Stabilized finite element formulations for liquid membranes and their application to droplet contact
Stabilized finite element formulations for liquid membranes and their application to droplet contact
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DOI：
10.1002/fld.3905
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发表时间：
2014-07
影响因子：
1.8
通讯作者：
R. Sauer
中科院分区：
文献类型：
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作者：
R. Sauer
提出了一种适合分析液膜及其接触行为的液膜配方。在用于膜表面描述的曲线坐标系的一般框架中，给出了控制强形式和弱形式方程。特别强调了平面内平衡方程的稳定性，这对于液体膜的准静态描述是必不可少的。提出了两种新的稳定方案，仅影响平面内膜的行为，而不影响平面外膜的行为。进一步强调了施加非平凡接触角所需的线接触的描述。所提出的公式在考虑基于标准拉格朗日和基于等几何NURBS的有限元的有限元方法中离散化。计算接触算法制定了曲面和线的接触。给出了离散化公式的完全线性化。提出了大范围的数值例子来说明所提出的公式所捕获的不同物理方面。通过算例进一步分析了新稳定方案的性能。版权所有©2014 John Wiley & Sons， Ltd。
A liquid membrane formulation is presented that is suitable to analyze liquid films and their contact behavior. The governing strong form and weak form equations are presented in the general framework of the curvilinear coordinate system that is used for the surface description of the membrane. Particular emphasis is placed on the stabilization of the in‐plane equilibrium equations, which is essential for the quasi‐static description of liquid membranes. Two new stabilization schemes are proposed that affect only the in‐plane membrane behavior while leaving the out‐of‐plane membrane behavior unaffected. Further emphasis is placed on the description of line contact needed to impose nontrivial contact angles. The proposed formulation is discretized within the finite element method considering both standard Lagrange‐based and isogeometric NURBS‐based finite elements. Computational contact algorithms are formulated both for surface and line contact. The complete linearization of the discretize formulation is given. A large range of numerical examples is presented to illustrate the different physical aspects that are captured by the proposed formulation. The examples are further used to analyze the performance of the new stabilization schemes. Copyright © 2014 John Wiley & Sons, Ltd.