Computational Structural Mechanics of Strain Gradient Theory

Only a few problems of structural mechanics can be solved in analytical manner. Therefore, the contemporary evaluation of structural mechanics is mainly based on computational methods. Macroscopic samples are usually simulated in the frame of continuum mechanics. But when the length scale of small sized samples approaches dimensions in the micron scale, limitations of the conventional continuum theory become obvious. At the length scale of a few microns, a size effect in the sense smaller is stronger is often observed. This effect cannot be described by conventional continuum theory. Hence, so called strain gradient theories were introduced, which have a capability of describing structural size effects of mechanical properties. A gradient of strain represents the variation of strain on a short distance. Within strain gradient theory it is assumed that a gradient of strain increases the internal energy of a sample. In consequence, an increased material stiffness of small scaled samples is observed. This size effect occurs in the elastic and as well in the plastic deformation regime. However, there are still open questions in context with this theory. In particular, the role of the material parameters is unclear. Even though selected experiments were successfully described with plausible material parameters, there are other experiments which appear to be in contradiction with those parameters. The here proposed project is devoted to the solution of this problem. For this purpose, different deformation modes are distinguished in order to find a consistent set of parameters, which can accomplish agreement with all relevant experiments. The comparison between experiments and theory will be enabled with computer simulations using finite elements of the mixed type. Thereby, the mixed elements will be implemented in commercial software with user subroutines. The numerical method will be subjected to extensive verification and validation. Material parameters will be obtained by numerical fitting of experimental data. Moreover, the methodology of strain gradient theory will be applied to explanation of experiments of material fatigue. Experiments will be conducted at TU Wien and at the Erich Schmid Institute of the Austrian Academy of Sciences in Leoben. Computer simulations will be performed at the Vienna Scientific Cluster.