TheoreticaI Investigation of Controllable & Regular Fracture Theory station of Controllable & Regular Fracture Theory

摘要

Aiming to investigate the controllable fracture procedures and exploit the benefits of cracks, the paper theoretically analyzes the following essential aspects of Controllable and Regular Fracture Theory(CRFT) through both Engineering Control Theory and Fracture Mechanics: (a) The mathematical model of CRFT. In this item, any fracture procedure is regarded as a mathematical transformation named as Fracture Transformation, and a regular fracture procedure can be described as ε-Stability. (b) The fundamental analysis models of CRFT are presented after introducing Engineering Control Theory. A fracture procedure is considered as the behavior of the named "Crack System". (c) The conceptual stability of regular fracture procedure is investigated. With the help of Lyapunov's theory of stability in Engineering Control Theory, the stability of crack growth is analyzed. Using a transformation, the ε-Stability is proved to have the same meaning of the stability in Lyapunov's theory, and then can be described and analyzed by Lyapunov's stability theory. (d) A sufficient stability criterion of growing crack is established by means of Energy Method.