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首页> 外文期刊>Journal of Computational Physics >An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces
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An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces

机译：带有滑动界面的非线性弹性多分量问题的欧拉方法

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摘要

This paper is devoted to developing a multi-material numerical scheme for non-linear elastic solids, with emphasis on the inclusion of interfacial boundary conditions. In particular for colliding solid objects it is desirable to allow large deformations and relative slide, whilst employing fixed grids and maintaining sharp interfaces. Existing schemes utilising interface tracking methods such as volume-of-fluid typically introduce erroneous transport of tangential momentum across material boundaries. Aside from combatting these difficulties one can also make improvements in a numerical scheme for multiple compressible solids by utilising governing models that facilitate application of high-order shock capturing methods developed for hydrodynamics. A numerical scheme that simultaneously allows for sliding boundaries and utilises such high-order shock capturing methods has not yet been demonstrated. A scheme is proposed here that directly addresses these challenges by extending a ghost cell method for gas-dynamics to solid mechanics, by using a first-order model for elastic materials in conservative form. Interface interactions are captured using the solution of a multi-material Riemann problem which is derived in detail. Several different boundary conditions are considered including solid/solid and solid/vacuum contact problems. Interfaces are tracked using level-set functions. The underlying single material numerical method includes a characteristic based Riemann solver and high-order WENO reconstruction. Numerical solutions of example multi-material problems are provided in comparison to exact solutions for the one-dimensional augmented system, and for a two-dimensional friction experiment.
机译：本文致力于开发非线性弹性固体的多材料数值方案，重点是包括界面边界条件。特别是对于碰撞固体物体，希望允许较大的变形和相对滑动，同时采用固定的栅格并保持尖锐的界面。利用诸如流体体积之类的界面跟踪方法的现有方案通常会在材料边界上引入切向动量的错误传输。除了克服这些困难外，还可以通过利用控制模型来改进多种可压缩固体的数值方案，这些控制模型有助于应用为流体力学开发的高阶冲击捕获方法。尚未证明同时允许滑动边界并利用这种高阶震荡捕获方法的数值方案。本文提出了一种方案，该方案通过使用保守形式的弹性材料的一阶模型将气体动力学的幻影单元法扩展到固体力学，从而直接解决了这些挑战。使用详细推导的多材料黎曼问题的解决方案来捕获接口交互。考虑了几种不同的边界条件，包括固体/固体和固体/真空接触问题。使用级别设置功能跟踪界面。基本的单材料数值方法包括基于特征的Riemann求解器和高阶WENO重建。与一维增强系统和二维摩擦实验的精确解相比，提供了示例多材料问题的数值解。

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