Changing the properties of construction materials occurs continuously throughout the lifetime of the product. Methods of differential and integral calculus allow us to describe the degradation of properties of structural materials for limited periods of time, which is characterized by a slight change in the system (functions), with equally slight change in magnitude of the effect (of the argument). If the task is diagnostic of material properties throughout the life cycle of a product, namely the challenges facing such intelligent materials, it is necessary to apply the mathematical apparatus that allows describing the system with possible sudden imbalance.
Any construction material during use of the product, it takes several cycles, within which there is a sharp change in its properties. The number and length of these cycles are largely dependent on the material properties and its operating conditions. After hopping cycle properties of the system, which is usually short, but in this period of time the system goes into a qualitatively new state should restore the balance between the system and its subsequent smooth change. All these cycles are described in this paper using the apparatus of the theory of catastrophes.
Among the many functions of intelligent materials, one of the most important is - diagnostics, which puts high demands on the mathematical model. To describe the life cycle of intellectual material provides the relevant mathematical model of catastrophe theory to describe the degradation of properties intellectual material in each loop uses continuous functions. For these purposes, the example of carbon fiber in the defined list of indirect signs indicating the approach of the system to the bifurcation point (catastrophe).