Using constitutive models of the rate type in implicit finite-element calculations: error-controlled stress update and consistent tangent operator

Summary

The consistent tangent operator is important for efficient finite-element calculations. By means of a one-dimensional model problem, we explain how this operator can be calculated. Based on this, a general approach for obtaining the consistent tangent operator for constitutive equations of the rate type is given. In order to achieve reliable results in the finite-element calculations, an error controlled time integration of the constitutive law should be provided. Here an adaptive time integration method is used which is based on a control of the local error. The effects of the numerical time integration scheme are studied in detail with the help of a one-dimensional hypoplastic example. Further a finite-element example is given to show the performance of the presented general approach. Quadratic convergence of the equilibrium iteration is shown.