Curved Three‐Director Cosserat Shells with Strong Coupling

• Published in: Computer graphics forum Vol. 43; no. 8
• Main Authors: Löschner, F., Fernández‐Fernández, J. A., Jeske, S. R., Bender, J.
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01-12-2024
• Subjects: Angular velocity; Animation; Computer graphics; Coupling; Deformation; Degrees of freedom; Discretization; Newton methods; Shearing; Simulation
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.15183

Continuum‐based shell models are an established approach for the simulation of thin deformables in computer graphics. However, existing research in physically‐based animation is mostly focused on shear‐rigid Kirchhoff‐Love shells. In this work we explore three‐director Cosserat (micropolar) shells which introduce additional rotational degrees of freedom. This microrotation field models transverse shearing and in‐plane drilling rotations. We propose an incremental potential formulation of the Cosserat shell dynamics which allows for strong coupling with frictional contact and other physical systems. We evaluate a corresponding finite element discretization for non‐planar shells using second‐order elements which alleviates shear‐locking and permits simulation of curved geometries. Our formulation and the discretization, in particular of the rotational degrees of freedom, is designed to integrate well with typical simulation approaches in physically‐based animation. While the discretization of the rotations requires some care, we demonstrate that they do not pose significant numerical challenges in Newton's method. In our experiments we also show that the codimensional shell model is consistent with the respective three‐dimensional model. We qualitatively compare our formulation with Kirchhoff‐Love shells and demonstrate intriguing use cases for the additional modes of control over dynamic deformations offered by the Cosserat model such as directly prescribing rotations or angular velocities and influencing the shell's curvature.