arXiv subjects

Michael Wolfgang Kaiser

Publications and source records attributed to Michael Wolfgang Kaiser.

5 recordsLinked to original sources

arXiv2026

Hyperelastic Membranes with Implicitly Defined, Continuously Embedded Fibers

A novel mechanical model and corresponding finite element method for anisotropic, hyperelastic, curved membranes are proposed. Hyperelastic fibers are embedded into the otherwise isotropic membrane, being relevant, for example, in reduced models for biological tissues and textiles. The geometrically nonlinear mechanics is formulated based on first principles of continuum mechanics (finite strain theory). The employed differential operators are formulated in a coordinate-free manner, through a framework known as tangential differential calculus. This enables a (semi-)implicit description of the fiber geometry through the intersection of level sets of some scalar function with the explicitly defined membrane surface. The mechanical model of the implicit fibers is then coupled to the mechanics of the membrane. For the numerical analysis, finite elements are applied such that the resulting scheme is a hybrid between classical Surface FEM and fictitious domain methods. For smooth physical fields, higher-order convergence rates are obtained and confirm the success of the numerical method.

cs.CE↗

arXiv2026

Simultaneous analysis of curved Kirchhoff beams and Kirchhoff--Love shells embedded in bulk domains

A set of curved beams and shells is geometrically implied by level sets of a scalar function over some bulk domain. The mechanical model for each structure is based on the Kirchhoff--Love theory, that is, small displacements without shear deformations are considered. These models for individual geometries are extended to bulk models, simultaneously modeling the whole set of beams/shells on all level sets. A major focus is on the numerical analysis of such models. A mixed-hybrid and higher-order accurate Bulk Trace FEM is proposed that enables the use of standard $C^0$-continuous Lagrange elements with dimensionality of the bulk domain. That is, the higher-order continuity requirements of displacement-based formulations in context of the Kirchhoff--Love theory are successfully alleviated. Several numerical tests confirm the accuracy and higher-order convergence of the proposed methodology, also qualifying as benchmark test cases in future studies.

cs.CE↗

arXiv2025

Higher-order, mixed-hybrid finite elements for Kirchhoff-Love shells

A novel mixed-hybrid method for Kirchhoff-Love shells is proposed that enables the use of classical, possibly higher-order Lagrange elements in numerical analyses. In contrast to purely displacement-based formulations that require higher continuity of shape functions as in IGA, the mixed formulation features displacements and moments as primary unknowns. Thereby the continuity requirements are reduced, allowing equal-order interpolations of the displacements and moments. Hybridization enables an element-wise static condensation of the degrees of freedom related to the moments, at the price of introducing (significantly less) rotational degrees of freedom acting as Lagrange multipliers to weakly enforce the continuity of tangential moments along element edges. The mixed model is formulated coordinate-free based on the Tangential Differential Calculus, making it applicable for explicitly and implicitly defined shell geometries. All mechanically relevant boundary conditions are considered. Numerical results confirm optimal higher-order convergence rates whenever the mechanical setup allows for sufficiently smooth solutions; new benchmark test cases of this type are proposed.

cs.CE↗

arXiv2025

Simultaneous solution of incompressible Navier-Stokes flows on multiple surfaces

A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by all level sets of a scalar function, bounded by the three-dimensional bulk domain. This bulk domain is discretized with hexahedral finite elements which do not necessarily conform with the level sets but with the boundary. The resulting numerical method is a hybrid between conforming and non-conforming finite element methods. Taylor-Hood elements or equal-order element pairs for velocity and pressure, together with stabilization techniques, are applied to fulfil the inf-sup conditions resulting from the mixed-type formulation of the governing equations. Numerical studies confirm good agreement with independently obtained solutions on selected, individual surfaces. Furthermore, higher-order convergence rates are obtained for sufficiently smooth solutions.

cs.CE↗

arXiv2023

Simultaneous Analysis of Continuously Embedded Reissner-Mindlin Shells in 3D Bulk Domains

A mechanical model and numerical method for the simultaneous analysis of Reissner-Mindlin shells with geometries implied by a continuous set of level sets (isosurfaces) over some three-dimensional bulk domain is presented. A three-dimensional mesh in the bulk domain is used in a tailored FEM formulation where the elements are by no means conforming to the level sets representing the shape of the individual shells. However, the shell geometries are bounded by the intersection curves of the level sets with the boundary of the bulk domain so that the boundaries are meshed conformingly. This results in a method which was coined Bulk Trace FEM before. The simultaneously considered, continuously embedded shells may be useful in the structural design process or for the continuous reinforcement of bulk domains. Numerical results confirm higher-order convergence rates.

cs.CE↗