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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Consistent discretization of higher-order interface models for thin layers and elastic material surfaces, enabled by isogeometric cut-cell methods
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Consistent discretization of higher-order interface models for thin layers and elastic material surfaces, enabled by isogeometric cut-cell methods

机译：通过等几何切割单元方法实现的用于薄层和弹性材料表面的高阶界面模型的一致离散化

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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. (C) 2019 Elsevier B.V. All rights reserved.
机译：许多界面公式，例如基于渐近薄相间模型或材料表面理论，涉及高阶微分算子和不连续解场。在本文中，我们正朝着变异一致的离散化框架迈出第一步，该框架通过将等几何分析和切单元有限元方法的最新发展协同结合，自然地适应了这两个挑战。它的基础是弹性界面问题的混合变分公式化，它提供了位移和应力跳跃的途径，以结合一般的界面条件。通过平滑样条进行离散化后，可以一致地评估任意阶的导数，而切割单元网格可以在潜在的复杂界面处实现不连续求解。我们通过对三个特定的非平凡界面（薄层Benveniste-Miloh分类的两个方案和Gurtin-Murdoch材料表面模型的两个方案）进行的数值测试证明，我们的框架在几何上具有灵活性，并在体积和变形方面提供了最佳的高阶精度。接口。 （C）2019 Elsevier B.V.保留所有权利。

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