超高速撞击玄武岩材料的Riemann-SPH仿真参数分析与验证

刘晏东; 周琪; 李明涛

doi:10.11883/bzycj-2024-0440

超高速撞击玄武岩材料的Riemann-SPH仿真参数分析与验证

doi: 10.11883/bzycj-2024-0440

刘晏东^{1, 2,},
周琪^{1, 2},
李明涛^{1, 2, ,}

1.
中国科学院国家空间科学中心，北京 100190
2.
中国科学院大学计算机科学与技术学院，北京 100190

基金项目: 空间碎片与近地小行星防御科研专项（KJSP2023020303）

详细信息

作者简介:
刘晏东（2000－　），男，博士研究生，2205881310@qq.com

通讯作者:
李明涛（1982－　），男，博士，研究员，limingtao@nssc.ac.cn

中图分类号: O347.3; P185.7
计量
- 文章访问数: 255
- HTML全文浏览量: 33
- PDF下载量: 62
- 被引次数: 0
出版历程
- 收稿日期: 2024-11-11
- 修回日期: 2025-11-20
- 网络出版日期: 2025-11-21

Riemann-SPH simulation of hypervelocity impact on basalt material: parameter analysis and validation

LIU Yandong^{1, 2
,},
ZHOU Qi^{1, 2},
LI Mingtao^{1, 2
, ,}

1.
National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China
2.
University of Chinese Academy of Sciences, School of Computer Science and Technology, Beijing 100190, China

摘要

摘要: 为研究超高速撞击玄武岩材料光滑粒子流体动力学（smoothed particle hydrodynamics，SPH）仿真中的参数影响，基于现有Riemann-SPH方法对地面超高速撞击玄武岩实验进行了仿真分析与验证，发现SPH仿真结果受算法参数与材料模型参数影响较大，同时材料强度模型与损伤模型的影响存在耦合性。研究结果表明：超高速撞击SPH仿真中，考虑人工应力法可以避免固体冲击仿真中出现的拉伸不稳定性；对于超高速撞击场景，使用Wendland C²核函数并设置光滑长度半径内期望粒子数为2.5，可实现计算精度和效率的兼顾。其计算速度比变分辨率粒子分布方法提升了20倍以上；在地面实验的仿真中，弹丸材料可能发生相变，而玄武岩靶体在不同模型与参数组合下产生了相似的仿真响应结果。建议使用更符合岩石材料力学特性的Lundborg强度模型和Benz-Asphaug概率损伤模型，并考虑相变计算，最终得到参数搜索取值规律，即在反向搜索未知参数时，应以其他参数的合理取值为约束，从而避免较大的参数误差。在保证合理的模型参数情况下，仿真得到的撞击坑尺寸和动量传递因子与实验的误差在10%~20%范围内。相关参数取值方法为开展超高速撞击防御小行星SPH仿真及参数选择提供了依据。
- 超高速撞击 /
- SPH方法 /
- 行星防御 /
- 参数分析
Abstract: To study the effects of parameters in smoothed particle hydrodynamics (SPH) simulations of hypervelocity impacts on basalt, numerical analysis and validation were performed using the Riemann-SPH method based on ground-based impact tests. By adjusting various simulation parameters, the influence of parameters on the simulation can be obtained. Results show that both algorithmic and material parameters significantly influence the simulation, with coupling between strength and damage models. Applying the artificial stress method helps suppress tensile instability in solid impacts. Using the Wendland C² kernel with a target of 2.5 particles within the smoothing length optimizes both accuracy and efficiency, and variable-resolution particle distribution improves performance by over 20 times. In simulations, the impactor may undergo a phase transition, and different model and parameter combinations can yield similar responses. It is recommended to employ the Lundborg strength model and the Benz-Asphaug stochastic damage model, which better represent the mechanical behavior of rocky materials, and to account for phase transitions. Parameter search should be constrained by reasonably known values to avoid large errors or non-uniqueness. With reasonable parameters, simulated crater size and momentum transfer factor match experiments within 10–20% error. These strategies support SPH applications in asteroid defense and parameter selection.
- hypervelocity impact /
- SPH method /
- planetary defense /
- parameter analysis

HTML全文

图 1 Lundborg强度模型

Figure 1. Lundborg strength model

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图 2 撞击结果随时间的变化曲线

Figure 2. Time evolution curves of impact results

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图 3 不同撞击速度的仿真剖面图

Figure 3. Simulation cross-sectional views at different

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图 4 撞击速度为3.90 km/s时的靶体外观（红色虚线为完整坑，白色虚线为中心碗状深坑）

Figure 4. Appearance of the target at the impact velocity of 3.90 km/s (The red dotted line is the complete pit, and the white dotted line is the center bowl-shaped deep pit)

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图 5 不同$ {n}_{\text{target}} $的弹丸粒子形态

