应力波数值计算中的SPH方法

孙晓旺; 章杰; 王肖钧; 李永池; 赵凯

doi:10.11883/1001-1455(2017)01-0010-05

应力波数值计算中的SPH方法

doi: 10.11883/1001-1455(2017)01-0010-05

孙晓旺^1,,
章杰¹,
王肖钧¹,
李永池¹,
赵凯^{1, 2}

1.
中国科学技术大学近代力学系, 安徽合肥 230026
2.
北京理工大学科学与技术国家重点实验室, 北京 100081

基金项目:

国家自然科学基金项目 11402266

国家自然科学基金项目 11202206

国家自然科学基金项目 11472008

爆炸科学与技术国家重点实验室开放基金项目 KFJJ13-9M

爆炸冲击防灾减灾国家重点实验室开放基金项目 DPMEIKF201401

详细信息

作者简介:
孙晓旺(1987—)，男，博士研究生，xiaowang@mail.ustc.edu.cn

中图分类号: O383
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- 被引次数: 0
出版历程
- 收稿日期: 2015-06-16
- 修回日期: 2015-08-24
- 刊出日期: 2017-01-25

Application of SPH in stress wave simulation

1.
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, Anhui, China
2.
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

摘要

摘要: 对一维波动方程的SPH(smoothed particle hydrodynamics)格式和有限差分格式进行比较，并采用SPH法模拟了一维应力/应变波, 获得1个可衡量SPH法模拟应力波准确性的重要指标。结果表明，SPH法模拟应力波传播中采用的光滑长度必须不小于粒子间距；采用B-样条核函数和高斯型核函数能够获得良好的应力波图像，而二次型核函数不能，因此二次型核函数不适用于冲击动力学的数值计算。
- 爆炸力学 /
- 核函数 /
- 光滑长度 /
- SPH方法 /
- 应力波
Abstract: Obtaining accurate waveforms is significant in impact mechanics numerical calculation. This paper is to analyze how the kernel functions and smooth length affect the result of stress wave simulation. The SPH (smoothed particle hydrodynamics) formulations with different kernel functions and smooth lengths of one dimensional wave equation was compared with the finite difference formulation, which was derived in this paper. One dimensional stress and strain waves were simulated using the SPH method with different kernel functions and smooth lengths, and waveforms were gained accurately by B-spline and Gaussian kernels when the smooth length was equal to or greater than the particle interval. The wave velocity obtained by the quadratic kernel is below the theoretical value, no matter what the smooth length is. A parameter was deduced in this paper as roughly equal to the dimensionless wave velocity. Several conclusions were drawn. Firstly, the smooth length is equal to or greater than the particle interval, which is the necessary prerequisite for accurate stress wave simulation with SPH. Then, the quadratic kernel is not suitable in impact mechanics numerical calculation. Finally, the parameter deduced in this paper is a significant index to evaluate the stress wave simulation result of SPH.
- mechanics of explosion /
- kernel function /
- smooth length /
- SPH method /
- stress wave

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图 1 不同γ值下一维应力波在15 μs时的波形

Figure 1. Waveforms of one dimensional stress wave at 15 μs under different γ

下载: 全尺寸图片幻灯片

图 2 不同γ值下一维应变波在15 μs时的波形

Figure 2. Waveforms of one dimensional strain wave at 15 μs under different γ

下载: 全尺寸图片幻灯片

表 1 采用B-样条核函数在不同γ值下获得的一维应力波/应变波波速

Table 1. One dimensional stress/strain wave velocity obtained by B-spline kernel function using different γ

γ	α	c/c₀
γ	α	应力波	弹性应变波	塑性应变波
0.6	0.309	0.332	0.324	0.367
0.7	0.666	0.674	0.670	0.690
0.8	0.879	0.881	0.878	0.888
0.9	0.976	0.978	0.976	0.978
1.0	1.000	1.000	1.000	1.000
1.1	1.011	1.009	1.009	1.001
1.2	1.022	1.015	1.020	1.002
1.3	1.022	1.021	1.021	1.020
1.4	1.010	1.008	1.007	1.005
1.5	0.988	0.985	0.985	0.984

