Shape transformation using the modified Allen-Cahn equation

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. (C) 2020 Elsevier Ltd. All rights reserved.