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IGA-MPM: The Isogeometric Material Point Method
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.cma.2020.113346
Georgios Moutsanidis , Christopher C. Long , Yuri Bazilevs

Abstract We propose the use of Isogeometric Analysis (IGA) within the context of the Material Point Method (MPM), and refer to the approach as IGA-MPM. We use the idea of IGA, and its instantiation based on Non-Uniform Rational B-Splines (NURBS), to build higher-order accurate and smooth approximation for MPM. Higher-order smoothness yields a continuous representation of the strain rate, and, as a result, prevents jumps in the stress and other history variables as the material points cross the element boundaries. Furthermore, NURBS can exactly represent all conic sections and the corresponding symmetries in the solution, which may be important in some applications. Several numerical examples of increasing complexity are presented, and show the ability of IGA-MPM to eliminate the well known cell-crossing instability of the conventional MPM. In addition, the examples presented demonstrate improved accuracy, convergence, and symmetry preservation of IGA-MPM compared to the conventional MPM, both for rectilinear and curved geometries.

中文翻译:

IGA-MPM:等几何材料点法

摘要 我们建议在材料点法 (MPM) 的背景下使用等几何分析 (IGA),并将该方法称为 IGA-MPM。我们使用 IGA 的思想及其基于非均匀有理 B 样条 (NURBS) 的实例化,为 MPM 构建高阶准确和平滑的近似。高阶平滑产生应变率的连续表示,因此,当材料点跨越单元边界时,可以防止应力和其他历史变量的跳跃。此外,NURBS 可以准确地表示解中的所有圆锥截面和相应的对称性,这在某些应用中可能很重要。提出了几个增加复杂性的数值例子,并显示了 IGA-MPM 消除传统 MPM 众所周知的细胞交叉不稳定性的能力。
更新日期:2020-12-01
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