LMA - Laboratoire de Mécanique et d’Acoustique

I. Peshkov - A geometrical approach to continuum mechanics

Amphithéâtre François Canac, LMA

Le 2 octobre 2018 de 11h00 à 12h00

Ilya Peshkov
Institut de Mathématiques de Toulouse
Université Paul Sabatier

We discuss a geometrical approach to continuum mechanics and demonstrate that solids and fluids can be described from a unified geometrical standpoint. The principal field of the theory is the distortion field which can be seen as the non-holonomic basis triad and describes the deformation and rotation of material elements. Such triads account for the rotation degree of freedom which can be associated with the rotation degree of freedom of the microstructure. We then discuss how such a theory can be used to model turbulent flows and dispersive solid media which exhibits non-dissipative energy exchange between different scales. Some numerical examples will be demonstrated.

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