ABSTRACT
In mechanics, the concept of a continuous medium (see, e.g., Malvern, 1969) is based on a simplification of physical reality, which consists in disregarding the molecular structure of matter and picturing it as being without gaps and empty spaces. Further, i t is supposed that all the mathematical functions in the theory are continuous functions, except for a finite number of interior surfaces (denoted as discontinuity surfaces) separating the continuity regions. This concept makes i t possible to define the physical quantities such as density, velocity, stress, etc. at a mathematical point, which is the most important factor for modelling purposes. Consequently, the mathematical methods of differential and integral calculus immediately become available for the study of physical phenomena, and mathematical models can be constructed on the basis of physical concepts using common mathematical tools.
