一种面向非共格性界面的分级式多尺度力学模型及应用

Within the context of solid mechanics, the effects of a solid-solid interface represent the impact of interfacial free energy, interfacial stress, and interfacial mechanical responses on the overall mechanical behavior of composites at both micro- and macro-scales. The focus is often placed on a length-scale dependence naturally introduced by the inclusion of the interfacial phase. The research objective of this project is to establish an incoherent interface-oriented hierarchical model on computational nanomechanics. Several modern mechanical theories including molecular mechanics, classical micromechanics of defects in solids, as well as a hierarchical multiscale configuration are employed to tackle a few critical problems necessary for the analysis. Rational characterization of the property of solid-solid interfaces at micro and nano-scale is the first step. The physical origin of the influential effects of solid-solid interfaces is explored in great detail at nanoscale. Subsequently, the characterization parameters of interface properties at both scales are correlated and coupled to perfect the interfacial constitutive relationship at the microscale. This condition, together with the deformation configuration and three-phase force balance condition across the interface, form a complete description of interface modeling. An incoherent interface-oriented hierarchical model on micro and nanomechanics of defects in solids can now be seamlessly constructed by the coupling of these field equations uniquely designed for interfaces and those classical ones for bulk phases. The proposed model is to be validated by its application on a few classical micromechanical problems with deterministic solutions. It possesses optimistic potentials for better understanding the influential effects of interfaces originated from particle-substrate boundaries and provides useful guidelines for the artificial design of nanocomposites.

在力学范畴内固体界面效应是指界面自由能、界面应力与力学响应性能对复合材料的宏细观力学行为的影响和修正，其思路是研究由引入界面相所诱发的空间尺度依赖关系。本项目拟运用细观力学、分子力学和分级式多尺度框架等现代力学理论与计算方法研究非共格性界面效应分析中几个具体的关键问题，围绕界面的热力学和力学响应特性在细观和纳观尺度下的合理表征，揭示固体间界面特性在纳观尺度下的物理根源，进而探讨其在细纳观尺度下的关联和耦合，完备细观尺度中组建的非共格性界面力学模型。再与经典细观力学理论体系通过一般曲线坐标中的曲面和空间映射分析实现耦合，建立以界面力学效应分析为中心的分级式跨细纳观尺度计算力学理论和方法，并应用于一类具有明确解的经典细观力学问题的界面力学效应研究中。项目研究目标的实现将增加纳米复合材料宏细观力学性能对增强体与基底之间的界面基本热力学参数和力学响应性能依赖关系的理解。

理论和实验均已表明，表界面残余应力、表界面应力、表界面薄膜刚度、表界面弯曲刚度等表界面力学性能对纳米材料和结构的应力分布和宏观力学性能具有重要影响，影响的强度随纳米材料和结构特征尺寸的减小而迅速增强。在项目执行期内，首先，本项目采用大规模分子动力学计算机模拟，计算了多种典型bcc和fcc晶面/晶界的表界面自由能、表界面应力和表界面薄膜刚度系数。其次，在细观尺度下对固体表界面的力学响应行为进行了分析，定义了表界面应变、表界面应力、表界面本构关系、表界面应力的散度和表界面应力平衡关系，并推导了正交曲线坐标系中一般空间曲面上这些表界面弹性场对表界面位移及其表界面梯度的显性表达。再次，实现了纳观尺度和细观尺度下的界面弹性刚度系数之间的关联，重点解决了晶面/晶界的各向异性本质与细观模型中各向同性基本假设之间的矛盾。最后，基于所建立的分级式多尺度计算力学模型，针对两类经典细观力学问题开展了应用研究，重点分析了表界面残余应力、表界面薄膜刚度和表界面弯曲刚度等参量对经典解答的影响和修正效应，明确了这些参量在纳米材料和结构力学性能分析中的角色。通过坑洞/夹杂的表界面力学性能优化设计，能够极大改善弹性基体中的应力分布和应力集中，当表界面残余应力和弹性刚度系数为正值时，应力分布趋于平缓，应力集中降低，纳米材料和结构的等效力学性能得到优化，反之纳米材料和结构则更易失效。对于纳米接触力学问题，当只考虑接触边界的薄膜刚度时，接触应力明显被高估，相应地，接触刚度明显被低估。由于接触边界弯曲刚度的引入，经典细观力学的解答可以得到进一步修正，与工程实际更加贴合。截至2018年12月，本项目共计发表了标注项目批准号的SCI论文14篇，其中含JCR一区论文6篇。在项目执行期内，项目负责人共计参加14次国内外力学学术会议并做报告，其中含国际会议4次。依托本项目，在项目执行期内已培养毕业博士生2名、毕业硕士生4名、指导本科毕业论文10篇。