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表 2 采用高斯型核函数在不同γ值下获得的一维应力波/应变波波速

Table 2. One dimensional stress/strain wave velocity obtained by Gaussian kernel function using different γ

γ	α	c/c₀
γ	α	应力波	弹性应变波	塑性应变波
0.4	0.068	0.075	0.080	0.081
0.5	0.330	0.339	0.337	0.341
0.6	0.650	0.656	0.654	0.653
0.7	0.862	0.867	0.866	0.870
0.8	0.958	0.962	0.961	0.960
0.9	0.990	1.000	1.000	1.000
1.0	0.996	1.001	1.001	1.001
1.1	1.000	1.001	1.001	1.001
1.2	1.000	1.001	1.001	1.001

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表 3 采用二次型核函数在不同γ值下获得的一维应力波/应变波波速

Table 3. One dimensional stress/strain wave velocity obtained by quadratic kernel function using different γ

γ	α	c/c₀
γ	α	应力波	弹性应变波	塑性应变波
0.6	0.694	0.700	0.701	0.710
0.7	0.875	0.878	0.878	0.880
0.8	0.879	0.882	0.882	0.880
0.9	0.823	0.825	0.826	0.823
1.0	0.750	0.756	0.756	0.757
1.1	0.902	0.903	0.904	0.902
1.2	0.955	0.955	0.956	0.956
1.3	0.956	0.956	0.956	0.956
1.4	0.929	0.929	0.930	0.930
1.5	0.889	0.891	0.891	0.890

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参考文献(7)

[1]	Liu G R, Liu M B. Smoothed particle hydrodynamics: A meshfree particle method[M]. Singapore: World Scientific, 2003:309-341.
[2]	王肖钧, 张刚明, 刘文韬, 等.弹塑性波计算中的光滑粒子法[J].爆炸与冲击, 2002, 22(2):97-103. doi: 10.3321/j.issn:1001-1455.2002.02.001 Wang Xiaojun, Zhang Gangming, Liu Wentao, et al. Computations of elastic-plastic waves by smoothed particle hydrodynamics[J]. Explosion and Shock Waves, 2002, 22(2):97-103. doi: 10.3321/j.issn:1001-1455.2002.02.001
[3]	卞梁, 王肖钧, 肖卫国, 等.应力波和层裂计算中的光滑粒子法[J].中国科学技术大学学报, 2007, 37(7):706-710, 723. doi: 10.3969/j.issn.0253-2778.2007.07.003 Bian Liang, Wang Xiaojun, Xiao Weiguo, et al. Numerical simulation of stress waves and spallation by smoothed particle hydrodynamics[J]. Journal of University of Science and Technology of China, 2007, 37(7):706-710, 723. doi: 10.3969/j.issn.0253-2778.2007.07.003
[4]	章杰, 苏少卿, 郑宇, 等.改进SPH方法在陶瓷材料层裂数值模拟中的应用[J].爆炸与冲击, 2013, 33(4):401-407. doi: 10.3969/j.issn.1001-1455.2013.04.011 Zhang Jie, Su Shaoqing, Zheng Yu, et al. Application of modified SPH method to numerical simulation of ceramic spallation[J]. Explosion and Shock Waves, 2013, 33(4):401-407. doi: 10.3969/j.issn.1001-1455.2013.04.011
[5]	Monaghan J J. Particle methods for hydrodynamics[J]. Computer Physics Reports, 1985, 3(2):71-124. doi: 10.1016/0167-7977(85)90010-3
[6]	Gingold R A, Monaghan J J. Smoothed particle hydrodynamics: Theory and application to non-spherical stars[J]. Monthly Notices of the Royal Astronomical Society, 1977, 181(2):375-389. http://mnras.oxfordjournals.org/content/181/3/375.short
[7]	Johnson G R, Stryk R A, Beissel S R. SPH for high velocity impact computations[J]. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1/2/3/4):347-373. doi: 10.1016-S0045-7825(96)01089-4/