Intrinsic mixed-dimensional beam-shell-solid couplings in linear Cosserat continua via tangential differential calculus

We present an approach to the coupling of mixed-dimensional continua by
employing the mathematically enriched linear Cosserat micropolar model. The
kinematical reduction of the model to lower dimensional domains leaves its
fundamental degrees of freedom intact. Consequently, the degrees of freedom
intrinsically agree even at the interface with a domain of a different
dimensionality. Thus, this approach circumvents the need for intermediate
finite elements or mortar methods. We introduce the derivations of all models
of various dimensions using tangential differential calculus. The coupling
itself is then achieved by defining a mixed-dimensional action functional with
consistent Sobolev trace operators. Finally, we present numerical examples
involving a three-dimensional silicone-rubber block reinforced with a curved
graphite shell on its lower surface, a three-dimensional silver block
reinforced with a graphite plate and beams, and lastly, intersecting silver
shells reinforced with graphite beams.