王汉奎. 金属及碳管复合材料力学行为的物质点类方法研究. 清华大学博士学位论文，2011.9

数值模拟已经成为研究材料行为的一种重要手段,同时复杂的材料行为也对 数值算法提出了新的挑战。广泛用于微观模拟的分子动力学方法受计算能力限 制,模拟尺度小,而宏观方法又不能够反映材料微观尺度现象。本文采用同属粒 子类方法的宏观物质点法与微观分子动力学,提出了能够自适应调整的光滑分子 动力学方法;并采用分子动力模拟取得状态方程用于高速碰撞研究,以及采用物 质点法研究碳管增强的复合材料。
本文首先将自适应物质点法的思想引入光滑分子动力学中,提出了自适应光 滑分子动力学方法。在光滑分子动力学当中,引入能够随模拟变化的自适应网 格,针对自适应网格的要求,提出了一种满足任意处、任意份、任意级的网格处 理方式。结合光滑分子动力学计算过程,提出了背景网格细分的自适应准则,并 利用此方法研究了二维微摩擦以及三维纳米压痕等问题。
本文提出了分子动力学与物质点法结合的层级多尺度算法。利用分子动力学 模拟计算取得单晶铜的一系列的状态空间点,并以此获得能够描述相变的宏观状 态方程。通过与实验结果对比验证其正确性后,将其引入物质点法,模拟了超高 速碰撞碎片云问题。对铜弹打铜靶进行了一系列数值实验,提出弹丸熔化质量分 数计算的经验公式,此结果对空间碎片的防护有重要意义。
针对高组份比碳管复合材料微观模型难以生成的问题,本文首次提出了一种 适用于任意外形夹杂的复合材料微结构的生成算法即落管法。落管法可以保证在 满足碳管与碳管无穿透的前提下,生成与实验体积分数相一致的复合材料微观模 型。在此基础上进一步建立了考虑碳管与碳管间缠绕等加强连接作用的物质点模 型,考查了连接强度与碳管组份比对复合材料强度的影响。模拟表明碳管间连接 对复合材料有影响,但远不及碳管体积分数的影响大。此外,还以落管法生成的 模型为基础,建立复合材料的电阻网络模型,模拟结果表明碳管间电导决定了复 合材料的电导。

Numerical simulation is one kind of the major methods in research of materials sci- ence, and encounter new challenge. The molecular dynamics, which is widely used in the micro-scale simulation is constrained by the computational resource and very limited in the scales, while the macro-scale method can not describe the micro-scale phenomenon. A new adaptive smoothed molecular dynamics method is proposed based on the molecu- lar dynamics and the material point method, which are both belong to particle methods. Hypervelocity impact is then simulated by material point method where the equation of state come from molecular dynamics simulation. Carbon nanotube reinforced composite is also simulated by material point method.
Enlightened by the adaptive material point method, an adaptive smoothed molecular dynamics is proposed, which include the algorithm of the background mesh and refining rule. The algorithm is used to create the background mesh which can refine anywhere, anytime, any partitioin. The refining rule is used to choose which mesh to be refined. A 3D nanoindentation problem and a 2D micro-friction problem are investigated.
A multiscale method is proposed by coupling the molecular dynamics and the mate- rial point method. The equation of state is built on the parameters obtained from molec- ular dynamics simulation. The results of molecular dynamics were verified by the ex- periment data, and it is used in hypervelocity impact simulation, including debris cloud and penetration. Based on the results of the numerical experiments of a variety of copper projectiles penetrating thin copper plate, a formula is given to describe the melt fraction of the spherical projectile, and it is important to the protection from the space debris.
Traditionally, it is difficult to create the microstructure of composite with high vol- ume fractions of long curve fibers. A new method is proposed for the problem, which is called the falling-tube procedure. The method can be used to create the microstructure with the same volume fraction as the experiment without penetration between the fibers. The material point model with the special interaction between fibers is created on the falling results. From the tension test simulation and the shear test simulation, it is found that the composite strength is related to the special connection and the volume fraction. The volume fraction is much more important than the special connection to the strength. Besides, based on the geometry from the falling procedure, a resistor network is built to investigate the electrical property. It is found that the connection between fibers plays the leading role in electrical conduction of the composite.