剪切成带的稳定化多尺度无网格方法研究

Shear banding is a typical fracture mode in weapon materials under shock loadings. The onset and propagation of shear band is a complex dynamic procedure that bridging multiple scales, and should be studied by the multiscale numerical methods that coupling macro and micro models. Take the advantage of meshfree methods in large deformation problems, a stabilized multiscale meshfree method for shock loadings is proposed in this project. In order to overcome the key difficulties of combining meshfree and molecular dynamics simulation, the construction of multiscale meshfree basis functions and development of atomistic-to- particle coupling technique based on energy conservation in handshaking region are studied. By way of patch test and ghost force correction, the stability and consistency of couple scheme in the handshaking region can be ensured. Using above techniques, the corresponding multiscale numerical simulation program is coded and validated. Based on this program, the application study of shear banding under shock loadings is carried out, and the affect mechanism of micro defects to the onset and propagation of shear band is discussed.

冲击加载下剪切成带现象是武器材料失效的典型破坏模式，剪切带的起始与传播是一个跨尺度关联的复杂动力学过程，需要宏微观相结合的多尺度方法开展数值模拟研究。利用无网格方法在处理大变形问题中的优势，本项目提出了一种适用于冲击加载的稳定化多尺度无网格方法。为解决连接无网格与分子动力学模拟特有的难点问题，我们研究交接区内多尺度无网格基函数的构造以及发展基于能量守恒的原子-粒子界面耦合技术，通过分片测试和鬼力校正等策略，保证交接区内耦合格式的稳定性与相容性。基于以上技术，完成相关多尺度数值模拟程序的编写和验证。利用该程序开展冲击加载下剪切成带的应用研究，探讨微观缺陷对剪切带起始和传播的影响机制。

针对冲击加载下剪切带成核与演化多尺度数值模拟中的难点问题，本项目发展了连接分子动力学和无网格方法的若干关键技术，包括无网格基函数的构造、分片测试与校正以及稳定化格式，建立了能量守恒的原子-粒子多尺度耦合模拟方法。为合理模拟冲击加载下材料局部高温和热扩散效应，利用宏微观区域的法向能流作为边界条件来求解宏观粒子区域的温度扩散方程，离散格式在背景积分网格上构造，适用于材料形变和破坏情形。编写了有限元、无网格等连续介质力学方法与分子动力学模拟耦合的程序，完成了相关测试和验证工作。利用该程序开展了材料微结构对剪切带起始和传播影响机制的数值模拟研究，与高分辨率电镜实验观察结果吻合较好。