Convergence of computational methods and stability of self-balanced stresses under shrinkage of spherical inclusions of a damageable material

V. V. Struzhanov, Vyach. V. Bashurov

Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg

Abstract: Some iterative methods for calculating self-balanced stresses under shrinkage of a ball inclusion enclosed in a spherical matrix of a physically nonlinear damageable material. The stability of this system was studied using methods of catastrophe theory. It has been established that the beginning of divergence of the proposed iterative processes coincides with the moment of transition of the system to an unstable position of equilibrium.

Keywords: stability, self-balanced stresses, damageable material.

UDC: 539.3:517.946

Received: 02.12.2002

 English version: Journal of Applied Mechanics and Technical Physics, 2003, 44:4, 549–556

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