Schmidt, Felix
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Publication Access status: Open Access , Generalized Continua with Embedded Fibers and Dimension-Expanded Multi-scale Coupling(2026)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.Source Type:Doctoral ThesisSeries:Publication series of the Chair of Computational MechanicsVolume number:25 13 - Some of the metrics are blocked by yourconsent settings
Publication Generalized Continua with Embedded Fibers and Dimension-Expanded Multi-scale Coupling(2026)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.Source Type:Doctoral ThesisSeries:Publication series of the Chair of Computational Mechanics5 4 - Some of the metrics are blocked by yourconsent settings
Publication Access status: Metadata only , Variational formulation and monolithic solution of computational homogenization methods(2024); ; In this contribution, we derive a consistent variational formulation for computational homogenization methods and show that traditional FE and IGA approaches are special discretization and solution techniques of this most general framework. This allows us to enhance dramatically the numerical analysis as well as the solution of the arising algebraic system. In particular, we expand the dimension of the continuous system, discretize the higher dimensional problem consistently and apply afterwards a discrete null‐space matrix to remove the additional dimensions. A benchmark problem, for which we can obtain an analytical solution, demonstrates the superiority of the chosen approach aiming to reduce the immense computational costs of traditional FE and IGA formulations to a fraction of the original requirements. Finally, we demonstrate a further reduction of the computational costs for the solution of general nonlinear problems.Source Type:ArticleDOI:10.1002/nme.75671
