Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity. Part I: Theoretical formulation

A derivation of the projected algorithm for general isotropic three-invariant plasticity models under plane stress conditions is presented. It is obtained by consistently specializing the 3D formulation to the 2D subspace defined by the plane stress condition. Closed-form intrinsic algorithm linearization and a novel expression of the consistent tangent tensor are provided; these are also shown to directly emanate from the analogous quantities pertaining to the fully 3D case. A detailed discussion of the proposed implementation along with a representative set of numerical examples is provided in the second part of this paper [Valoroso, N., Rosati, L., 2008. Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity. Part II: Computational issues. International Journal of Solids and Structures, 46, 92–124.