AN IMMERSED MULTI-MATERIAL FINITE VOLUME-MATERIAL POINT METOHD FOR STRUCTURAL DAMAGE UNDER BLAST LOADING
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摘要: 结构在爆炸载荷作用下的毁伤现象涉及强非线性激波、固体结构极端变形和破坏破碎、强流固耦合, 给数值计算方法带来了极大的困难与挑战. 针对结构爆炸毁伤问题, 建立了浸没多介质有限体积物质点法(iMMFV-MPM), 采用基于黎曼求解器的多介质有限体积法(MMFVM)模拟爆炸产物和空气的多介质流体, 采用物质点法(MPM)模拟固体结构, 并将提出的基于拉格朗日乘子的连续力浸没边界法(lg-CFIBM)扩展到多介质流体中以处理流固耦合边界条件. 该算法在每个时间步严格满足流固耦合界面处的速度边界条件及动量守恒方程, 不需要重构流固耦合界面, 能够有效地模拟近场爆炸下爆炸产物与结构的相互作用、激波与结构的相互作用和演化以及结构的动态断裂和拓扑变化. 利用iMMFV-MPM对近场爆炸下方形钢筋混凝土靶板的失效模式、外爆载荷下建筑物的毁伤现象以及多腔室内爆炸试验进行了模拟, 模拟结果与相关实验数据吻合良好, 验证了所建立的流固耦合算法的有效性及精度.Abstract: Structural damage under blast loading always involves strong nonlinear shock-wave, extreme deformation, damage and breakage of solid structures, and strong fluid-solid interaction, which bring great difficulties to numerical simulation. In this paper, a novel immersed multi-material finite volume-material point method (iMMFV-MPM) is proposed to model the structural damage under blast loading. The multi-material finite volume method (MMFVM) is used to simulate the flow of explosives and surrounding air and specifically a TVD Riemann solver is adopted for shock simulation, while the material point method (MPM) is employed as solid solver for simulation of extreme deformation problem. The continuous-forcing immersed boundary method based on Lagrangian multiplier (lg-CFIBM) is extended to multi-material fluid to impose boundary conditions at the FSI interfaces. The lg-CFIBM can guarantee the boundary velocity conditions strictly at each time step and has no need to reconstruct FSI interfaces explicitly, which can effectively simulate the interaction between the explosion products and the building structure, the evolution of the shock wave around solid structure, and the dynamic fracture and topological change of the structure. Several numerical examples, including the damage pattern of a square reinforced concrete slab under close-in explosion, the structural damage of buildings under blast loading and the multi-chamber implosion tests, are simulated to verify and validate the proposed FSI algorithm, and numerical results are in good agreement with experiments.
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图 3 各浸没边界法边界条件施加示意图
Figure 3. Diagram of applying boundary conditions of different IBMs
图 9 iMMFV-MPM和MPM的压力云图结果
Figure 9. Pressure contour results of the iMMFV-MPM and the pure MPM
图 11 iMMFV-MPM模拟的钢筋混凝土靶板中心点位移时程曲线
Figure 11. Central deflection curve of the reinforced concrete slab by iMMFV-MPM
图 13 流场压强云图与建筑物损伤云图
Figure 13. Pressure contour in fluid domain and damage contour in building
图 14 流场体积分数截面云图与建筑物压力云图
Figure 14. Volume of fraction contour on the plane of
$z = 300\;{\text{mm}}$ and pressure contour in building
图 17 主爆室侧墙中心点处的压强曲线
Figure 17. Pressure curve at the center of sidewall in explosion room
图 18 各时刻中截面上的流场压强云图和体积分数云图
Figure 18. Pressure contour and volume of fraction contour of middle plane at different instants
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