Effects of softening in elastic‐plastic structural dynamics

Softening, understood as unstable behaviour of material or structural components, is considered herein for its possible consequences on the overall behaviour of discrete dynamic models of elastic–plastic beam structures, in the absence of geometric effects. It is shown that multiplicity of incremental solutions (response bifurcations) and manifestations of overall instability may occur. The bifurcated responses may exhibit different scenarios for the same excitation: e.g. shakedown or local damage up to failure. An insight into and criteria for such occurrences are achieved by formulating the rate and the finite increment problem as linear complementarity problems. Period doubling and deterministic chaos under harmonic excitation are observed when reversible (holonomic) softening behaviour is assumed. The strong sensitivity of the phenomena investigated with respect to the choice of the structural model is pointed out. The findings are elucidated by illustrative examples.