A homogenisation strategy for micromorphic continua based on particle mechanics

Materials with a granular microstructure frequently fail in narrow zones due to strain localisation. Examplarily, one may look at the shear-zone development in dry sand during bi- and triaxial loading, where grains in the shear-zone exhibit large displacements and rotations. Furthermore, localisation is also observed in materials, where the microstructure consists of grains and a binding material, such as for example metal-casting moulds. Here, sand grains are bound together via a polyurethan-based material and macroscopic material failure originates from the deformation and breakage of the binder material. Within a continuum-based modelling approach, these microstructural effects can be accounted for by the consideration of an additional microcontinuum at each material point of the macroscopic body. These extended continuum theories, such as the micromorphic continua and its micropolar and microstrain sub-formulations, assume a characteristic microcontinuum deformation on a lower scale and have been successfully applied in the field of granular media. Exemplarily, in the framework of a micropolar continua, it is possible to contact forces to stresses and couple stresses via an appropriate homogenisation technique. This method includes the introduction of a Representative Elementary Volume (REV) on the mesoscale situated between the particle and the continuum scale. In this contribution, a homogenisation strategy based on a particle-centre-based REV definition is presented that is generally valid for micromorphic and micropolar continua. Therefore, a grain-binder microstructure is investigated, where particle rotations contribute to the micropolar part, while binder deformations yield the additional macromorphic character. Numerical examples are given, where results from discrete-element simulations are locally averaged and show the individual activation of the microcontinuum characteristics in the localised zones. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)