Séance Séminaire

Séminaire ACSIOM

Modelling and computing generalized continua via complexes: an example of linear Cosserat models

It is often necessary to introduce microscopic degrees of freedom in continuum mechanics. In 1909, the Cosserat brothers introduced such a model that incorporates a pointwise rotation to elasticity. As an example of the micropolar theory, the Cosserat model describes, for instance, granular media. In this talk, we first observe connections between generalized continuum models and Hilbert complexes and the Bernstein-Gelfand-Gelfand (BGG) construction. This connection leads to a systematic approach to understand (and potentially generalize) micropolar models. Based on this observation, we derive numerical discretization of the Cosserat models using distributional finite elements and ideas from Finite Element Exterior Calculus. The resulting scheme is robust with the physical parameters (locking-free) including the Lamé constant and a coupling parameter: when the coupling parameter goes to zero, the scheme solves standard elasticity; when the parameter is infinity, the scheme solves a high-order couple stress problem.