the body under loading can be singled out of a system of admissible states. This chapter also includes accounts on stresses, equilibrium equations, stress transformation, principal stresses, and constitutive equations for an elastic solid. This chapter also introduces static field variables which are stresses and kinematic field variables which are displacements and strains.