Klaus Hackl, klaus.hackl@rub.de
Co-authors: Muhammad Sabeel Khan
Modeling of microstructures in a Cosserat continuum using relaxed energies
A continuum model for granular materials exhibiting microstructures is presented using the concept of energy
relaxation. In the framework of Cosserat continuum theory the free energy of the material is enriched with
an interaction energy potential taking into account the counter rotations of the particles. The total energy
thus becomes non-quasiconvex, giving rise to the development of microstructures. Relaxation theory is then
applied to compute its exact quasiconvex envelope. It is worth mentioning that there are no further assumptions
necessary here. The computed relaxed energy yields all possible field fluctuations of displacements and microrotations as minimizers. We show that the material behavior can be divided into three different regimes. Two
of the material phases are exhibiting microstructures in rotational and translational motion of the particles,
respectively, and the third one is corresponding to the case where there is no internal structure of the deformation
field. The properties of the proposed model are demonstrated by carrying out numerical computations. The
obtained results exhibit a number of unexpected features, for example the transition between distributed and
localized microstructures.