OTM analysis of debris cloud under hypervelocity impact
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摘要: 空间碎片超高速撞击是典型的高温、高压、高应变率的极限力学问题，涉及材料复杂的动态响应，对传统的数值方法提出了巨大挑战。最优运输无网格（OTM）方法通过有机结合最优运输时间积分理论、局部最大熵无网格近似、物质点抽样、基于物理的裂纹扩展算法以及大规模并行计算策略，克服了传统数值方法瓶颈，在理论上保证了不同形式能量耗散的自主耦合分配，为超高速撞击仿真预测提供了高效的解决方案。采用基于OTM方法自主研发的极限力学仿真软件ESCAAS，对不同质量（3、10 g）的铜飞片以不同撞击角度（5.4°、11.7°）和不同撞击速度（5.55、5.12 km/s）撞击铝合金靶板的过程进行数值模拟，获得碎片云的形貌、靶板穿孔孔径等结果，与实验测量数据吻合良好，显示出OTM方法及ESCAAS软件可以作为超高速撞击的有力数值分析手段。Abstract: The hypervelocity impact (HVI) of space debris is a typical extreme mechanics problem at high temperature, high pressure and high strain rate. The HVI involves the complex dynamic response of materials. Numerical methods have become very useful and important tools to predict the complex phenomena and look into the details of the entire process. However, the accurate simulation of the HVI is a grand challenge in scientific computing that places exacting demands on physics models, numerical solvers and computing resources. The optimal transportation meshfree (OTM) method is a meshfree updated-Lagrangian methodology for fluid and solid dynamic flows, possibly involving multiple phases, viscosity and general equations of state, general inelastic and history-dependent constitutive relations, arbitrary variable domains and boundary conditions and the interaction between fluid flows and highly deformable structures. The rationale behind the approach is combining concepts from the optimal transportation (OT) theory with material-point sampling, local maximum entropy (LME) approximation, the seizing contact, variational material point failure algorithm, and overcomes the essential difficulties in grid-based numerical methods like Lagrangian and Eulerian finite element method. Owing to those advantages, the OTM method provides an efficient and accurate solution for HVI simulation. In this paper, large scale three-dimensional numerical simulations on the HVI of the copper projectiles with different thicknesses (3.45, 5.13 mm), different masses (3, 10 g), different impact angles (5.4°, 11.7°) and different impact velocities (5.55, 5.12 km/s) impacting the Al6061-T6 plate with different thicknesses (2.87, 4.39 mm) were performed within the software ESCAAS based on the OTM method using a dynamic load balancing MPI/Pthreads parallel implementation. The dynamic response of material including phase transition in the high strain rate, high pressure and high temperature regime expected in this paper was described by the use of a variational thermomechanical coupling constitutive model with the SESAME equation of state, Grüneisen equation of state, rate-dependent J2 plasticity with power law hardening and thermal softening. The simulation results are in good agreement with the experimental measurements, which indicates the capacity of the OTM method and the ESCAAS software for HVI simulation.
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Key words:
- hypervelocity impact /
- OTM method /
- crack propagation /
- meshfree
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图 6 工况1不同时刻下碎片云轮廓
Figure 6. Debris cloud outlines at different moments of 3 g copper impact (condition 1)
图 7 工况1碎片云形貌对比情况 (6.4 μs)
Figure 7. Debris cloud shape comparison at 6.4 μs (condition 1)
图 9 工况2不同时刻下碎片云轮廓
Figure 9. Debris cloud outlines at different moments of 10 g copper impcat (condition 2)
图 10 工况2碎片云形貌对比情况 (7.6 μs)
Figure 10. Debris cloud shape comparison at 7.6 μs (condition 2)
表 1 材料物性参数
Table 1. Material parameters
材料 密度/
(kg·m−3)杨氏模量/
GPa泊松比 临界能量释放率/
(kJ·m−2)OFHC铜 8930.0 129.0 0.35 250.0 Al6061-T6铝合金 2700.0 68.9 0.33 100.0 
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表 2 材料本构模型参数
Table 2. Parameters of material constitutive model
材料 σ0/MPa $ {\varepsilon }_{0}^{\mathrm{p}} $ $ {\dot{\varepsilon }}_{0}^{\mathrm{p}} $ n m l Tm/K OFHC铜 120.0 0.0278 1.0 0.45 1.0 1.0 1790.0 Al6061-T6铝合金 270.0 0.0025 1.0 0.148 0.01389 1.0 1200.0
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