New Open-Access Publication in Acta Mechanica

7 Juli 2026

We are happy to announce the publication of the article"Mixed Finite Elements for Geometrically Exact Beams Using Discontinuous Rotations and Discrete Curvature" as an open-access paper in the journal Acta Mechanica.

In this paper, we present a novel mixed finite-element formulation for geometrically exact (Simo-Reissner) beams that introduces the moment vector as an additional independent field. This mixed formulation enables an element-local, discontinuous approximation of rotations, resulting in a simple and efficient discretization framework. Rotation discontinuities are treated consistently through the concept of discrete curvature, while objectivity is preserved at the discrete level by interpolating relative rotations using a multiplicative split of the rotation field. Numerical benchmark examples demonstrate optimal convergence rates and excellent accuracy, independent of the beam's slenderness and the order of approximation. In particular, the proposed lowest-order element completely avoids rotation interpolation by employing element-constant rotations only.

 

Humer, A., Steinbrecher, I., and Pechstein, A., 2026,
“Mixed Finite Elements for Geometrically Exact Beams Using Discontinuous Rotations and Discrete Curvature”, Acta Mechanica.

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