The finite element method is an established and well-understood standard tool for simulating structural mechanical processes. In order to use the method in practice, one needs software systems that, in addition to the general mathematical framework, also incorporate the material laws of those materials that are represented in the structures to be simulated. While corresponding material algorithms exist for numerous established material classes, this is e.g. hardly the case for viscoelastic materials. An important aspect here is that proven mathematical models for such materials exhibit memory effects, i.e. the current state of deformation depends not only on the current load, but on the entire previous history. This is a significant difference to common material models which has significant software engineering implications for the algorithms to be used.
In view of this background, the Numerical Simulation team is concerned with the development and implementation of numerical methods with which such memory-based models can be treated reliably and efficiently. The current focus of work is on mathematical models based on differential equations of fractional (i.e. non-integer) order. Experience has shown that such models are particularly well suited to accurately describing the behavior of viscoelastic materials over longer periods of time. From a theoretical point of view, the so-called diffusive representation of the occurring differential and integral operators has significant advantages because, compared to traditional representations, it leads to algorithms that require less computing time, have a significantly lower memory requirement for handling the process history and can be integrated into existing, proven finite element packages with little software effort.