缩比弹体侵彻混凝土问题中尺寸效应的机理研究

With the earth penetration weapon development and the evaluation of shelter assessment, penetration in concrete has become one of the most popular topics in both weapon design and protective structure engineering. With experimental tests, numerical simulations and theoretical analysis, this project aims to explore the size effect mechanism of projectile penetration in concrete and reveal the relationship between the projectile diameter size and penetration resisting stress. With reduced-scale projectiles penetration tests, the dimensionless penetration depth is analyzed against the projectile diameter. Then the replica scaling law of concrete penetration is modified with respect to Bažant size effect law whereby the scope of application should be discussed. Based on mesoscale discrete method LDPM, the concrete structural size effect is numerically studied where the character length and gradient theory are introduced. The modified numerical model is then adopted to investigate the size effect of penetration in concrete. Based on dynamic spherical cavity expansion analysis, the dimensionless parameters are used to achieve the mass and moment conservations where the strain gradient is coupled with yield criterion. The derivative governing equations are solved with Runge-Kutta method numerically to obtain the projectile diameter related penetration resisting stress. Through this project, a better understanding on size effect of projectile penetration in concrete is hopefully to be achieved which will help to enrich the concrete penetration study and further guide the protective concrete shelters design and safety assessment against projectile penetration.

随着钻地武器发展及防护结构评估需要，混凝土侵彻问题成为武器研发和土木工程安全防护领域的热点问题。本项目拟针对混凝土侵彻问题中尺寸效应现象开展试验、仿真以及理论分析研究，揭示侵彻尺寸效应机理，探索弹径尺寸影响规律。通过几何相似缩比弹体侵彻混凝土靶试验，分析无量纲化侵深与弹体尺寸的规律，结合Bažant尺寸效应律对混凝土侵彻相似模型进行完善，确定其适用范围；基于细观离散元LDPM对混凝土结构尺寸效应进行数值模拟，引入梯度理论和材料特征长度并进行参数标定，基于优化的仿真模型对缩比弹体侵彻混凝土进行仿真研究。基于动态球形空腔膨胀分析，引入含梯度理论的混凝土材料本构关系，对质量守恒、动量守恒方程组进行无量纲化处理，得到微分形式的控制方程组，采用龙格库塔法数值求解，获得弹径尺寸相关的阻应力形式。该项目研究将丰富混凝土侵彻研究的内涵，对混凝土防护工事抗侵彻的设计与安全评估产生重要的影响。

在钻地弹的毁伤评估研究中，动能弹冲击混凝土的侵彻深度是表征武器侵彻性能和防护结构抗侵彻能力的重要指标。由于大尺寸真实弹体侵彻混凝土试验研究花费金额巨大且试验条件较难实现，因此大部分的侵彻研究主要基于缩比弹体侵彻试验开展，其尺寸远小于真实炮弹、导弹尺寸，研究缩比弹体侵彻获得的侵彻规律能否直接应用到真实弹体侵彻的研究中尚待商榷。关键问题在于缩比弹体侵彻混凝土问题的相似律是否成立，若无量纲化的侵深与弹径尺寸无关，则侵深无量纲模型才能推广到真实弹体侵彻混凝土模型。.探索缩比弹体侵彻混凝土问题中的尺寸效应，明确弹径尺寸与无量纲侵深的关系，揭示弹径尺寸和骨料尺寸对于侵彻阻应力的影响规律，阐明混凝土侵彻尺寸效应机理。根据缩比弹体侵彻混凝土试验数据，建立了弹径尺寸相关的侵彻深度计算模型。基于细观离散单元法LDPM引入梯度理论，多尺度模拟混凝土侵彻，仿真模拟了弹径尺寸对侵彻阻力和侵深的影响规律。通过在空腔膨胀分析中引入耦合梯度理论的混凝土材料屈服准则，获得了弹径尺寸相关的阻应力方程。相关结果表明：侵彻阻力与弹径与骨料直径之比相关，在其值接近1-3时侵彻阻力与弹径相关度较大，随着该系数增大阻力函数相关性减弱；引入材料特产长度的失效准则可以较好仿真混凝土侵彻尺寸效应，其规律满足大于骨料直径的弹体侵彻混凝土阻力模型描述。.本研究的结论为科学地分析缩比弹体侵彻混凝土问题，奠定了理论基础，提供了科学支撑。