Modeling of microstructures in a cosserat continuum using relaxed energies

Khan, M.S. and Hackl, K.

Volume: 27 Pages: 103-125
DOI: 10.1007/978-3-319-75940-1_6
Published: 2018

Granular materials tend to exhibit distinct patterns under deformation consisting of layers of counter-rotating particles. In this article, we are going to model this phenomenon on a continuum level by employing the calculus of variations, specifically 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 displacement and micro-rotation field fluctuations as minimizers. Based on a two-field variational principle the constitutive response of the material is derived. Results from numerical computations demonstrating the properties of relaxed potential are shown. © 2018, Springer International Publishing AG, part of Springer Nature.

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