Hi
Isotropic hardening means, sigma_yield ll be same under both the tension (sigma_tension_yield) and compression loading(sigma_comp_yield). and the total sigma_y=sigma_tensio_yield+sigma_comp_yield.
In the case of isotropic hardening, If you increase the tensile yield strength by some means, at the same time your compressive stress ll also get increased. Hence, you get a increased radius of the yield surface. with the same shape with increased size of yield surface. and your total sigma_y ll no more remain constant. It ll get increased.
It doesn't mean that you can not perform the unloading with isotropic hardening. You can do unloading, But the only thing you ll get same increased yield strength for compression also.
Whereas in the case of kinematic hardening, we observed Bouschinger's effect. It means if you increase the tensile yield strength (sigma_tension_yield) by some means, your compressive strength (sigma_comp_yield) ll get reduced. But the total sigma_y=sigma_tensio_yield+sigma_comp_yield. remains constant always.
and you ll get a shift in your yield surface but the shape and size remains constant.
Hope so this ll help you to understand the difference between the Kinematic Hardening and Isotropic Hardening
regards
Vijay Kumar Sutrakar