Abstract
An analytical method is developed to determine the moment of destruction of thin coatings on pipes and spherical vessels. The coating material works at the stage of elasticity; it has the property of strain softening, that is, destruction with increasing deformation occurs in the process of stress drop. The properties of the coating material are described by convex-concave potentials both under uniaxial tension and in a plane stress state. To determine the moment of destruction, methods of the mathematical theory of catastrophes are applied, which allow one to find all the equilibrium positions of systems and the point of loss of stability of the deformation process.
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