ABSTRACT
Matter is known to be discrete or discontinuous at the microscopic level. All materials are composed of molecules or atoms with empty space between them. Solids, liquids, and gases differ in the average spacing of molecules. In the continuum model of matter, the discrete molecular structure of matter is ignored, and it is treated as a continuous medium. Kinematics is the branch of mechanics that deals with the analysis and description of deformation and flow of matter without referring to the forces that produce the deformation or motion. There are two basic methods of describing the deformation or flow of materials: Lagrangian and Eulerian methods. The material time derivative operates on quantities referred to a fixed coordinate system, unlike the convected time derivative which operates on quantities referred to a convected coordinate system. Constitutive equations are equations that relate dynamical (stress) variables to appropriate kinematical variables. Not all materials follow the same form of a constitutive equation.
