Consistent discretization of higher-order interface models for thin layers and elastic material surfaces, enabled by isogeometric cut-cell methods
Consistent discretization of higher-order interface models for thin layers and elastic material surfaces, enabled by isogeometric cut-cell methods
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DOI：
10.1016/j.cma.2019.03.010
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发表时间：
2019-06
影响因子：
7.2
通讯作者：
Z. Han;S. Stoter;Chien-Ting Wu;Changzheng Cheng;Angelos Mantzaflaris;S. Mogilevskaya;D. Schillinger
中科院分区：
文献类型：
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作者：
Z. Han;S. Stoter;Chien-Ting Wu;Changzheng Cheng;Angelos Mantzaflaris;S. Mogilevskaya;D. Schillinger
许多界面公式，例如基于渐近薄界面模型或材料表面理论，涉及高阶微分算子和不连续解场。在这篇文章中，我们正在采取的第一步变分一致的离散化框架，自然地适应这两个挑战，协同结合最近的事态发展，在等几何分析和切割单元有限元方法。它的基础是混合变分制定的弹性界面问题，提供了访问跳跃的位移和应力纳入一般的界面条件。在用光滑样条离散化后，可以一致地评估任意阶的导数，而切割单元格网格可以在潜在的复杂界面处实现不连续的解决方案。我们通过数值试验证明了三个特定的非平凡的接口（两个制度的Benveniste-Miloh分类的薄层和Gurtin-Murdoch材料表面模型），我们的框架是几何灵活的，并提供了最佳的高阶精度在散装和界面。
Many interface formulations, e.g. based on asymptotic thin interphase models or material surface theories, involve higher-order differential operators and discontinuous solution fields. In this article, we are taking first steps towards a variationally consistent discretization framework that naturally accommodates these two challenges by synergistically combining recent developments in isogeometric analysis and cut-cell finite element methods. Its basis is the mixed variational formulation of the elastic interface problem that provides access to jumps in displacements and stresses for incorporating general interface conditions. Upon discretization with smooth splines, derivatives of arbitrary order can be consistently evaluated, while cut-cell meshes enable discontinuous solutions at potentially complex interfaces. We demonstrate via numerical tests for three specific nontrivial interfaces (two regimes of the Benveniste–Miloh classification of thin layers and the Gurtin–Murdoch material surface model) that our framework is geometrically flexible and provides optimal higher-order accuracy in the bulk and at the interface.