ABSTRACT
In this chapter, the basic concepts from continuum mechanics are presented. Most of the basic concepts utilized in this book involve treating the soil as a continuum. The continuum assumption, disregarding the discrete nature at small scale, implies that any material attribute is continuously distributed and defined at all points in a material body. Of course, in the subsequent chapters these are adapted for the mechanics of fluid-filled particulate (porous) media (soils), which we idealize as continua.
Starting with the definitions of strains and stresses, the equations for ‘stress transformation’ are developed including the definition of principal stresses. Identifying stress and strain as tensors, the necessary algebra for carrying out stress transformation are presented and implemented in a simple MATLAB program. The graphical method of stress transformation using Mohr’s circle along with its MATLAB program is also presented. After presenting the state of stress for the three-dimensional situation, the states of stress for the two-dimensional situations (viz. plain strain, and axi-symmetric conditions) are also described.
