Shape transformation using the modified Allen–Cahn equation. (September 2020)

• Record Type: Journal Article
• Authors: Kim, Hyundong; Yoon, Sungha; Wang, Jian; Lee, Chaeyoung; Kim, Sangkwon; Park, Jintae; Kim, Junseok
• Is Part Of: Applied mathematics letters. Volume 107(2020)
• Publication Date: 2020-09
• Subjects: Phase-field -- Allen–Cahn equation -- Shape transformation -- Metamorphosis; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2020.106487
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we propose a phase-field model for the shape transformation and its simple numerical method. The proposed phase-field model is based on the Allen–Cahn equation, which is a second-order nonlinear parabolic partial differential equation and originally arises from modeling phase separation in alloys. The numerical scheme is a hybrid method using the operator splitting method. To validate the proposed phase-field model for the shape transformation, we perform two- and three-dimensional shape metamorphosis. The proposed phase-field model is also compared with the linear interpolation. The computational results demonstrate that the proposed mathematical model satisfactorily and naturally simulate the shape transformation.