Continuum Mechanics – Material Independent and Dependent Equations

Continuum mechanics in its rational formulation is a central element within mechanics. The basic concepts can be easily transferred to many special cases, with kinematics, stress models, balance equations, and constitutive laws being the most important elements of the theories. It also applies here that statics is the special case in Newton’s sense. Selected historical stages are briefly described below. The three-dimensional continuum theory is then briefly discussed. Finally, a note on the one- and two-dimensional special cases is given. The chapter is written from the point of view of a solid-state mechanics. However, numerous equations can easily be transferred to fluids.