A Fourier transformation-based temporal integration scheme for viscoplastic solids subjected to fatigue deterioration

A Fourier transformation-based temporal integration (FTTI) scheme is proposed, which adapts the conventional FE method for modeling the viscoplastic deterioration in a structure subjected to cyclic loading. The response fields are represented by a Fourier series which assumes a temporal scale separation: a microchronological (short time) scale arises from the oscillatory loading and a macrochronological (long time) scale is due to the slow material relaxation resulting from yielding and damage evolution. The original dynamic boundary value problem (BVP) is approximated by the stationary BVP on the microchronological scale. Alternation of the displacement field on the macrochronological scale is correlated with evolution of the history variables by means of a high order adaptive cycle jump method. Performance and significant acceleration of the FE simulations is demonstrated at different loading scenarios for a constitutive damage model where the progressive damage accumulation is driven by viscoplastic yielding.