Localization in shell expansion in biaxial loading conditions

Abstract
The development of plastic instabilities in a thin shell loaded in biaxial traction in its tangent plane is difficult to justify when the constitutive material is elasto-plastic with a Von Mises yield surface. The criterion for the activation of bands of localization is not fulfilled except for strongly negative strain hardening parameters (in other words, a strong strain softening effect which is probably never met). On the contrary, the use of a Tresca yield surface leads to bands for perfectly plastic materials. The simulations of plastic instabilities in an expanding hemisphere of tantalum with a Steinberg plasticity model show the same tendencies: the use of a Von Mises yield surface gives no localization whereas the use of a Tresca surface gives a localization pattern which looks like the one observed experimentally.