An isogeometric finite element formulation for phase transitions on deforming surfaces

Zimmermann, Christopher; Toshniwal, Deepesh; Landis, Chad M.; Hughes, Thomas J. R.; Mandadapu, Kranthi K.; Sauer, Roger A.

doi:10.1016/j.cma.2019.03.022

Title: An isogeometric finite element formulation for phase transitions on deforming surfaces

Journal Article · Mon Jul 01 00:00:00 EDT 2019 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2019.03.022· OSTI ID:1567165

Zimmermann, Christopher ^[1]; Toshniwal, Deepesh ^[2]; Landis, Chad M. ^[2]; Hughes, Thomas J. R. ^[2]; Mandadapu, Kranthi K. ^[3];

^[1]

RWTH Aachen Univ. (Germany). Aachen Inst. for Advanced Study in Computational Engineering Science (AICES)
Univ. of Texas, Austin, TX (United States). Inst. for Computational Engineering and Sciences
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences Division; Univ. of California, Berkeley, CA (United States). Dept. of Chemical and Biomolecular Engineering

This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial differential equations (PDEs) that live on an evolving two-dimensional manifold. For the phase transitions, the PDE is the Cahn–Hilliard equation for curved surfaces, which can be derived from surface mass balance in the framework of irreversible thermodynamics. For the surface deformation, the PDE is the (vector-valued) Kirchhoff–Love thin shell equation. Both PDEs can be efficiently discretized using C¹-continuous interpolations without derivative degrees-of-freedom (dofs). Structured NURBS and unstructured spline spaces with pointwise C¹-continuity are utilized for these interpolations. The resulting finite element formulation is discretized in time by the generalized-α scheme with adaptive time-stepping, and it is fully linearized within a monolithic Newton–Raphson approach. A curvilinear surface parameterization is used throughout the formulation to admit general surface shapes and deformations. The behavior of the coupled system is illustrated by several numerical examples exhibiting phase transitions on deforming spheres, tori and double-tori.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1567165

Alternate ID(s):: OSTI ID: 1636225

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Vol. 351, Issue C; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 23 works

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