An integration procedure based on multi‐surface plasticity for plane stress plasticity: Theoretical formulation and application

An integration procedure designed to satisfy plane stress conditions for any constitutive law initially described in 3D and based on classical plasticity theory is presented herein. This method relies on multi‐surface plasticity, which allows associating in series various mechanisms. Three mechanisms have ultimately been used and added to the first one to satisfy the plane stress conditions. They are chosen to generate a plastic flow in the 3 out‐of‐plane directions, whose stresses must be canceled (σ₃₃,σ₁₃, and σ₂₃). The advantage of this method lies in its ease of use for every plastic constitutive law (in the general case of the non‐associated flow rule and with both nonlinear kinematic and isotropic hardening). Method implementation using a cutting plane algorithm is presented in its general framework and then illustrated by the example of a J2‐plasticity material model considering linear kinematic and isotropic hardening. The approach is compared with the same J2‐plasticity model that has been directly derived from a projection of its equations onto the plane stress subspace. The performance of the multi‐surface plasticity method is shown through the comparison of iso‐error and iso‐step contours in both formulations, and lastly with a case study considering a hollow plate subjected to tension. Copyright © 2014 John Wiley & Sons, Ltd.