Riemann solutions and spacetime discontinuous Galerkin method for linear elastodynamic contact
Riemann solutions and spacetime discontinuous Galerkin method for linear elastodynamic contact
复制标题
线性弹动力接触的黎曼解和时空不连续伽辽金方法
DOI：
10.1016/j.cma.2013.11.021
复制
发表时间：
2014
影响因子：
7.2
通讯作者：
R. Haber
中科院分区：
文献类型：
--
作者：
R. Abedi;R. Haber
我们推导出黎曼解的粘，滑动和分离接触模式的线弹性材料与各向同性库仑摩擦关系，并探讨其数值实现。Riemann解保留了基本弹性动力学系统的特征结构，并隐含了与某些数值模型中使用的准静态条件不同的动态接触条件。在粘滑过渡的标准库仑模型中，非物理不连续性会导致数值模拟中的接触模式颤振。我们重申库仑关系，以消除这些人为的不连续性，并消除需要算法的补救措施。在突然的分离到接触过渡的不连续响应是物理上合理的，我们提出了一个正则化方案来解决这种情况。我们实现了自适应时空不连续伽辽金（SDG）代码内的黎曼接触解决方案，并报告数值结果表明该模型的有效性。
We derive Riemann solutions for stick, slip and separation contact modes in a linear elastic material with an isotropic Coulomb friction relation and explore their numerical implementation. The Riemann solutions preserve the characteristic structure of the underlying elastodynamic system and imply dynamic contact conditions that are distinct from the quasi-static conditions used in some numerical models.Nonphysical discontinuities in the standard Coulomb model at stick–slip transitions can cause contact-mode chatter in numerical simulations. We restate the Coulomb relation to remove these artificial discontinuities and eliminate the need for algorithmic remedies. Discontinuous response at abrupt separation-to-contact transitions is physically reasonable, and we propose a regularization scheme to address this case. We implement the Riemann contact solutions within an adaptive spacetime discontinuous Galerkin (SDG) code and report numerical results that demonstrate the model’s efficacy.