Abstract
AbstractMorphological changes in lipid bilayer vesicles are due to phase transitions and surface deformations occurring in unison. We present a dynamic chemo‐mechanical finite element model to study such changes. This is achieved by coupling two fourth order partial differential equations (PDEs): The Cahn‐Hilliard [2] mass balance equation based on irreversible thermodynamics, and the Kirchhoff‐Love [1] rotation free thin shell equation. The Helmholtz free energy consists of Helfrich energy to model elastic bending, and also includes in‐plane elastic energy with a finite shear modulus for the purpose of regularization. The geometry is discretized by C1‐continuous NURBS shape functions. An implicit second order accurate generalized‐α scheme is used for time integration. Newton‐Raphson iterations are utilized to solve the resulting linearized weak form monolithically. The proposed formulation is illustrated by a numerical example.
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