On the optimisation of viscoplastic constitutive modelling using a numerical feedback damping algorithm

The authors propose a mathematical model that, in the presence of a constant time step algorithm and a smooth evolution of a state variable, increases the performance of the numerical process, forces the convergence of the numerical solution and, consequently, improves the overall quality of the results. This method reduces the total number of time steps of a simulation process and minimizes the necessary CPU time. The proposed algorithm is based on the mathematical adjustment of the evolution of a chosen state variable. The resulting numerical signals are analysed and properly characterised. Several numerical signals, obtained from different non-linear simulation examples and conditions, are studied. Based on the characterisation of the numerical signals and considering that the numerical results reflect the behaviour of a vibratory system—the numerical code—with its own intrinsic mass, spring and dashpot elements, the authors develop a numerical damping algorithm and present its implementation. The algorithm is applied and tested with a non-linear finite element example, using a viscoplastic constitutive model. The authors also present a set of numerical validation tests consisting of the simulation of the development of residuals stresses that arise from the fabrication process of particle reinforced metal matrix composites (MMC). The cooling down stage of an AlSiCp 20% vol. MMC is simulated. In order to evaluate the performance of the algorithms, some results, obtained with and without the application of the optimisation algorithm, are presented and thoroughly compared. The numerical damper algorithm proves to be very efficient.