Abstract
Professor Germain has proposed in [Germain, 1973] a theory of Cosserat continua obtained through the principle of virtual power. We propose here an application of that theory to the elastoplastic behaviour of polycrystals. We put forward a model of continuum with microstructure representing a material body, the elements of which are single crystals. Crystals may deform with elasto-plastic behavior, with the plastic rules given through a multiple slip method.
The field of orientation of the crystal lattice is a microscopic kinematic descriptor of the system; correspondingly the lattice spin is a kinematic unknown. As customary in the theory of continua with microstructure, a balance condition for the micro-momentum is associated with this unknown.
First we recall the main equations of Cosserat continua, then we present a kinematic description of polycrystals and, finally, we establish the constitutive equations for the case at issue.
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Brocato, M., Ehrlacher, A., Tamagny, P. (2000). Application of the theory of Cosserat media to the elasto-plastic behaviour of polycrystals. In: Maugin, G.A., Drouot, R., Sidoroff, F. (eds) Continuum Thermomechanics. Solid Mechanics and Its Applications, vol 76. Springer, Dordrecht. https://doi.org/10.1007/0-306-46946-4_2
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DOI: https://doi.org/10.1007/0-306-46946-4_2
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