Smoothing elastoplastic stress–strain curves obtained by a critical modification of conventional models

We first modify conventional one-dimensional perfectly elastoplastic constitutive model into a smooth one by shortening the switch-on time (or switch-on strain or switch-on stress) through a smooth factor (rho). This modification can be realized by assigning a piecewise constant yield stress .... When (rho)=1 we recover to the original model. By employing the same strategy to one-dimensional kinematic hardening model as well as to one-dimensional mixed-hardening model, we found that the newly modified models, besides provide a more smooth transition from elasticity to plasticity, are able to describe strain hardening effect, the Bauschinger effect, cyclic hardening effect, strain ratcheting behavior and even more complicated cyclic behavior. Then, we extend the same idea to modify a multi-dimensional mixedhardening model. Instead of the conventional zero-measure yield surface, the new model allows plasticity to happen in some non-zero-measure yield volume in stress space, which is the main reason to cause smooth elastoplastic stress–strain behavior; moreover, the original yield surface has to be viewed mathematically as a limiting surface of the new model. Because the new model shares the same governing equations as the original model has, it is thermodynamically consistent as the original model is. From computational aspect, since stress points are no longer confined on the yield surface, the new model is more easily to numerically implement than the original model, and the conventional numerical design to match the consistency condition, e.g. the radial return method, is now no more needed for the new model.