Figure 5. Particle morphology of projectiles with different $ {n}_{\text{target}} $

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图 6 采用不同拉伸不稳定性处理方法后的粒子分布

Figure 6. Particle distributions using different tensile instability treatment methods

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图 7 变分辨率粒子分布法测试

Figure 7. Testing of the variable resolution particle distribution method

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图 8 不同强度模型下弹丸状态分布

Figure 8. State distribution of projectiles under different intensity models

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图 9 工况2～ 4的靶体损伤（黑色虚线为撞击坑）

Figure 9. Target damage diagrams of cases 2～4 (The black dotted line is the crater)

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图 10 溅射物质量与动量的速度分布

Figure 10. Velocity distribution of ejecta mass and momentum

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图 11 不同$ {Y}_{\mathrm{M}} $的靶体剖面

Figure 11. Cross-sectional views of the target body with different $ {Y}_{\mathrm{M}} $

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表 1 仿真参数

Table 1. Numerical simulation parameters

材料	用途	密度/(kg·m⁻³)	形状尺寸/mm	速度/(km·s⁻¹)	A_res/mm	q	状态方程	强度模型
铝	弹丸	2785	球体，d = 6	2.30/3.47/3.90	0.5	1	Tillotson^[45]	Johnson-Cook^[36]
玄武岩	靶体	2876	圆柱，$\varnothing $123.3×123.3	−	0.5	1.01	Tillotson^[45]	Lundborg

材料	剪切模量/GPa	Y₀/MPa	μ	Y_M/MPa	损伤模型	m	k/m⁻³	σ_b/MPa
铝	26.5				最大拉应力损伤模型			2 500^[39]
玄武岩	22.7	26.5^[47]	0.6^[48]	300^[47]	Benz-Asphaug概率损伤模型	10.0	2.7×10⁴¹	9.62

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表 2 不同撞击速度的仿真与实验对比

Table 2. Comparison of simulation and experimental results at different impact velocities

速度/(km·s⁻¹)	坑直径			坑深度			动量传递因子β
速度/(km·s⁻¹)	实验^[15] /mm	仿真/mm	误差/%	实验^[15] /mm	仿真/mm	误差/%	实验^[15]	仿真	误差/%
2.30	42	35	−16.7	10	10	0	1.96	1.57	−19.9
3.47	52	43	−17.3	12	14	16.7	2.39	2.02	−15.5
3.90	55	48	−12.7	13.5	15	11.1	2.51	2.19	−12.7

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表 3 变分辨率粒子分布法测试结果

Table 3. Test results of the variable resolution particle distribution method

A_res	q	总粒子数	总质量	粒子数占比/%	总质量误差/%
1	1.00	1 000 000	1 000 000	100	0
1	1.01	89 859	994 575	8.96	−0.54
1	1.03	10 323	982 158	1.03	−1.78
2	1.00	125 000	1 000 000	100	0
2	1.01	29 714	993 986	23.77	−0.60
2	1.03	5 762	979 872	4.61	−2.01

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表 4 相似结果时的不同工况参数

Table 4. Different case parameters for similar results

工况	强度模型	Y₀/MPa	损伤模型	σ_b/MPa	坑直径/mm	坑深度/mm	β
1	Lundborg	26.5	Benz-Asphaug概率	9.62	48	15	2.19
2	恒定强度	66.0	Benz-Asphaug概率	9.85	38	16	2.20
3	Lundborg	26.5	最大拉应力	33.0	50	15	2.20
4	Drucker-Prager	146.0	最大拉应力	50.0	84	12	2.22

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表 5 不同极限强度下的仿真结果

Table 5. Simulation results under different ultimate strengths

Y_M/MPa	m	k/(m⁻³)	σ_b/MPa	坑直径/mm	坑深度/mm	β	ɛ_d/%
300	9.5	9.0×10³⁹	8.75	49	16	2.21	4.35
1 000	9.5	9.0×10³⁹	8.75	49	15	2.15	33.84
3 500	9.5	9.0×10³⁹	8.75	48	13	2.20	48.04
3 500	9.5	1.2×10⁴⁰	8.49	68	14	2.58	44.69

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表 6 不同$ {Y}_{0} $的$ m $、$ k $参数

Table 6. m and k for different $ {Y}_{0} $

Y₀/MPa	m	k/(m⁻³)	σ_b误差/%	坑直径误差/%	坑深度误差/%	β误差/%
20.0	9.5	9.0×10³⁹	−10.7	−10.9	18.5	−12.0
26.5	10.0	2.7×10⁴¹	−1.7	−12.7	11.1	−12.7
30.0	9.75	2.5×10⁴⁰	0.5	−16.4	11.3	−15.1
35.0	9.0	5.0×10³⁷	−2.0	−18.2	7.4	−16.3

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