Natural mixed-dimensional couplings in Cosserat continua via tangential differential calculus
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We present an approach to coupling mixed-dimensional continua leveraging the mathematically enriched Cosserat micropolar model, which maintains its fundamental degrees of freedom even when reduced to lower-dimensional domains, relating to shells, plates, and beams. This natural agreement of degrees of freedom at interfaces with different dimensionalities eliminates the need for intermediate finite elements or mortar methods. We derive models of various dimensions using tangential differential calculus and achieve the coupling through a mixed-dimensional action functional with consistent Sobolev trace operators. Finally, we present numerical examples and conclude with potential future developments.