One-step semi-implicit integration of general finite-strain plasticity models

Using the Kroner-Lee elastic and plastic decomposition of the deformation gradient, a differential-algebraic system is obtained (in the so-called semi-explicit form). The system is composed by a smooth nonlinear differential equation and a non-smooth algebraic equation. The development of an efficient one-step constitutive integrator is the goal of this work. The integration procedure makes use of an explicit Runge-Kutta method for the differential equation and a smooth replacement of the algebraic equation. The resulting scalar equation is solved by the Newton-Raphson method to obtain the plastic multiplier. We make use of the elastic Mandel stress construction, which is power-consistent with the plastic strain rate. Iso-error maps are presented for a combination of Neo-Hookean material using the Hill yield criterion and a associative flow law. A variation of the pressurized plate is presented. The exact Jacobian for the constitutive system is presented and the steps for use within a structural finite element formulation are described .