基于Lagrange及SPH算法的花岗岩侵彻数值模拟

靳绍虎; 刘科伟; 黄进; 杨家彩; 靳少博

doi:10.11858/gywlxb.20200665

基于Lagrange及SPH算法的花岗岩侵彻数值模拟

doi: 10.11858/gywlxb.20200665

中南大学资源与安全工程学院，湖南长沙　410083

基金项目: 湖南省自然科学基金（2018JJ3656）

详细信息

作者简介:
靳绍虎（1993－），男，硕士，主要从事侵彻及爆炸动力学研究. E-mail：396774099@qq.com

通讯作者:
刘科伟（1982－），男，博士，副教授，主要从事爆破技术和岩土工程等研究.E-mail：kewei_liu@126.com

中图分类号: O347
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出版历程
- 收稿日期: 2020-12-31
- 修回日期: 2021-03-14

Numerical Simulation of Granite Penetration Based on Lagrange and SPH Algorithm

School of Resources and Safety Engineering, Central South University, Changsha 410083, Hunan, China

摘要

摘要: 为研究不同算法对弹体侵彻花岗岩模拟的影响，基于仿真分析软件LS-DYNA中的Lagrange算法及SPH（Smooth particle hydrodynamics）算法，采用Lagrange、SPH-Lagrange耦合及SPH算法分别对弹体侵彻、贯穿花岗岩靶体进行数值模拟，并从计算效率、侵彻深度、速度衰减、靶体损伤、Mises应力分布多方面对比模拟结果，分析3种算法用于研究岩石侵彻问题的优势和不足。研究表明：Lagrange算法的计算效率最高，计算精度高，但存在单元畸变、无撞击溅射、无后坑区等问题；SPH算法的计算效率最低，但模拟效果良好；SPH-Lagrange耦合算法兼具二者优势，但会导致应力滞后和应力波不稳定衰减。在大型模拟中应优先选用Lagrange算法和SPH-Lagrange耦合算法。
- 弹体侵彻 /
- 花岗岩靶体 /
- Lagrange算法 /
- SPH-Lagrange耦合算法 /
- SPH算法
Abstract: To study the influence of different algorithms on penetration simulations of granite target subjected to projectile, Lagrange, SPH-Lagrange coupling and SPH (smooth particle hydrodynamics) algorithms are used for penetration simulations, based on Lagrange and SPH algorithms within LS-DYNA software. By comparing the numerical results through calculation efficiency, penetration depth, velocity attenuation, target damage and Mises stress distribution, the advantages and disadvantages of three algorithms are obtained. The results show that: Lagrange algorithm has the highest calculation efficiency and accuracy, but it has some problems such as element distortion, no impact sputtering, and no back-pit area. Although SPH algorithm has the lowest calculation efficiency, the calculated target damage is basically consistent with experiment. SPH-Lagrange coupling algorithm has both advantages, but it can produce stress hysteresis and unstable stress wave attenuation. Lagrange and SPH-Lagrange coupling algorithms are preferred in large-scale simulation.
- projectile penetration /
- granite target /
- Lagrange algorithm /
- SPH-Lagrange coupling algorithm /
- SPH algorithm

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图 1 实验试件

Figure 1. Experiment sample

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图 2 计算模型

Figure 2. Model of projectile and granite target

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图 3 模型描述

Figure 3. Model description

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图 4 不同网格尺寸下侵深-时间关系曲线

Figure 4. Time history of penetration depth with different mesh sizes

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图 5 不同侵彻速度下侵深-时间关系曲线

Figure 5. Time history of penetration depth with different velocities

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图 6 侵彻速度为1426 m/s时靶体的损伤

Figure 6. Target damage at an impact velocity of 1426 m/s

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图 7 靶体损伤云图

Figure 7. Target damage of 800 mm model

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图 8 质点峰值振动速度

Figure 8. PPV of target points

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图 9 0.04 ms时Mises应力分布

Figure 9. Von Mises stress at 0.04 ms

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图 10 侵深-时间和速度-时间关系曲线

Figure 10. Time history of penetration depth and velocity

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图 11 靶体损伤云图

Figure 11. Target damage of 100 mm model

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图 12 0.04 ms时Mises应力分布

Figure 12. Von Mises stress at 0.04 ms

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图 13 采用不同算法得到的侵彻速度-时间关系曲线

Figure 13. Time history of velocity with different algorithm

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表 1 侵彻实验数据

Table 1. Test results of projectile penetration

No.	Launch velocity/(m·s⁻¹)	Depth of penetration/mm	Mass of the residual projectile/g
1	1196	118.80	31.65
2	1426	146.02	31.42
3	1430	155.80	31.32
4	1600	163.90	30.83

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表 2 子弹材料参数

Table 2. Properties of test projectile

ρ_p/(kg·m⁻³)	Poisson’s ratio	E_t/GPa	C	Failure strain
7850	0.3	6.1	0.219	1.5

E/GPa	f/GPa	β	P	VP
211	1.3	1	3.3	0

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表 3 RHT模型参数

Table 3. Parameters of RHT material model

Mass density/(kg·m⁻³)	Elastic shear modulus/GPa	Eroding plastic strain	Parameter for polynomial EOS B₀
2670.0	21.0	2.0	1.68

Parameter for polynomial EOS B₁	Parameter for polynomial EOS T₁/GPa	Failure surface parameter A	Failure surface parameter N
1.68	47.1	1.60	0.56

Compressive strength/MPa	Relative shear strength	Relative tensile strength	Lode angle dependence factor Q₀
150.0	0.38	0.10	0.64

Lode angle dependence factor B	Parameter for polynomial EOS T₂/GPa	Reference compressive strain rate/s^–1	Reference tensile strain rate/s^–1
0.05	0	3.0×10⁻⁵	3.0×10⁻⁶

Break compressive strain rate/s^–1	Break tensile strain rate/s^–1	Compressive strain rate dependence exponent	Tensile strain rate dependence exponent
3.0×10²⁵	3.0×10²⁵	0.0085	0.012

Pressure influence on plastic flow in tension	Compressive yield surface parameter	Tensile yield surface parameter	Shear modulus reduction factor
0.001	0.40	0.70	0.48

Damage parameter D₁	Damage parameter D₂	Minimum damaged residual strain	Residual surface parameter AF
0.042	1.0	0.012	1.60

Residual surface parameter NF	Grüneisen parameter γ	Hugoniot polynomial coefficient A₁/GPa	Hugoniot polynomial coefficient A₂/GPa
0.60	0	47.10	79.13

Hugoniot polynomial coefficient A₃/GPa	Crush pressure/MPa	Compaction pressure/GPa	Porosity exponent
48.36	50.0	6.0	4.0

Initial porosity
1.01

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表 4 网格尺寸与侵彻深度

Table 4. Mesh size and penetration depth

No.	Mesh size	Penetration depth/mm	No.	Mesh size	Penetration depth/mm
1	1∶1	60.98	4	1∶4	119.07
2	1∶2	98.37	5	1∶5	123.33
3	1∶3	108.15	6	1∶6	126.50

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