Two-scale Time Homogenization for Isotropic Viscoelastic- Viscoplastic Homogeneous Solids Under Large Numbers of Cycles

A two-scale time homogenization approach for coupled viscoelastic-viscoplatic (VE-VP) homogeneous solids and structures subjected to large numbers of cycles, is proposed. The main aim is to give a description of the long time behaviour, by calculating the evolution of internal variables within the structure, while reducing the computational overhead. This method consists in decomposing the original VE-VP initial-boundary problem into coupled micro-chronological (fast time scale) and macro-chronological (slow time-scale) problems. The proposed methodology was implemented and studied for J2 VP coupled with VE using fully implicit time integration and a return-mapping algorithm. An illustration of the time homogenization on a simple case is presented and a good agreement with the reference solution is observed.