Prevention of cyclic instability at the modeling of elasto-plastic deformation at large strains under proportional and non-proportional loading

The cyclic instability phenomenon is investigated at the modeling of large elasto-plastic strains. The instability is observed at large strains for some elasto-plastic material models with a kinematic hardening in contrast to the small strain case. The cyclic instability manifests itself as a changing of shape, sizes or location of the hysteresis loop during cycling. In partial case the cyclic instability leads to the stress ratcheting. Responses of 50 various models of elasto-plastic material have been considered under proportional loading (cyclic simple shear) and non-proportional loading (combined cyclic simple shear and tension-compression). Causes of the cyclic instability are analyzed and conditions ensuring the cyclic stability of elasto-plastic models are proposed.