Rotating plasticity and nonshakedown collapse modes for elastic–plastic bodies under cyclic loads

• Elastic plastic hardening materials under cyclic loading are studied.
• Both static and reduced kinematic approaches are used to study collapse modes.
• Finite element realizations and mathematical programming techniques are implemented.
• A body may fail by rotating plasticity mode rather than the alternating plasticity one.

Different plastic collapse modes may have different effects on the overall behaviour and load-bearing capacity of an elastic–plastic structure subjected to variable loads, and they may even be determined by different material plastic constants (for general plastic hardening materials). Both lower bound static and upper bound reduced kinematic approaches have been implemented with appropriate finite element realizations and mathematical programming techniques to study the nonshakedown modes for elastic plastic bodies under cyclic loads. For sufficiently complex structure and loading program, it has been firstly demonstrated that an elastic–plastic body may fail by rotating plasticity collapse rather than the simpler alternating plasticity one among other possible modes. That and other results also lead to interesting problems for further studies.