An eulerian mixed formulation for viscoplastic materials

This paper presents an eulerian mixed formulation for viscoplastic materials. The algorithm is formulated in terms of deviatoric stress, velocity and hydrostatic pressure using a Fractional Step algorithm that allows the use of equal order of interpolation for the three variables. The constitutive law is based on the viscoplasticity theory of Perzyna with the Von Mises yield criterion. The Jaumann rate of Cauchy stress tensor is used to ensure the objectivity of the constitutive law. A splitting scheme based on a two-step Taylor–Galerkin algorithm for the advective terms plus a fourth-order Runge–Kutta scheme for the sources has been used to improve the accuracy of the method.