English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the zaia usage as premium feature

ZAIA

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the access of premium content as premium feature

Premium Content

Zendy Tools

Zendy Open

This paper presents a general theory and isogeometric finite elementimplementation for studying mass conserving phase transitions on deformingsurfaces. The mathematical problem is governed by two coupled fourth-ordernonlinear partial differential equations (PDEs) that live on an evolvingtwo-dimensional manifold. For the phase transitions, the PDE is theCahn-Hilliard equation for curved surfaces, which can be derived from surfacemass balance in the framework of irreversible thermodynamics. For the surfacedeformation, the PDE is the (vector-valued) Kirchhoff-Love thin shell equation.Both PDEs can be efficiently discretized using $C^1$-continuous interpolationswithout derivative degrees-of-freedom (dofs). Structured NURBS and unstructuredspline spaces with pointwise $C^1$-continuity are utilized for theseinterpolations. The resulting finite element formulation is discretized in timeby the generalized-$\alpha$ scheme with adaptive time-stepping, and it is fullylinearized within a monolithic Newton-Raphson approach. A curvilinear surfaceparameterization is used throughout the formulation to admit general surfaceshapes and deformations. The behavior of the coupled system is illustrated byseveral numerical examples exhibiting phase transitions on deforming spheres,tori and double-tori.

An isogeometric finite element formulation for phase transitions on deforming surfaces