Description of scenarios of transition of material from an operable to inoperable state using an equation of fold catastrophe theory
Using the apparatus of catastrophe theory, the synergetic effect, whereby damage accumulation in polymer materials at various scales is considered, has been calculated. It has been shown that a change in the properties of polymer materials can be represented as a consecutive transition of the system from one stable state to another, for which the intrinsic astable mode is characteristic. The transition from one stable state to another proceeds through the bifurcation point, the value of which is determined using functions with one active variable of “fold” type.
Keywordspolymer materials synergetics catastrophe theory degradation fracture
Unable to display preview. Download preview PDF.
- 1.New in Synergetics: A Look into the Third Millennium. Collected Papers, Ed. by G. G. Malinetskii and S. P. Kurdyumov (Nauka, Moscow, 2002) [in Russian].Google Scholar
- 2.S. L. Bazhenov, A. A. Berlin, A. A. Kul’kov, and V. G. Oshmyan, Polymer Composite Materials (Intellekt, Dolgoprudnyi, 2010).Google Scholar
- 3.I. A. Aleksandrov, A. N. Muranov, and G. V. Malysheva, “Study of the influence of the deformation properties of binders on the processes of destruction of carbon-fiber-reinforced polymers,” Vse Materialy. Entsikl. Sprav., No. 7, 40–45 (2012).Google Scholar
- 4.N. I. Baurova, “The dynamics of destruction processes of polymer composite materials,” Entsikl. Inzh.-Khim., No. 2, 19–25 (2013).Google Scholar
- 6.V. A. Zorin and N. I. Baurova, “Analysis of performance of elements of metal structures using the catastrophe theory,” Vestn. Mosk. Avtomob.-Dorozh. Gos. Tekhn. Unov. (MADI), No. 1, 7–10 (2009).Google Scholar
- 7.V. I. Arnol’d, The Catastrophe Theory, 5th ed. (URSS, Moscow, 2007) [in Russian].Google Scholar
- 8.I. Prigogine, From Being to Becoming. Time and Complexity in the Physical Sciences (Mir, Moscow, 1985) [in Russian].Google Scholar
- 9.V. A. Ostreikovskii, Analysis of Stability and Controllability of Dynamical Systems Using the Catastrophe Theory Methods: A Textbook (Vyssh. Shk., Moscow, 2005) [in Russian].Google Scholar