Consistent stiffness matrix in FE calculations of elasto-plastic bodies

In order to preserve the quadratic convergence of the Newton-Raphson method applied to elasto-plastic finite element calculations, the consistent stiffness matrix must be used. Here, the consistent stiffness matrix is derived for the generalized trapezoidal rule. Special attention is paid to the case in which the integration is performed from an elastic to an elasto-plastic state and it is shown that the movement of the contact stress influences the consistent stiffness matrix significantly. As an example, the von Mises material model with mixed isotropic/kinematic hardening is considered and numerical results are presented showing the superiority of the consistent stiffness matrix derived here not only compared with the continuum stiffness matrix, but also compared with the traditional consistent stiffness matrix where the influence of the contact point is ignored.