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A Damageable Spring

Chipman J. C., Roux A., Shillor M., Sofonea M.

Machine Dynamics Research

2011

Vol. 35, No. 1

82-96

The evolution of material damage in a nonlinear spring is modeled, analyzed, and numerically simulated. The material damage is described by a damage function whose evolution depends on the mechanical energy in the system and the damage threshold. The model is in the form of two coupled nonlinear ordinary differential equations. The existence of the unique solution is proved using arguments for evolutionary equations with maximal monotone operators, differential equations, and fixed points. The scaling properties of the model are discussed. A numerical algorithm for the problem is presented and four simulations of the system behavior depicted. In particular, the changes in the oscillations of the system as damage progresses are shown.