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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 Access status: Open Access , Cn-continuous mortar method for Isogeometric Analysis(2024)In recent years, isogeometric methods, using NURBS (Non-Uniform Rational B-Splines) as basis functions, have gained increasing attention. These methods offer exceptional flexibility in geometric modelling and the ability to adjust the smoothness of the piecewisedefined shape functions on a single patch as needed. This feature makes isogeometric analysis particularly attractive in the context of higher-order differential equations. However, to maintain this characteristic in the case of multiple patches, it must be appropriately accounted for in domain coupling. This work addresses this challenge by presenting a novel method for implementing general non-conforming weak Cn-continuous domain couplings within the framework of isogeometric analysis. This approach builds upon the established mortar method and extends it by imposing additional constraints on derivatives up to a specified order. Within this study, the method is comprehensively elucidated using an abstract variational framework. This encompasses discretisation within the context of isogeometric analysis, selection of the dual space, efficient handling of crosspoints and wirebaskets, and the evaluation of mortar integrals. A significant emphasis is also placed on the construction of isogeometric approximation spaces which a priori fulfil the higher-order coupling conditions. Furthermore, the performance and applicability of the method are investigated in various engineering problems, including elasticity, heat conduction, diffusion and Phase-Field-Crystal modelling. This is achieved through a series of simulations that substantiate the applicability and efficiency of the approach in various technical domains.Source Type:Doctoral ThesisSeries:Publication series of the Chair of Computational MechanicsVolume number:14 5 - 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 Cn-continuous mortar method for Isogeometric Analysis(2024-02-19)This work presents an innovative approach to tackle the challenge of implementing general non-conforming weak Cn-continuous domain couplings in isogeometric analysis. Building on the established mortar method, the approach extends it by introducing additional constraints on derivatives up to a specified order. The study comprehensively elucidates the method within an abstract variational framework, covering aspects such as discretisation in isogeometric analysis, dual space selection, efficient handling of crosspoints and wirebaskets, and the evaluation of mortar integrals. Special attention is given to constructing isogeometric approximation spaces that inherently satisfy higher-order coupling conditions. The performance and applicability of the method are explored in diverse engineering problems, including elasticity, heat conduction, diffusion, and Phase-Field-Crystal modelling. Through a series of simulations, the study demonstrates the efficiency and applicability of the approach in various technical domains.Source Type:DissertationSeries:Publication series of the Chair of Computational Mechanics8 4
