Generalized Continua with Embedded Fibers and Dimension-Expanded Multi-scale Coupling

Microstructured and fiber-reinforced materials exhibit mechanical behavior that cannot always be captured by classical continuum models. Bending-dominated mechanisms, size effects and non-local interactions require formulations that go beyond first-gradient Cauchy continua, while fully resolved three-dimensional simulations of the underlying microstructure are often computationally extensive.
This work develops higher-order modeling and simulation frameworks that bridge this gap. Embedded slender reinforcements are described either by continuous second-gradient fiber models or by geometrically exact Cosserat beams coupled to a surrounding threedimensional matrix. Through consistent kinematic coupling and static condensation, these descriptions lead to effective higher-order continua capable of representing fiberinduced stiffness and curvature effects efficiently.
In addition, a continuous higher-order multi-scale formulation based on dimension expansion is proposed. By combining macroscopic Taylor expansions with microscopic fluctuation fields and energetically consistent averaging, the framework derives generalized macroscopic stresses directly from the microstructure and includes the classical FE² method as a special case. The resulting approaches provide a coherent computational framework for investigating micro-structured materials within an isogeometric analysis setting.