This work is mainly concerned with both strain accumulation under cycles of plastic deformation, and instability due to cyclic strain accumulation.

An elastic-plastic strain-hardening solid in a quasi-static state of finite deformation is considered. A new, general variational principle is established for the boundary-value problem in which incremental displacements are prescribed on one portion of the boundary surface of a body and increments of nominal traction are prescribed on the remaining portion. Both Eulerian and Lagrangian formulations of this general variational principle are given. It is shown that certain extremum principles of Hill and Murphy and Lee may be considered as special cases of the newly established variational theorem.

A constitutive relation describing cyclic strain accumulation under very restricted conditions of steady-state cycling is proposed. This constitutive equation, which has not yet been verified experimentally, is further simplified for the case of fully-reversed cyclic loading. In this work a combination of the above constitutive relation and Hill's stability criterion for elastic-plastic solids is employed in the analysis of the effects of cyclic strain accumulation on the stability of solids under fully-reversed repeated loading. It is shown analytically that certain structural elements which may be initially stable for a given range of load or deformation, can progressively become unstable because of cyclic strain accumulation.

Instability due to cyclic strain accumulation is analyzed theoretically for thin cylindrical shells under fully-reversed cyclic torsion, repeated axial loading and cyclic biaxial loading where constant stress ratios are maintained during the repeated loading programmes. In all cases considered, the analysis suggests that plastic stability analyses based on monotonic loading alone may be unsafe.