Secret and joy of configurational mechanics: From foundations in continuum mechanics to applications in computational mechanics

Over the recent years configurational mechanics has developed into a very active and successful topic both in continuum mechanics as well as in computational mechanics. On the continuum mechanics side the basic idea is to consider energy variations that go along with changes of the material configuration. Configurational forces are then energetically dual to these configurational changes. Configurational forces take the interpretation as being the driving forces in the kinetics of defects; like e.g., cracks, inclusions, phase boundaries, dislocations and the like. On the computational side it turns out that a discretisation scheme brings in artificial, discrete configurational forces that indicate in a certain sense the quality, e.g., of a finite-element mesh. This information can then be used to optimize the nodal material positions. Surprisingly, even driven by energetical arguments, it turns out that a finite element mesh optimized with respect to discrete configurational forces also renders superior results in terms of classical error measures. The manuscript will span the field from the underlying theoretical foundations over the algorithmic challenges to various computational applications