Abstract
The Present paper proposed a new constitutive equation that is applicable to proportional and non-proportional cyclic combined loading at the wide range of strain-rate from static to impact by introducing the inner-state variables. Using the variables, we can describe the behavior of materials without distinction between loading and unloading. Namely in this equation the loading state is described by the angle between the inner-state variable increment tensor and the stress tensor. Using this constitutive equation, some dynamic and static stress-strain relations for cyclic combined loadings of tension and torsion were calculated. As a result, Bauschinger effect can be expressed naturally for impact tensile load and unload as well as static one.
