The asymptotic behavior of perfectly elastoplastic model under periodic square generalized strain paths

Abstract

The perfectly elastoplastic model has been investigated previously under rectilinear generalized strain paths and cyclic circular strain paths. Being subsequent to these studies we subject the model to cyclic square generalized strain paths, for which the effects of nonproportionality of generalized strains and piecewise continuity of generalized strain rates can be investigated. It is found that the cyclic responses depend on the amplitude ratio and also on the initial generalized stress. The criterion of elastic shakedown is provided and the concept of elastic shakedown attractors is introduced. Then the behavior is classified in the space of initial generalized stresses. The boundaries of four elastic shakedown regions and elastic region are derived. It is only for larger values of amplitude ratio that the region IV appears. The formula used to estimate the closeness to the limit point is developed, and using that concept we derive a formula to evaluate the error induced when an asymptotic response is used to replace the exact one. For larger amplitude ratio the asymptotic response is almost identical to the exact response.

Key words:

• perfectly elastoplastic model
• fixed point
• elastic shakedown attractor
• asymptotic behavior