Modeling and analysis of non-explosive underwater shock loading using a PD-SPH coupling method
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摘要: 鉴于舰艇抗爆炸冲击性能评估面临强非线性流固耦合、结构大变形及损伤破坏演化等关键力学问题挑战，通过耦合近场动力学（peridynamics, PD）和光滑粒子流体动力学（smoothed particle hydrodynamics, SPH）的各自优势，构建适用于水下爆炸冲击模拟的高效PD-SPH数值模型。采用SPH模拟水下冲击波传播及其流固耦合效应，通过PD方法精确表征固体结构从弹性变形至渐进损伤破坏的全过程力学行为，建立非药式水下爆炸冲击波加载装置的PD-SPH数值模型。针对大规模粒子计算效率瓶颈，开发基于区域分解与数据通信机制的多GPU (graphics processing unit)并行计算框架。系统验证和并行效率测试表明，该方法可准确预测冲击波壁面压力和靶体动态变形，成功复现薄板结构的典型裂纹扩展模式，并可用于开展复杂夹层板毁伤全过程模拟。在超过500万个粒子的复杂流固耦合场景中，8卡RTX4090相比单卡RTX4090加速比为4.13，并行效率为51.6%，实际计算时间可以压缩到近1 h。同时，多GPU并行与传统CPU (central processing unit)并行相比，加速比可达9倍以上。Abstract: The evaluation method of ship's explosion shock resistance is challenged by some key mechanical problems, such as strong nonlinear fluid-structure coupling, large-deformation and failure evolution of solid structure. By coupling the respective advantages of peridynamics (PD) and smoothed particle hydrodynamics (SPH), an efficient PD-SPH numerical model suitable for underwater explosion shock simulations was developed. The SPH method was employed to simulate underwater shock wave propagation and fluid-structure interaction, while the PD method accurately characterized the complete mechanical behavior of solid structures from elastic deformation to progressive damage failure. A PD-SPH numerical model was established for non-explosive underwater shock loading devices. In the non-ordinary state-based peridynamics (NOSB-PD) framework, the Johnson-Cook damage model was introduced. To suppress the occurrence of numerical instability, the artificial stiffness form was introduced by increasing the internal constraints between particles. To improve the computational efficiency in large-scale simulations, a multi-GPU (graphics processing unit) parallel computing framework based on domain decomposition and data-communication mechanisms was established. The domain decomposition was carried out through the Eulerian format. When particles move from one domain to another, the physical quantities of the particles were exchanged for information. Model validation and parallel efficiency tests demonstrate that the proposed method can accurately predict shock wave wall pressure and target dynamic deformation, successfully reproduce typical crack propagation patterns in thin-plate structures and simulate the entire damage process of complex grid sandwich structure. In complex fluid-structure coupling scenarios with more than 5 million particles, the 8*RTX4090 achieved an acceleration ratio of 4.13 compared to a single RTX4090, with a parallel efficiency of 51.6%. The actual calculation time can be reduced to 1 hour. Meanwhile, compared with traditional CPU (central processing unit) parallelism, the multi-GPU parallelism can achieve an acceleration ratio of more than 9 times. The research outcomes provide a high-precision and efficient numerical analysis tool for the design of explosion-resistant naval structures, offering significant reference value for engineering applications of fluid-structure interaction in underwater explosion problems.
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图 3 非药式水下爆炸冲击波加载装置
Figure 3. Non-explosive underwater explosion shock wave loading device
图 4 非药式水下爆炸装置冲击波波阵面时程
Figure 4. Front shock wave evolution of a non-explosive underwater shock device
图 5 不同加载速度下靶板中心的压力时程曲线和初始压力峰值随飞片冲击速度的变化
Figure 5. Pressure histories and pressure peak-velocity curves measured at the center of the plate at different impact velocities
图 6 不同方法得到的圆盘中心点位移和速度曲线
Figure 6. Deflection and velocity-time histories obtained by using different methods
图 7 典型时刻的靶体变形云图（位移模量云图，单位：mm）
Figure 7. Diagram of target deformation at different times
图 8 不同飞片冲击速度下薄板JC模型损伤变量云图
Figure 8. Damage cloud images of thin plates at different flyer impact velocities
图 9 格栅夹层结构PD粒子分布及格栅单元尺寸
Figure 9. PD particle distribution in the grid sandwich structure and grid cell size
图 10 水下爆炸冲击波作用下格栅夹层板背气板中间挠度时程曲线
Figure 10. Middle deflection history curves of back-air plate of grid sandwich structure subjected to underwater explosion shock wave
图 11 飞片速度500 m/s下格栅夹层板典型时刻速度和损伤云图
Figure 11. Velocity and damage cloud contours of the grid sandwich structure subjected to flyer impact velocities 500 m/s at typical times(飞片速度500 m/s?)
图 12 不同飞片速度下格栅夹层板上下板的等效塑性应变分布
Figure 12. Equivalent plastic strain distribution of the upper and lower plates of the grid sandwich panel at different flyer impact velocities
E/GPa ν ρ/(kg·m−3) AJC/MPa BJC/MPa NJC $ {\dot{\varepsilon }}_{\text{0}} $/s−1 73.4 0.33 2800 167 444 0.44 0.00125 CJC Dc Dth T0/K MJC Tm /K D1 0.015 1.0 0.12 293.0 2.31 775 0.013 D2 D3 D4 D5 0.013 −0.5 −0.011 0 
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表 2 模拟时长0.6 ms的不同CPU/GPU下的计算时间
Table 2. Computation time on different CPU/GPU with a simulation duration of 0.6 ms
CPU/GPU数量 配置 计算耗时/min 加速比 1 AMD EPYC 9654(96核) 624 0.59 2 RTX3090 371 1.00 3 4*RTX3090 152 2.44 4 4*RTX4090 69 5.38
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表 3 不同GPU配置下的格栅夹层薄板破坏全过程模拟的计算耗时
Table 3. Computation time of the whole process of grid sandwich thin-wall structure for different GPUs
GPU数量 配置 计算耗时/min 加速比 并行效率/% 1 RTX4090 339 1.00 100.0 4 4*RTX4090 114 3.08 77.0 8 8*RTX4090 82 4.13 51.6
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