Nonlinear Dynamical Effects and Observations in Modeling and Simulating Damage Evolution in a Cantilevered Beam

Abstract

This study investigates the nonlinear dynamic failure characteristics of a notched cantilever beam using numerical finite element models and experiments with various displacement loads at the root of the beam. Damage states of the beam are represented as quasi-static equilibrium points and, subsequently, all significant damage events are modeled as bifurcations (qualitative changes) in the set of stable equilibria for the structure-damage system using a set of low-order normal forms. When analytical models are used to interpret trends in data from the beam as it undergoes different routes to failure, the state-space relationship between estimated crack length and rate of change of crack length exhibits elastic-plastic transitions, which depend on the effects of damage accumulation and the load history. It is suggested that these transitions could be used as a series of milestones for rendering a prognosis. It is demonstrated that nonlinear normal forms do simulate a variety of damage evolution phenomena using a few key parameters, which must be evaluated in future works.