Semi-implicit methods for the dynamics of elastic sheets

JOURNAL OF COMPUTATIONAL PHYSICS

卷:399

Article

Alben, Silas¹  Gorodetsky, Alex A.²  Kim, Donghak²  Deegan, Robert D.^3,4 

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Michigan, Dept Aerosp Engn, Ann Arbor, MI 48109 USA

[3] Univ Michigan, Dept Phys, Ann Arbor, MI 48109 USA

[4] Univ Michigan, Ctr Study Complex Syst, Ann Arbor, MI 48109 USA

关键词: Elastic;    Buckling;    Dynamics;    Semi-implicit;    Bending;    Stretching;   

DOI  :  10.1016/j.jcp.2019.108952

来源: Elsevier

【 摘 要 】

Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints that arise in explicit methods while avoiding much of the complexity of fully-implicit approaches. For a triangular lattice discretization with stretching and bending springs, our semi-implicit approach involves discrete Laplacian and biharmonic operators, and is stable for all time steps in the case of overdamped dynamics. For a more general finite-difference formulation that can allow for general elastic constants, we use the analogous approach on a square grid, and find that the largest stable time step is two to three orders of magnitude greater than for an explicit scheme. For a model problem with a radial traveling wave form of the reference metric, we find transitions from quasi-periodic to chaotic dynamics as the sheet thickness is reduced, wave amplitude is increased, and damping constant is reduced. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free