Evaluation of Accuracy and Stability of the Classical SPH Method Under Uniaxial Compression

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• 作者：R. Das ; P. W. Cleary
• 关键词：Smoothed particle hydrodynamics ; Elasticity ; Uniaxial compression ; Stress waves ; Convergence ; Stability
• 刊名：Journal of Scientific Computing
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：64
• 期：3
• 页码：858-897
• 全文大小：5,529 KB
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• 作者单位：R. Das (1)
  P. W. Cleary (2)
  
  1. Department of Mechanical Engineering, Centre for Advanced Composite Materials, University of Auckland, Auckland, 1010, New Zealand
  2. CSIRO Mathematics, Informatics and Statistics, Normanby Road, Clayton, VIC, 3168, Australia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algorithms
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1573-7691

文摘

The accuracy and stability of the classical formulation of the smoothed particle hydrodynamics (SPH) method for modelling compression of elastic solids is studied to assess its suitability for predicting solid deformation. SPH has natural advantages for simulating problems involving compression of deformable solids arising from its ability to handle large deformation without re-meshing, complex free surface behaviour and tracking of multiple material interfaces. The ‘classical SPH method- as originally proposed by Monaghan?(in Ann Rev Astron 30:543-74, 1992, Rep Prog Phys 68:1703-759, 2005), has become broadly established as a robust method in different areas, especially involving fluid flows. However, limited attention has been paid to understanding of its numerical performance for elastic deformation problems. To address this, we evaluate the classical SPH method to explore its stability, accuracy and convergence and the effect of numerical parameters on elastic solutions using a generic uniaxial stress test. Short term transient and long term uniform state SPH solutions agree well with those from the finite element method (FEM). The SPH elastic deformation solution showed good convergence with increasing particle resolution. The tensile instability stabilisation method was found to have little impact on the solution, except for higher values of the correction factor which then produce small amplitude benign artificial banded stress patterns. The use of artificial viscosity is able to eliminate the instability and improve the accuracy of the solutions. Overall, the classical SPH method appears to be robust and suitable for accurate modelling of elastic solids under compression.